Number Series. Consecutive odd/even numbers, Consecutive prime / composite numbers, Squares/cubes of some numbers with/without

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3 NUMBER SERIES Number series problems deal with numbers. While attempting to solve the question, you have to check the pattern of the series. Series moves with certain mathematical operations. You have to check the pattern. Type of questions asked in the examination : (i) Find the missing term(s). (ii) Find the wrong term(s). Number Series In this type of series, the set of given numbers in a series are related to one another in a particular pattern or manner. The relationship between the numbers may be Consecutive odd/even numbers, Consecutive prime / composite numbers, Squares/cubes of some numbers with/without variation of addition or substraction of some number, Sum/product/difference of preceding number(s), Addition/subtraction/multiplication/division by some number, and Many more combinations of the relationship given above. Directions : (1 to 13) Find the missing numbers : Ex 1. 3, 5, 7, 9, 11, 13, 15, 17,? (A) 14 (B) 19 (C) 15 (D) 21 (B) Each term has a common difference = + 2. Hence, next term = = 19. Ex 2. 2, 3, 5, 7, 11,?, 17 (A) 14 (B) 13 (C) 10 (D) 12 (B) The series is made up of consecutive prime numbers. Therefore, the missing term is 13. Ex 3. 1, 4, 9, 16, 25,? (A) 35 (B) 36 (C) 37 (D) 49 (B) Each term is a square of 1, 2, 3, 4 and so on 1 2 = 1, 2 2 = 4, 3 2 = 9, 4 2 = 16, 5 2 = 25. Hence, next term = 6 2 = 36. Ex 4. 2, 5, 10, 17,? (A) 24 (B) 25 (C) 26 (D) 27 (C) Each term is a square of 1, 2, 3, 4 and so on and 1 is added to it, i.e , (2) 2 +1, (3) 2 +1,...= 2, 5, 10, Hence, next term = (5) = 26. Ex 5. 2, 3, 10, 15, 26, 35,? (A) 48 (B) 51 (C) 49 (D) 50 (D) The series exhibits the pattern of n 2 + 1, n 2 1, alternately, n taking values 1, 2,... Ex 6. 1, 8, 9, 64, 25, 216,?,? (A) 49, 64 (B) 343, 64 (C) 49, 512 (D) 343, 512 (C) Odd positioned digits are squares of 1, 3, 5 and so on, i.e. 1 2 = 1, 3 2 = 9, 5 2 = 25 and so on. Similarly, even positioned digits are cubes of 2, 4, 6, etc., i.e. 2 3 = 8, 4 3 = 64, 6 3 = 216. Therefore, the next term would be 7 2 i.e. 49 and 8 3 = 512 respectively. Ex 7. 0, 7, 26,?, 124, 215 (A) 51 (B) 37 (C) 63 (D) 16 (C) Each term is a cube of 1, 2, 3, 4 and so on and 1 subtracted from it, i.e , 2 3 1, 3 3 1, 4 3 1, 5 3 1, Therefore, the term replacing the question mark would be = 64 1 = 63. Ex 8. 3, 4, 10, 33, 136,? (A) 240 (B) 430 (C) 685 (D) 820 (C) The terms of the series are, previous term 1 + 1, previous term 2 + 2, previous term and so on. Hence, the next term will be = = 685. Ex 9. 11, 15, 21, 29,? (A) 40 (B) 41 (C) 37 (D) 39 (D) This series consists of increasing numbers. The pattern is +4, +6, +8,... Ex 10. 3, 6, 18, 72, 360,? (A) 720 (B) 1080 (C) 1600 (D) 2160 (D) The sequence in the given series is 2, 3, 4, 5, 6. Hence, the missing number is =2160. Ex 11. 6, 12, 7, 11, 8, 10, 9,? (A) 8 (B) 9 (C) 11 (D)10 (B) Alternate series [Difference series] (i) 6, 7, 8, 9 (ii) 12, 11, 10,? Ex 12. 0, 5, 22, 57, 116,? (A) 205 (B) 216 (C) 192 (D) (A) Difference Difference Hence, the next term = 205 PAGE # 1

4 Ex , 158, 172, 182,? (A) 210 (B) 193 (C) 197 (D) 203 (B) = 7, The difference between 151 & 158 is seven (7) = 14, The difference between 158 & 172 is (14) = and so on, Missing term = = 193. Direction : (14 to16) Find the wrong term : 14. 2, 5, 9, 11, 14 (A) 2 (B) 5 (C) 9 (D) 11 (C) Series : + 3, + 3, + 3,... The next term is got by adding 3 in preceeding term = 5, = 8 9 is wrong term , 100, 1100, 11000, , (A) (B) (C) 100 (D) (D) Given series is : is wrong. The correct term is , 6, 11, 17, 23, 32, 41 (A) 6 (B) 17 (C) 23 (D) 32 (C) Given series is : 24 2, 6, 11, 17, 23, 32, EXERCISE-1 EXERCISE-2 PAGE # 2

5 ALPHABET SERIES Alphabet Series problems deals with alphabets and Alpha-Numeric. While attempting to solve the question, you have to check the pattern of the series. Type of questions asked in the examination : (i) Find the missing term(s). (ii) Find the wrong term(s). Position of Alphabet : (i) Alphabet in order : Alphabet Series In these types of questions, a series of single or pairs of groups of letters is given. The terms of the series form a certain pattern as regards the position of the letters in the English alphabet. (ii) Alphabet in reverse order : Z Y X W V U T S R Q P O N M L K J I H G F E D C B A Directions : (1 to 7) Find the missing term : Ex 1. A, C,?, G, I (A) E (B) D (C) F (D) H (A) Series consists of alternate letter in order. So, the missing term would be E. Ex 2. V, T, R,?, N,? (A) O,M (B) P,M (C) L,P (D) P,L (D) Given series consists of alternate letters in reverse order. So, the missing terms would be P and L. Ex 3. A, C, F,?, O (A) G (C) H (B) Hint (B) J (D) K A C F J O Ex 4. DC, DE, FE,?, HG, HI (A) FE (B) FG (C) GF (D) GH (B) Hint D C +2 D E F E FG H G H I Ex 5. CIR, GMV, KQZ, OUD,? (A) RYH (B) SYH (C) SZI (D) SYI (B) There is a continuous difference of 4 letters between the first letter of each group, second letter of each group and third letter of each group. So the missing term would be SYH. Ex 6. ZSD, YTC, XUB, WVA,? (A) VWZ (B) UVW (C) VXY (D) UWZ (A) The first letter of each group is in continuation in backward direction. The second letter of each group is in continuation in forward direction. The third letter of each group is in continuation in backward direction. Therefore, the missing term would be VWZ. Ex 7. KTE, SBM, AJU, IRC,? (A) OZL (B) QYZ (C) QZL (D) QZK (D) First letter of each group differ by 8 letters. Second letter of each group differ by 8 letters. Third letter of each group differ by 8 letters. Therefore, the missing term would be QZK. Directions : (8 to 9) Find the wrong term (s) : Ex 8. Ex 9. DOU, EPV, FQW, GRX, HTY, ITZ (A) EPV (B) FQW (C) GRX (D) HTY (D) In every term first, second and third letter is in alphabetical order to its next term respectively. Fourth term is not following the same rule. Hence, HTY is the wrong term and should be replaced by HSY. ABC, DGJ, HMR, NTA, SBK, ZKV (A) DGJ (B) HMR (C) NTA (D) SBK (C) First letter of first, second, third,...terms is moved three, four, five,...steps forward respectively. Similarly, second letter is moved five, six, seven,...steps forward respectively and third letter is moved seven, eight, nine,...steps forward respectively. Hence, NTA is the wrong term and should be replaced by MTA. Alpha-Numeric Series A series in which both alphabets and number are used. Direction : (10) Find the missing term : Ex 10. F3X, H7U, J15R, L31O,? (A) M46L (B) N44L (C) N63L (D) N44M (C) The first letter of each term is moved two steps forward and the last letter is moved three steps backward to obtain the corresponding letters of the next term. The numbers form the sequence = 7, = 15, = 31, = 63. So, the missing term would be N63L. 3 PAGE # 3

6 Direction : (11) Find the wrong term : Ex 11. D4V, G10T, J20R, M43P, P90N (A) G10T (B) J20R (C) M43P (D) P90N (A) First letter of every term is moved three steps forward in each next term. Second number of every term of the pattern 2 + 1, 2 + 2, 2 + 3,...and third letter of every term is moved two steps backward. Hence, G10T is the wrong term and should be replaced by G9T. EXERCISE-1 4 PAGE # 4

7 LETTER REPEATING SERIES Letter Repeating Series These type of questions usually consists of a series of small letters which follow a certain pattern. However, some letters are missing from the series. These missing letters are then given in a proper sequence as one of the alternatives. Pattern of such questions is that some letters in sequence are missing. (i) The letters may be in cyclic order (clockwise or anti-clockwise). (ii) To solve a problem, we have to select one of the alternative from the given alternatives. The alternative which gives a sequence form of letters is the choice. Directions : (1 to 6) Which sequence of letters when placed at the blanks one after the other will complete the given letter series? Ex 1. Ex 2. a _ a b _ b a _ a _ a b (A) babb (B) abba (C) baba (D) aabb (A) we proceed step by step to solve the above series : Steps : 1. We have two letters a and b making the series. 2. The first blank space should be filled in by 'b' so that we have one a followed by one b. 3. Second blank space should be filled in by 'a' so that the same pattern followed till end. a _ cab _ a _ c _ b c (A) bbac (C) abba (B) abab (D) bcba Direction : (7) The series given below is based on the letter series, In the series, some letters are missing. Select the correct alternative. If more than five letters are missing, select the last five letters of the series. Ex 7. x _ xxy _ x _ xy _ yxx yy _ y (A) xyyyy (B) xxyyx (C) yxxyx (D) xyxyx (C) The pattern of series is xy/xxyy/xxxyyy... Direction : (8) There is a letter series in the first row and a number series in the second row. Each number in the number series stands for a letter in the letter series. Since in each of that series some term are missing you have to find out as to what those terms are, and answer the questions based on these as given below in the series. Ex 8. _ m i a x _ i r x a m a 4 _ 5 _ 7 3 _ 6 The last five term of the letter series are (A) r m x i a (B) x m r a i (C) x r m a i (D) r m i x a (D) a = 6, i = 5, m = 3, r = 4 and x = 7 the letter series runs as rmiax mirxa irmax rmixa. By taking the letter in the groups of five, we find that first letter of the first group (i.e. r) is the third letter of the second group and the last two letters have interchanged their positions. The same rule applies in others groups also. EXERCISE (D) Ex 3. Sol- Ex 4. Ex 5. Sol- Ex 6. Sol- Series is abc/ abc/ abc/ abc. So, pattern abc is repeated. _ abb _ a _ baa _ b (A) baba (B) abba (C) aabb (D) aaab (C) Series is aabb/ aabb/ aabb. So, pattern aabb is repeated. ba _ cb _ b _ bab _ (A) acbb (B) bcaa (C) cabb (D) bacc (D) The series is b a b c/b a b c/b a b c So, pattern babc is repeated ab _ aa _ caab _ c _ abb _ c (A) bbcaa (B) bcbca (C) cabac (D) cbbac (D) Series is abc / aabc / aabbc / aabbcc bc _ b _ c _ b _ ccb (A) cbcb (B) bbcb (C) cbbc (D) bcbc (A) Series is bccb / bccb / bccb. So, pattern bccb is repeated PAGE # 5

8 MISSING TERM IN FIGURE Missing Term in Figure In such type of questions, a figure, a set of figures, an arrangement or a matrix is given each of which bears certain characters, be it numbers, letters or a group or combination of letters or numbers, following a certain pattern. Directions : (1 to 10) Find the missing term/number(s) : Ex 4. B C O Q M N (A) A (C) G? S R (B) D (D) P (A) In each column, the sum of top & bottom letter is equal to the order of the middle letter in that column. Ex 1. Ex 5. (A) 125 (B) 25 (C) 625 (D) 156 (C) Clearly (1 + 3) 2 = 16 (15 + 6) 2 = (21) 2 = 441 (10 + 5) 2 = (15) 2 = 225 missing number in figure] ( ) 2 = (25) 2 = 625. (A) 10 (B) 9 (C) 8 (D) 6 (B) In the first set, 2 2 = 4, In the second set, 3 9 = 27 2 x = 18, x = ? Ex Ex 2. (A) 16 (B) 14 (C) 20 (D) 22 (B) In the first diagram, (3 4 6) = 72 and the number on the sides twice as the number on the opposite vertex. 3 2 = 6, 6 2 = 12, 4 2 = 8 (A) 64 (B) 36 (C) 34 (D) 60 (A) Moving clockwise, in every quarter region, value of numbers gets doubled. 2 2 = 4, 8 2 = 16, 16 2 = 32, 32 2 = 64, = 256. In the second diagram, (1 2 3) = 6 and the number on the sides twice as the number on the opposite vertex. 3 2 = 6, 2 2 = 4, 1 2 = 2 In the Third diagram, (7 4 5) = 140 and the number on the sides twice as the number on the opposite vertex. 7 2 = 14, 5 2 = 10, 4 2 = 8. Ex 3. Ex ? 10 4 (A) 120 (B) 100 (C) 125 (D) 64 (C) In the first column, = 53 In the second column, = 90 So, missing number, = 125. (A) 0 (B) 5 (C) 10 (D) 15 (B) In first figure, (14 + 6) 2 2 = 16 In second figure, (12 + 5) 3 1 = 14 In third figure, (11 + 4) 10 1 = 5 6 PAGE # 6

9 Ex 10. Which one number can be placed at the sign of interrogation? Ex ? (A) 262 (B) 622 (C) 631 (D) 631 (B) In first figure, ( ) = 551. In second figure, ( ) = 246. In third figure, missing number = ( ) = (A) 5 (B) 6 (C) 8 (D) 9 (D) In first figure, = 93 In second figure, = 79 So, In third figure, x = 67, x = 9 4? Ex ? (A) 5 (B) 19 (C) 27 (D) 89 (D) In first figure, (6 3) + (5 15) = = 93. In second figure, (4 8) + (18 + 1) = = 50. In third figure, missing number = (9 6) + (7 5) = = PAGE # 7

10 ALPHABET- TEST Alphabetical Order You have to arrange the given words in order in which they are arranged in a dictionary. In a dictionary the words are placed in alphabetical order w.r.t. the second alphabet of the words and so on (that is, third alphabet, fourth alphabet...). Directions : (1 to 2) Arrange the given words in the correct alphabetical order. Ex 1. Late, Long, Liver, Last, Load, Luminous, Loan, Lock. The given words can be arranged in the alphabetical order as : Last, Late, Liver, Load, Loan, Lock, Long, Luminous. Ex 2. Arrange the given words in alphabetical order and tick the one that comes last. Heavy, Heredity, Hesitate, Hedge, Hero, Haste, History, Hinderance The given words can be arranged in the alphabetical order as : Haste, Heavy, Hedge, Heredity, Hero, Hesitate, Hinderance, History Clearly, History comes last. Ex 3. Arrange the given words in the order they occur in dictionary. 1.SIGN 2.SOLID 3.SCENE 4.SIMPLE (A) 3, 1, 2, 4 (B) 3, 1, 4, 2 (C) 3, 4, 1, 2 (D) 3, 4, 2, 1 (B) The correct alphabetical order of the given words is : SCENE, SIGN, SIMPLE, SOLID. Thus, the correct sequence is 3, 1, 4, 2. Letter-Word Problems Ex 4. How many pairs of letter in the word DABBLE have as many letters between them as in the Alphabet series? (A) Nil (B) One (D) Two (D) More than three (D) Letters in the given Word : Letters in the Alphabet A B A B D A B D C B B B L E B C D E A B B L E A B C D E Ex 5. Ex 6. In the word PARADISE how many pairs of letters are there which have as many letters between them in the word as in the alphabet? (A) None (B) One (C) Two (D) Three (D) Letter in the given word : Letter in the alphabet (i) P A R P Q R (ii) A R A D A B C D (iii) A D I S E A B C D E Number of letters skipped in between adjacent letters in the series are increased by one. Which of the following alternatives observes this rule? (A) KMPTY (B) IJKOT (C) HJMQT (D) DFIJK (A) K L M N O P Q R S T U V W X Y Clearly, in letter series KMPTY, the number of letters skipped in between adjacent letters in the series are increased by one. Alphabetical Quibble Ex 7. In this type of questions, generally a letter-series is given, be it the English alphabets from A to Z or Z to A. The candidate is then required to trace the letters satisfying certain given conditions as regards their position in the given sequence or the sequence obtained by performing certain given operations on the given sequence. If the alphabet series is written in a reverse order, which of the following will be the seventh letter to the left of eighth letter from your right? (A) L (B) M (C) O (D) P (C) The new alphabet series is : Z Y X W V U T S R Q P O N M L K J I H G F E D C B A The eight letter from the right is H. The seventh letter to the left of H is O. Ex 8. If the first four letters of the word ANTHROPOMORPHISM are rewritten in the reverse order followed by the next four rewritten in the reverse order followed by the next four letters in the reverse order and so on, which letter will be twelfth from the left end in the rewritten order? (A) O (B) H (C) M (D) P (C) The new arrangement is as follows: HTNAOPORPROMMSIH. PAGE # 8

11 Word Formation by Unscrambling Letters In this type of questions, a set of English letters is given in a jumbled order. The candidate is required to arrange these letters to form a meaningful word. Ex 9. Arrange the following group of letters such that when arranged in a specific order, meaningful word is formed. V A H Y E (A) 2, 3, 4, 5, 1 (B) 3, 2, 5, 1, 4 (C) 3, 5, 2, 1, 4 (D) 1, 5, 2, 3, 4 (C) The given letter, when arranged in the order 3, 5, 2, 1, 4. form the word HEAVY. Word Formation using Letters of a given Word Ex 10. A meaningful word starting with A is made from the first, the second, the fourth, the fifth and the sixth letters of the word CONTRACT, which of the following is the middle letter of the word? (A) C (B) T (C) O (D) R (B) The first, the second, the fourth, the fifth and sixth letters of the word CONTRACT are C, O, T, R and A respectively. The meaningful word will be ACTOR and T will be the required letter. Direction : (11) In the following question, find which one word can not be made from the letters of the given word. Ex 11. TEMPERAMENT (A) METER (B) PETER (C) TENTER (D) TESTER The word TEMPERAMENT contains all the letters of the word TESTER except S. So, the word TESTER cannot be formed. EXERCISE PAGE # 9

12 CODING-DECODING Coding-Decoding A code is a system of signals. Coding is, therefore, a method of transmitting a message between sender and receiver which cannot be understood or comprehended by a third person. The coding decoding test is set up to judge the candidate s ability to decipher a particular word/ message and break the code to decipher the message. In coding, actual alphabets/words/ terms/numbers are replaced by certain other alphabets/words/terms/symbols etc. according to a specific rule. To solve these type of questions we have to detect the rule and then answer the questions. Decoding : It is a method to find the meaning of something that has written in code. Letter-Letter Coding Ex 1. (B) In these type of questions, the letters in a word are replaced by certain other letters according to a specific rule to form its code. The candidate is required to detect the coding pattern / rule and answer the questions accordingly. If in any code language, KUMAR is coded as LVNBS, How is EMOTIONAL coded in that language. (A) FNQUJQBM (B) FNPUJPOBM (C) GNPUJPOBM (D) GNQUJQOBM Similarly, E M O T I O N A L F N P U J P O B M Ex 3. Similarly, C A S T L E D C V X Q K If PAINTER is written in a code language as NCGPRGP, then REASON would be written as : (A) PCYQMN (B) PGYQMN (C) PGYUMP (D) PGYUPM (C) P A I N T E R N C G P R G P Ex 4. Similarly, R E A S O N P G Y U M P If in any code language NATIONAL is written as MZGRLMZO than how is JAIPUR written in that language. (A) QZRKFI (B) PZRKFI (C) QZRIFK (D) QARKFI N A T I O N A L M Z G R L M Z O 14+13=27 (A) 1+26 = = = = = = = 27 Similarly, J A I P U R Q Z R K F I = = = = = = 27 Ex 2. If JAPAN is coded as KCSES, then the code for CASTLE will be - (A) DCIJOB (B) DCJKRD (C) DCKMSG (D) DCVXQK (D) J A P A N K C S E S Letter-Number Coding Ex 5. In these types of questions, either numerical code values are assigned to a word or alphabetical code letters are assigned to the numbers. In a certain code, if TREE is coded as 7100, FROG as 2159, how is FREE coded in that code? (A) 2100 (B) 3100 (C) 1003 (D) 1002 (A) T R E E F R O G Hence, F R E E PAGE # 10

13 Ex 6. In a certain code, C is coded as 0, E as 7, T as 4, I as 9, P as 1, R as 3, and U as 5. How is coded in that code? (A) PICTRUE (B) PICTURE (C) RICTPUE (D) PCTUREI (B) P I C T U R E Ex 7. Ex 8. If OX is coded as 39, what will be the code number for LION? (A) 20 (B) 25 (C) 38 (D) 50 (D) By their natural position in alphabet, O 15, X 24 So, OX = ( ) = 39 Hence, L I O N = ( ) = 50 If AJAY is written as 1117, then in same code NAMA would be written as: - (A) 5114 (B) 5411 (C) 5141 (D) 4511 (C) Hence A J A Y Substitution Coding Ex 9. Ex N A M A In these types of questions, some particular objects are assigned code names. Then a question is asked that is to be answered in the code language. If paper is called eraser, eraser is called bag, bag is called scale, scale is called pencil and pencil is called paper, what will a person write with? (A) Pencil (B) Paper (C) Eraser (D) Bag (B) A person will write with a pencil and a pencil is called paper. If water is called food, food is called tree, tree is called sky, sky is called wall, on which of the following does a fruit grow? (A) Water (B) Food (C) Tree (D) Sky (D) Clearly, a fruit grows on a tree. As given that tree is called sky, a fruit grows on sky. Puzzle Based Coding Ex 11. Ex 12. In this type of questions, some messages are given in the coded language and the code for a particular word or message is asked. To analyses such codes, any two messages bearing a common word are picked up. The common code word will thus represent that word. Proceeding similarly by picking up all possible combinations of two, the entire message can be decoded and the order for individual words found. In a certain code language 389 means run very fast. 964 means come back fast and 487 means run and come. Which digit in the language means come? (A) 7 (B) 9 (C) 4 (D) 8 (C) In the second and third sentences, common number is 4 and common code is come. Hence, number 4 stands for come. In a certain code language, ken poti means good morning, hu shang means come on, and hu ken sue means come for good. Which word in that language does mean for? (A) shang (B) ken (C) sue (D) hu (C) In the second and third statements, the common code word is come and the common word is hu. So, come means hu. In the first and third statements, the common code word is good and the common word is ken. So, good means ken. Thus, in third and above statements for means sue. Column Coding Ex 13. Decode the underlined letters in column I from the same row of choices provided under column II. Each small letter in column II stands for some capital letter in column I. However, the small letters in column II are not arranged in the same order as their corresponding letters in column I. The code is the same for all the terms in column I. Column Column 1. H N T B Z v b h n t 2. C T N Z B t h n w v 3. D N B Z C x h v t w 4. O H N T Z t b h i n 5. T Z O B K n i v e t From terms 1 & 2, in column (I), NTBZ is common. From col. (II) we have vhnt common. Hence H=b & C = w. From term-3, NBZC have already occurred and the code for D must be a letter which did not appear in the earlier codes. Thus, the codes for D is x. From term-4 HNTZ have occured earlier. The letter which has not occured earlier is the code for O, that is, i. From term-5 TZOB have occured earlier. The letter which has not occured earlier is the code for K, that is e. The code of underlined letters are given in the following table Letter H C D O K Code b w x i e 11 PAGE # 11

14 MATHEMATICAL OPERATIONS Mathematical Operations This section deals with questions on simple mathematical operation. There are four fundamental operations, namely : Addition i.e. + ; Subtraction i.e. ; Multiplication i.e., x; and Division i.e.,. There are also statements such as Less than i.e, < ;greater than i.e, > ; equal to i.e, = ; and not equal to i.e, etc. Such operations are represented by symbols different from the usual ones. The candidate has to make a substitution of real signs and solve the equation accordingly. W hile attempting to solve a mathematical expression, proceed according to the rule BODMAS that is, Brackets, Of, Division, Multiplication, Addition & Subtraction.We can perform addition or subtraction in any order. Ex 1. What is the value of (48 12) =? (A) 10 (B) 0.6 (C) 2 (D) 18 (D) given expression = (48 12) = (Solving Bracket) = (Solving Division) = (Solving Multiplication) = 18 (Solving Addition) Ex 2. What is the value of =? (A) 120 (B) 116 (C) 112 (D) 114 (D) Given expression = (Solving Division) = (Solving Addition) = 114 Problems - Solving by Substitution Ex 3. In these type of questions, you are provided with substitutes for various mathematical symbols or numerals followed by a questions involving calculations of an expression or choosing the correct / incorrect equations. The candidate is required to put in the real signs or numerals in the given equation and then solve the questions as required. If + means, means, means + and means, then what will be the value of =? Ex 4. (A) 20 (B) 52 (C) 12 (D) None of these (A) Using the correct symbols, = = 20 If L denotes x, M denotes, P denotes + and Q denotes, then 8 P 36 M 6 Q 6 M 2 L 3 =? 13 (A) 6 (C) (B) 6 1 (D) 5 (D) Using the correct symbols, Given expression = = = 5 Ex 5. It being given that : > denotes +, < denotes, + denotes, denotes =, = denotes less than and denotes greater than, find which of the following is a correct statement. (A) > 4 = < 1 (B) 3 > 2 > 4 = < 2 (C) 3 > 2 < < 2 (D) < < 3 (C) Using proper notations, we have : (A) given statement is < or 11 < 2, which is not true. 2 (B) given statement is < or 9 < 4, which is not true. (C) given statement is > or 1 > 0, which is true. (D) given statement is > or 2 5 > 0, which is not true. Interchange of signs and numbers Ex 6. Find out to sign to be interchanged for making the given equation correct = 10 (A) + and (B) + and (C) and (D) + and (B) By making the interchanges given in (A), the equation as = 10 or 109 = 10 which is false By making the interchanges given in (B), the equation as =10 or 10=10 which is true By making the interchanges given in (C), the equation as = 10 PAGE # 12

15 Ex 7. or 109 = 10 which is false By making the interchanges given in (D), the equation as = 10 or 89 = 10 which is false Which one of the four interchanges in signs and numbers would make the given equation correct? = 4 (A) + and, 2 and 3 (B) + and, 2 and 5 (C) + and, 3 and 5 (D) None of these (C) By making the interchange given in (A), we get the equation as = 4 or 0 = 4, which is false. By making the interchange given in (B), we get the equation as = 4 or 6 = 4, which is false. By making the interchange given in (C), we get the equation as = 4 or 4 = 4, which is true. Deriving the appropriate conclusions In these type of questions, certain relations between different sets of elements is given (in terms of less than, greater than or equal to ) using either the real symbols or substituted symbols. To analyses the given statements and then decide which of the relations given as alternatives follows from those given in the statements. Directions : (8 to 9) In the following questions : means is equal to means is not equal to + means is greater than means is less than means is not greater than means is not less than Now select the correct alternative in each of the following questions : Ex 8. a b c implies (A) a b + c (B) b + a c (C) c b + a (D) b + a c (B) With the notations given, we have : a b c means a < b < c From option (A), a b + c means a < b > c, this is not true. From option (B), b + a c means b > a <c, this is true. From option (C), c b + a means c < b > a, this is not true. From option (D), b + a c means b > a > c, this is not true. Ex 9. a + b + c does not imply (A) b a + c (B) c b a (C) c a + b (D) b a c (D) With the notations given, we have : a + b + c means a > b > c From option (A), b a + c means b < a > c, this is true. From option (B), c b a means c < b < a, this is true. From option (C), c a + b means c < a > b, this is true. From option (D), b a c means b < a < c, this is not true. Ex 10. Ex 11. What is the value of A if each letter represents a different digit? (A) 3 (B) 4 (C) 5 (D) 7 (B) In the following question the value of A and B are 4 and 5 respectively If 4, 3 = 6, 18, 4 = 12, then what will be the value to 24, 7? (A) 21 (B) 27 (C) 72 (D) 56 (D) Here sing, implies square and implies multiplication = 6, = 12. Therefore, = 56. PAGE # 13

16 DIRECTION SENSE TEST There are four directions such as North, South, East and West. The word NEWS came from North, East, West and South. There are four regions : (i) North-East ; (ii) North-West ;(iii) South-East ; (iv) South-West. WEST S III Q II NORTH O SOUTH I IV P R EAST The directions OP, OS, OQ and OR are : North-East direction ; North-West direction ; South-West direction ; and South-East direction respectively. NOTE : The candidate must distinguish between the regions and directions, i.e., between North-East region and North-East direction. If you move with your face Eastwards, your left hand is towards North and your right hand is towards South. Similarly the positions of the directions of the hands can be fixed when you move in any of the other three directions. Ex 1. Ex 2. Mohan travels 7 km Eastwards, then he turns right and travels 3 km and further turns right again and travels 11 km. How far is he from the starting point? (A) 5 (B) 14 (C) 21 (D) 23 (A) The movement of Mohan from A to D as shown in figure. Now, DE = (CD CE) = (CD AB) = (11 7) = 4 km 2 2 Required distance = AD = DE AE = 2 2 D DE BC = 2 2 ( 4) (3) = 5 km 4km A 7 km 3 km E 7 km 11 km B 3 km A man walks 9 km due East and then 12 km due South. How far is he from the starting point? (A) 15 km (B) 6 km (C) 7 km (D) None of these (A) The movement of man from A to C as shown in figure. Clearly, required distance AC = 9 km 2 2 AB BC A B = = 15 km C C 12 km Ex 3. Ex 4. Ex 5. Ex 6. Ex 7. The time on the watch is quarter to three. If the minute-hand points to North-East, in which direction does the hour hand point? (A) South-West (B) South-East (C) North-West (D) North-East (A) The required position of E S clock as shown in figure. 12 Clearly, if minute hand points towards North-East 9 3 then hour hand will point 6 towards South-West. N W If I stands in up side down position with my face pointing Northwards, in what direction will my right-hand point? (A) East (B) West (C) North (D) South (B) When I stand on my head with my face pointing Northwards. Clearly, my left hand will point towards East and my right hand will point towards West. From his house, Rajan went 25 km to the North. Then he turned West and covered 20 km. Then he turned South and covered 15 km. Finally, turning to East, he covered 20 km. In which direction was he from his house? (A) East (B) West (C) North (D) South (C) The movements of Rajan are as shown in fig. (A to B, B to C, C to D and D to E) Clearly, his final position is E which is to the North of his house at A. Raj walked 20 metre towards South. Then he turned to his left and walked 25 metre. He then turned to his left and walked 20 metre. He again turned to his right and walked 10 metre. At what distance is he from the starting point and in which direction? (A) 35 metre, East (B) 35 metre, North (C) 40 metre, East (D) 60 metre, East (A) the movements of Raj are as shown in figure Raj's distance from the starting point A = AE = (AD + DE) = (BC + DE) = ( ) m = 35 m. So, E is to the East of A. A 20 m B 25 m 10 m D E 20 m C If South-East becomes North, North-East becomes West and so on, what will South become? (A) North-East (B) South - West (C) South (D) North - West 14 PAGE # 14

17 Ex 8. Ex 9. (A) The initial and the final position of the directions as shown in the figure. Clearly, as observed in the figure, South will become North-East. W NW N NE SW SE S Initial position E SE S SW W E N NE Final position NW A man is facing North-West. He turns 90º in the clockwise direction and then 135º in the anti-clockwise direction. Which direction is he facing now? (A) East (B) West (C) North (D) South (B) As shown in the Fig. the man faces in the direction OA. After moving 90º clockwise, the man faces in the direction OB. On moving to 135º anti-clockwise, he faces in the direction OC, which is West. A B C 135º 90º A man is facing North-West. He turns 90º in the clockwise direction, then 180º in the anti-clockwise direction and then another 90º in the same direction. Which direction is he facing now? (A) South (B) South-West (C) West (D) South-East (D) As shown in fig. the man initially faces in the direction OA. On moving 90º clockwise, he faces in the direction OB. On further moving 180º anti-clockwise, he faces in the direction OC. Finally on moving 90º anti-clockwise, he faces in the direction OD, which is South-East. O Ex 11. Ex 12. I run along the sides of a square field ABCD where C is to the North-East of A and D is to the South-East of B. Starting from A in anti-clockwise direction, in which direction shall I be running after crossing C? (A) East (B) West (C) North (D) South (B) The required position of the square field ABCD as shown in the figure. Starting from A in the anti-clockwise direction. I will move from A to D, D to C, C to B and B to A. Clearly, I will be running in the West direction after crossing C. North B C A D West South East A and B start walking in opposite directions. A walked 5 km, B walked 6 km. Thereafter both turned to their right and walked 2 km. They turned to right again and walked 3 km, again turned to right and walked 2 km. How much distance apart are they from each other? (A) 2 km (B) 13 km (C) 3 km (D) 5 km (D) A and B he facing North and South direction respectively at initial position O. The movement of A from O to W (O to X, X to Y, Y to Z and Z to W) and the movement of B from O to R (O to P, P to Q, Q to S, S to R) as shown in figure. Clearly, required distance = RW = RO + OW = (OP PR) + (OX XW) = (6 3) + (5 3) = = 5 km. X 5 km W 2 km 2 km Y 3 km Z O S 2 km 3 km R 6 km Ex 10. While facing East you turn to your left and walk 10 m then turn to your left and walk 10 m, and now you turn 45º towards your right and go straight to cover 25 m. Now, in which direction are you from your starting point? (A) North-East (B) South-West (C) South-East (D) North-West Q 2 km P (D) The movement from A to D as shown in the figure. Clearly, the final position i.e. D is to North-West of A. D 25 m 45º C 10 m B 10 m A 15 PAGE # 15

18 SEATING ARRANGEMENT Seating Arrangements In these type of questions, some clues regarding seating or placing sequence (linear or circular or rectangular) of some persons or items is given. The candidate is required to form the proper sequence using these clues and answer the given questions accordingly. Linear Seating Arrangements Ex. 1 Who among P, Q, R, S and T is in the exactly middle while standing in a line? (i) Q is to the immediate right of T. (ii) S is exactly between P and T. (iii) Q is exactly between T and R. (A) P (B) Q (C) R (D) T (D) On the basis of information, we have the arrangement of the persons in a line as under:- P S T Q R Directions : (2 to 4) Study the given information and answer the question that following. Five persons are standing in a queue. One of the two persons at the extreme ends is a Professor and the other is a Businessman. An Advocate is standing to the right of a student. A Author is to the immediate left of the Businessman. The Student is between the Professor and the Advocate. Ex. 2 Ex. 3 Ex. 4 Counting from the left the Author is at which place? (A) First (B) Second (C) Third (D) Fourth Which of the following is in the exactly middle of the queue? (A) Professor (B) Advocate (C) Student (D) Businessman If Advocate and the Businessman exchange their positions, also the Author and the Student, then who will be standing to the left of the student? (A) Author (B) Businessman (C) Professor (D) Advocate : (2 to 4) On the basis of the information given in the question, we have the arrangement of standing order of persons as per figure. Circular Seating Arrangements 5. Five persons were playing cards game sitting in a circle all facing the centre. Mukund was to the immediate left of Rajesh, Vijay was to the right of Anil and between Anil and Nagesh. Who was to the immediate right of Nagesh? (A) Vijay (B) Rajesh (C) Anil (D) Mukund (D) Rajesh Anil Mukand Nagesh Vijay Directions : (6 to 8) Read the following information and answer the questions that follow : (i) Six friends A, B, C, D, E and F are sitting in a closed circle facing the centre. (ii) E is to the immediate left of D. (iii) C is exactly between A and B. (iv) F is between E and A. 6. Who is to the immediate left of B? (A) A (B) C (C) D (D) E 7. Who is to the immediate right of C? (A) A (B) B (C) D (D) E 8. W hich of the above given statements is superfluous? (A) (i) (B) (ii) (C) (iii) (D) All are required. : (6 to 8) Clearly, in the circle the arrangement is as shown : 6. (C) Clearly, D is to the immediate left of B. 7. (A) Clearly, A is to the immediate right of C. 8. (D) Since all the statements are necessary to determine the arrangement, none of them is superfluous. B C D A E F 2. (D) Author is fourth from the left. 3. (B) Advocate is in the middle of queue. 4. (B) Businessman will be to the left of Student if Advocate and Businessman, Author and Student exchange their positions. 16 PAGE # 16

19 RANKING & ORDERING -TEST Number Quibble In these type of questions, generally a set, group or series of numerals is given and the candidate is required to find out how many times a number satisfying the conditions, specified in the question occurs. Ex 1. How many 5's are there in the following sequence which are immediately followed by 3 but not immediately preceded by 7? (A) One (B) Two (C) Three (D) Four (C) Clearly, there are three such numbers. Ex 2. In the following number series how many 8 s are there which are exactly divisible by the numbers which are preceded and followed by it? (A) 1 (B) 2 (C) 3 (D) 4 (D) As per the question Thus, four such numbers are there Alphabetical Quibble In these type of questions, generally a letter-series is given, be it the English alphabets from A to Z or a randomised sequence of letters. The candidate is then required to trace the letters satisfying certain given conditions as regards their position in the given sequence or the sequence obtained by performing certain given operations on the given sequence. Ex 3. How many W's are there in the following series which are immediately followed by W but not immediately preceded by K? D W W D H K V D W Z D W W W D D W K W W D K K D H C (A) One (C) Three (D) None (B) Two (C) Clearly, W s satisfying the given conditions can be marked as under D W W D H K V D W Z D W W W D D W K W W D K K D H C Ex 4. How many L s are there which do not have R preceding them and also do not have T following them? Z Q S T L R M N Q N R T U V X R L T A S L T Q R S L T (A) 1 (B) 2 (C) 3 (D) 5 (A) Z Q S T L R M N Q N R T U V X R L T A S L T Q R S L T Alpha-Numeric Quibble In these type of questions a jumped sequence of some letters, numbers and symbols is given and the candidate is required to find out how many times a number or a letter or a symbol satisfying the conditions, specified in the question occurs. Directions : (5 to 6) Study the following arrangement of symbols, letters and numbers to answer the questions given below it : = F 2 K S 7 5 # $ P L V M U E 6 Q G 9 3 & T Y Ex 5. How many such letters are there in the arrangement each of which is either immediately preceded by a symbol or immediately followed by a number, but not both? (A) Three (B) Four (C) Five (D) None of these (D) The letters satisfying the given conditions are shown as under : = F 2 K S 7 5 # $ P L V M U E 6 Q G 9 3 & T Y Clearly, there are 8 such letters. Ex 6. How many such consonants are there in the above arrangement each of which is immediately followed by a consonant but not immediately preceded by a symbol? (A) Nil (B) One (C) Two (D) Three (B) We know that of the 26 letters of English alphabet, five letters namely A, E, I, O, U are vowels, while remaining are consonants. The consonants satisfying the given conditions may be shown as under : = F 2 K S 7 5 # $ P L V M U E 6 Q G 9 3 & T Y Clearly, there is only one such consonant. Ranking Test In these type of questions, generally the ranks of a person both from the top and from the bottom are mentioned and the total number of persons is asked. However, sometimes this question is put in the form of a puzzle of interchanging seats by two persons. Useful Tips 1. Position of person from upward = [Total number of persons - position of person from down] Position of person from downward = [Total number of persons - position of person from up] PAGE # 17

20 3. Position of person from right = [Total number of persons - position of person from left] Position of person from left = [Total number of persons - position of person from right] Total number of persons = [Position of person from upward/right + position of person from downward / left] 1 Ex 7. In a row of girls, Mridula is 18th from the right and Sanjana is 18th from the left. If both of them exchange their position, Sanjana becomes 25th from the left, how many girls are there in the row? (A) 40 (B) 41 (C) 42 (D) 35 (C) Sanjana s new position is 25th from left. But it is the some as Mridula s earlier position which is 18th from the right. Then the total number of girls are = (rank from left + rank from right) 1 = ( ) 1= 43 1 = 42. Ex 8. Anil and Sunil are ranked seventh and eleventh respectively from the top in a class of 31 students. What will be their respective ranks from the bottom in the class? (A) 20 th and 24 th (B) 24 th and 20 th (C) 25 th and 21 st (D) 26 th and 22 nd (C) Number of students behind Anil in rank = (31 7) = 24 So, Anil is 25 th from the bottom. Number of students behind Sunil in rank = (31 11) = 20 So, Sunil is 21 st from the bottom. Ordering Test In such type of questions, clues are given regarding comparisons among a set of persons or things with respect to their qualities. The candidate is required to analyses the whole information, form a proper ascending/descending sequence and then answer the given questions accordingly. Ex 9. A is shorter than B but much taller than E. C is the tallest and D is shorter than A and taller than E. Which one is the shortest? (A) A (B) E (C) B (D) D (B) According to the given statement E < D < A < B < C Ex 10. A is richer than B. C is richer than A. D is richer than C. E is the richest of all. If they are made to sit in the above degree of richness who will be in the middle position (central position)? (A) A (B) B (C) C (D) D (C) According to the given statement C is in the middle position. Ex 11. Ashok is older than Suresh, Vivek is not youngest. Raju is older than Ashok and Vivek is not older than Suresh. Which one of the following statements must necessarily be true? I. Vivek is as old as Ashok II. Vivek is as old as Raju III. Vivek is as old as Suresh IV. Suresh is younger than Vivek (A) Only I (B) Only II (C) Only III (D) Either III or IV (C) According to the given statement V = S < A < R Directions : (12 to 13) Read following information carefully and answer the questions given below it : (i) P, Q, R, S and T are five friends. (ii) Q is elder to T. (iii) R is younger to P. (iv) P is younger to T. (v) S is elder to P. Ex 12. Who among the following is the eldest? (A) P (B) Q (C) S (D) Data inadequate Ex 13. Who among the following is the youngerst? (A) P (B) R (C) T (D) Data inadequate : (12 to 13) Thus, sequence of their age becomes Q >T > S > P > R or Q >S > T > P > R or S >Q > T > P > R 12. (D) According to a given statement there are three sequences, as follows : Q >T > S > P > R or Q >S > T > P > R or S >Q > T > P > R Hence the answer is data inadequate 13. (B) Clearly, R is the youngerst. 18 PAGE # 18

21 BLOOD-RELATIONS Blood Relations Problems on Blood Relations involve analysis of information showing blood relationship among members of a family. In the questions, a chain of relationship is given in the form of information and on the basis of these information relation between any two members of the chain is asked. Students are supposed to be familiar with the knowledge of different relationship in a family. Grandfather's son Grandmother's son Grandfather's only son Grandmother's only son Mother's or Father's mother Mother's or Father's father Grandfather's only daughter-in-law Grandmother's only daughter-in-law Mother's or Father's son Mother's or Father's daughter Mother's or Father's brother Mother's or Father's sister Husband's or wife's sister Husband's or wife's brother Son's wife Daughter's husband Brother's son or Sister's son Brother's daughter or Sister's daughter Uncle or Aunt's son or daughter Sister's husband Brother's wife Father or uncle Father or uncle Father Father Grandmother Grandfather Mother Mother Brother Sister Uncle Aunt Sister-in-law Brother-in-law Daughter-in-law Son-in-law Nephew Niece Cousin Brother-in-law Sister-in-law Remark : A relation on the mother s side is called maternal while that on the father s side is called paternal. Thus, mother s brother is maternal uncle while father s brother is paternal uncle. Note : To build a family tree, certain standard notations are used to indicate a relationship between the members of the family. + stand for male person. stand for female person. +/ male or female person. stand for married couple. +/ B +/ A +/ A +/ B Tree Diagram of Blood Relation Asuming Your Self as Male + A is Son or Daughter of B. B is uncle or aunt of A. 19 PAGE # 19

22 Tree Diagram of Blood Relation Asuming Your Self as Female Direct-Relationship Relation Puzzle Ex 1. Ex 2. In these type of questions, around about description is given in the form of certain small relationship and you required to analyses the whole chain of relations and decipher the direct relationship between the persons concerned. Pointing towards a man in the photograph, Archana said, He is the son of the only son of my grandmother. How is that man related to Archana? (A) Cousin (B) Nephew (C) Brother (D) Son (C) Only son of Archana s grandfather means Archana s father & his son is Archana s brother. Pointing to a photograph, a lady tells Amit, "I am the only daughter of this lady and her son is your material uncle." How is the speaker related to Amit's father? (A) Sister-in-law (B) Wife (C) Either (A) or (B) (D) Neither (A) nor (B) (B) The lady who is talking to Amit is the daughter of the lady in the photograph. The son of that lady who is the brother of the lady who is talking to Amit. The brother of this lady is the maternal uncle of Amit. The lady is the mother of Amit & wife of Amit s Father. Ex 3. In these type of questions, mutual blood relations of more than two persons are mentioned. The candidate is required to analysis the given information, work out a family chart and then answer the given questions. Rohit and Rohan are brothers. Soniya and Sunita are sisters. Rohit s son is Sunita s brother. How is Rohan related to Soniya. (A) Father (B) Brother (C) Grand Father (D) Uncle (D) Rohit s son is Sunita s brother means Rohit is Sunita s father. Rohit and Rohan are brothers. Sunita and Soniya are sisters. So, Rohan is the uncle of Soniya. Directions : (4 to 6) P,Q,R,S,T,U,V & W are the family members. Q is the sister of V and V is the brother of R. P whose s father is W, is husband of T. S is the husband of Q and U is the son of V. P is the father of Q. Ex 4. How U is related with T? (A) Son (C) Grandson (B) Mother (D) Nephew Ex 5. How S is related with R? (A) Son (B) uncle (C) Brother-in-law (D) Brother Ex 6. How W is related with R? (A) Grand father (B) uncle (C) Son (D) Brother 20 PAGE # 20

23 : (4 to 6) + W Father Wife P + Father Husband S + Sister Q Son + + T V U Brother 4. (C) U is son of V and V is son of T. U is grandson of T. 5. (C) S is husband of Q and Q is sister of R. S is brother -in- law of R. 6. (A) R is son of P and P is son of W. W is grandfather of R. Coded Relation In such questions, the relationship are represented by certain specific symbols such as +,,,,, etc. The candidate is then required to analyse some given codes to determine then relationship between a set of persons, or to express a given relationship in the coded form. + R Ex 7. A + B means A is the son of B, A B means A is the wife of B. A B means A is the brother of B, A B means A is the mother of B, A = B means A is the sister of B. Which of the following represents P is the maternal-uncle of Q? (A) R P Q (C) P + R Q (B) P R P is brother of R. Ex 8. R Q R is mother of Q. P is maternal uncle of Q. (B) P R Q (D) P + R Q A B means A is the sister of B, A B means A is the daughter of B, A B means A is the son of B. On the basis of this information you have to tell, how is P related to S in the relationship P Q R S (A) Brother (C) Grandson (D) According to the directions Q Son P + Daughter +/ S Sisters R Daughter (B) Son P is the son of the daughter of S. (D) Daughter s son 21 PAGE # 21

24 PUZZLE-TEST Puzzle Test This chapter comprises of questions given in the form of puzzles, involving certain number of items, persons or things. You are required to analyses the given information of clue and answer the questions accordingly. Hints for Handling The Questions : Generally, several condition in the form of information are given with the question. So, do not make hurry to mix all the given information, instead go step by step. To avoid confusion while solving such questions, you should symbolize persons, items by dot, lines etc. Classification Type Puzzles This type consists of questions in which certain items belonging to different groups or possessing different qualities are given along with some clues with the help of which the candidate is required to group and analyses the given items and answer the questions accordingly. Directions : (1 to 3) Read following information carefully and answer the questions given below it : (i) A and B are good in Biology & Chemistry. (ii) A & C are good in Biology & Physics. (iii) C, D & E are good in Physics & History. (iv) C & E are good in Physics & Mathematics. (v) D & B are good in Chemistry & History. Ex 1. Ex 2. Who is good in Physics, History & Mathematics but not in Biology? (A) D (B) C (C) A (D) E Who is good in Physics, History, Mathematics & Biology? (A) C (B) E (C) D (D) B Ex 3. Who is good in Physics, Chemistry & History? (A) C (B) E (C) D (D) B : (1 to 3) By given information we can make the following table : Person A B C D E Biology Chemistry Physics History Maths x x x x x x x x x 1. (D) Clearly, E is good in Physics, History & Mathematics but not in Biology. 2. (A) Clearly, C is good in Physics, History, Mathematics & Biology. 3. (C) Clearly, D is good in Physics, Chemistry & History. 8. Which two subjects are studied by more than 2 students? (A) English and Hindi (B) Chemistry and Hindi (C) Physics and Sanskrit (D) Chemistry and English 9. Who are the students studying only two subjects? (A) L and O (C) L and P (B) O and P (D) M and N 10. Who are not studying Biology, Sanskrit and Physics? (A) M, N and P only (C) M and N only (B) N and O only (D) M, N and O only Directions : (11 to 15) Read the following information and then find out the answers to the questions that follow. (i) Mansi, Gautami, Roza, Farida and Akshada who are teachers in a school teach different subjects. (ii) Mansi and Gautami teach Hindi and English. (iii) Roza and Farida teach English and Geography. (iv) Farida and Mansi teach Maths and Hindi. (v) Akshada and Gautami teach History and Marathi. 11. Who among them teach the maximum number of subjects? (A) Mansi and Akshada (B) Gautami and Farida (C) Roza and Gautami (D) Farida and Mansi 12. Who among them teaches three subjects? (A) Mansi (C) Farida (B) Gautami (D) Akshada 13. The common subject that Mansi, Gautami and Roza teach is (A) History (C) Marathi (B) Maths (D) English PAGE # 22