NMT_07 (NTIONL MTHEMTIS TLENT ONTEST) PRIMRY LEVEL - V & VI STNRS PRT -. Which one of the following numbers is NOT the sum of two prime numbers? () 4 () 30 () 67 () 4 = 9 + 5 30 = 3 + 7 = 9 +. is a square and P = P. The perimeter of the rectangle PQ is 80 cm. The perimeter of in cms is P 90 90 Q () 00 () 0 () 40 () 60 PQ = = = x P = Q = y y P y (x + y) = 80 x + y = 40 x x x If x = 3y 4y = 40 y = 0 cm Q x = 30 cm Perimeter = 4x = 0 cm of 3. Saket added up all the even numbers from to 0. Then, from the total he obtained, he subtracted all odd numbers between 0 and 00. The answer he would have obtained is () 0 () 0 () 30 () 50 dding even nos. = + 4 + 6 + + 98 + 00 dding odd nos. = + 3 + 5 + + 97 + 99 + + + (5o times) 50 orporate Head Office Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5
Page # NMT_PRIMRY LEVEL 4. The value of 4 8 is 4 8 () 6 () 4 () 4 () 6 4 8 4 8 = 4 8 4 = 7 8 4 = 6 5. is a rectangle. =8 cm and = 6 cm. Q is the midpoint of. P,R are on and respectively such that P= cm, R = cm. rea of the shaded triangle in square cms is Q P R () () 3 () 4 ()6 Join ER Now, rea of PQR = rea of rectangle rea of remaining triangles + rectangle Q P = 8 6 4 4 5 3 8 8 = 48 [4 + 0 + + 8] = 48 [34] = 4 E R 6. The Rishimoolam of a number is defined as follows. onsider the number 34. y multiplying its digits,3 and 4, we obtain x 3 x 4 = 4. gain, multiplying the digits of 4, we get x 4 = 8. We say 8 is the Rishimoolam of the numbers 34. If 0 is the Rishimoolam, we say the number has no Rishimoolam. Which one of the following has no Rishimoolam? () 736 () 647 () 83 ()69 69 = 6 9 = 54 54 = 5 4 = 0 0 = 0 = 0 0744-0967, 08003899588 www.motioniitjee.com info@motioniitjee.com
NMT_PRIMRY LEVEL Page # 3 7. Two circles touch two parallel lines as shown in the diagram. The radius of each circle is cm. The distance between the centres of the circles is 5 cm. The area of the shaded region is square cms is () 5 () 0 () 0 () 0 + ra of shaded region = 5 7 = 0 5 8. Sumrud wrote two consecutive integers, one of which ends in a 5. He multiplied both. He squared the answer. The last two digits of his answer is () 50 () 40 () 0 () 00 The number is of the form 5, 6 30 or 4, 5 0 Their product will end with a zero Now, on squaring, we will get zeros Last two digits will be 00 9. Vishwa wrote a number on each side of 3 cards. In each card, the numbers written on the sides are different. One side of each card is a prime number and the other sides had 44, 59 and 38 respectively. Given that the sum of the numbers on each card is the same, the difference between the largest and the second largest of the prime numbers on the cards is () 6 () 7 () 9 () 4 3 cards 6 numbers 3 prime no. 3 no. given 44, 59, 38 Sum of numbers on 3 cards is same Smallest prime no. = Let's add it to 59 59 + = 6 Now other prime numbers could be 6 44 = 7 & 6 38 = 3 One set of 3 prime numbers =, 7, 3 3 7 = 6 orporate Head Office Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5
Page # 4 NMT_PRIMRY LEVEL 0. The number of three digit number abc such that a x b x c = 5 is () () 6 () 8 () 9 For a b c = 5 Take numers, 3, 5 3 5 5 3 3 5 6 such numbers 3 5 5 3 5 3 PRT -. Five chairs cost as much as desks, 7 desks cost as much as tables and 3 tables cost as much as sofas. If the cost of 5 sofas is Rs 550, then the cost of a chair (in Rs) is. Let hairs be, esks be, Tables be T, Sofas be S. If cost of 5 Sofas = Rs.550 ccording to question, 5 = 7 = T 3T = S ost of Sofa = 550 050Rs. 5 ost of Table = 350 700Rs. 3 ost of esks = 700 00Rs. 7 ost of hairs = 00 480Rs. 5. The average age of a class of 0 children is.6 years. 5 new children joined with an average agee of. years. The new average of the class (to one decimal place). Total of 0 children =.6 0 = 5 years New total = 5 + 5. = 5 + 6.0 = 33 years New average = 33 5 =.5 years 0744-0967, 08003899588 www.motioniitjee.com info@motioniitjee.com
NMT_PRIMRY LEVEL Page # 5 3. 3 is a two digit prime and when we reverse its digits, the number 3 obtained is also a prime number. The number of two digit numbers having this property is. Such numbers are, 3, 3, 7, 7, 37, 73, 97, 79 4. In a garden there are two plants. One plants is 44cm tall and the otheris 80 cm tall. The first plant grows 3 cm in every months and the second 5 cm in every 6 months. The number of months after which the two plants will have equal height is. In first 6 months, grows = 44 + 9 = 53 grows = 80 + 5 = 85 If this continuous for next 48 months, = 44 + 9 9 = 5 = 80 + 5 9 = 5 No. of months = 54 44cm 80cm 5. In 5 days a man walked a total of 85 KM. Every day he walked 4 KM less than the previous day. The number of KM he walked on the last day is. In 5 days distance covered = 85 km Let first day distance covered = a difference = 4 km 5 85 [ a 4 4] a = 9km n Sum [a (n )d] 6. In the adjoining figure, is parellel to. The value of x is. 35 49 x = 360 35 = 35 [complete angle] = 80 [35 + 3] = 80 66 = 4 x = 80 4 [linear pair] x = 66 7. In Mahadevans cycle shop for children, there are unicycles, having only one wheel, bicycles, having two wheels and tricycles, having three wheels. Samrud counts the seats and wheels and finds that there are totally 7 seats and 3 wheels. The number of bicycles is more than tricycles. The number of unicycles in the shop is. If we take Tricycle = 3 = 3 icycle = 4 = 8 Unicycle = = Total wheels = 3 No. of unicycles = orporate Head Office Motion Education Pvt. Ltd., 394 - Rajeev Gandhi Nagar, Kota-5
Page # 6 NMT_PRIMRY LEVEL 8. There is a tree with several branches. Many parrots came to rest on the tree. When 6 parrots sat on each branch of the tree, all the branches were occupied but three parrots were left over. When 9 parrots sat on each branch. all parrots were seated but two branches were empty. If b is the number of branches and p is the number of parrots, the value of b + p is. Total no. of parrots in st case = 6 parrots on each branch + 3 p = 6b + 3 In nd case 9 parrots on each branch and branches with no parrots p = 9(b ) 6b + 3 = 9(b ) b = 7 p = 45 b + p = 5 9. The incomes of and are in the ratio 3:. Their expenditures ar eint he ratio 5:3. If each saves Rs 0,000, then s income is (in Rs). I : I = 3 : E : E = 5 : 3 I =? S = S = 0,000 Rs. I = E + S I = E + S 3x = 5y + 0,000 lso x = 3y + 0,000 3x 0, 000 x 0, 000 5 3 9x = 30,000 = 0x 50,000 0,000 = x I 3 0,000 = 60,000 Rs. 0. The radius of a circle is increased so that its circumference is increased by 5%. The area of the circle will increase by %. r, r be initial and final radius 5 (r r ) Given, 00 r r r 0 Now, change in area = (r r ) 00 r r = r 00 = 4 00 400 = 0.5% 0744-0967, 08003899588 www.motioniitjee.com info@motioniitjee.com