Lesson 4: PILI* Numerical Reasoning

Transcription

1 Lesson 4: PILI* Numerical Reasoning SECTION BREAKDOWN, SAMPLE QUESTIONS, TIPS Disclaimer: 12minprep is not affiliated, nor belongs to PI, which are the owners of Predictive Index Learning Indicator (PILI) test, also known as PLI and Predictive Success Cognitive Assessment. This website solely provides information on how to prepare for cognitive ability tests.

2 Numerical Reasoning Question Types on PILI Number series Number value Word problems

3 Note Explanations may give an impression that questions can t be solved quickly. But we re in lesson mode: If you practice properly, everything will flow faster and in auto mode. Calculators are not allowed! Keep Calm

4 Number Series Sample Question 1, 2, 4, 5, 10,?

5 Number Series - Sample Question Explained 1, 2, 4, 5, 10,? or or 2 +1 or 2 +2 or 2 Rule: +1, 2, +1, 2

6 Lowest Value Which of the following numbers has the lowest value? Only fractions 1/3 1/ Mixed 2/ /7 2/10+0.5

7 Lowest Value Tips: Master percentages, fractions, decimals Convert from one form to the other Memorize known fractions & percentage/decimal forms Simplify fractions Practice your estimation skill

8 Memorizing Values, Rules, and Formulas Fraction Decimal Percent ½ % 1/ % 2/ % ¼ % 1/ % 1/ % 1/ % 1/ % 1/ % 1/ % Bigger denominator smaller fraction A/B = B 1/A Percent= per 100 = value/100 Decimal to percentage: multiply by 100 Percentage to decimal: divide by 100

9 Lowest Value Sample Question Which of the following numbers has the lowest value? 2/3 5/6 5/8 4/7

10 Lowest Value Sample Question Which of the following numbers has the lowest value? 2/3 5/6 5/8 4/7

11 Lowest Value Sample Question Explained Which of the following numbers has the lowest value? Using % 2/3 5/6 5/8 4/7 = 2 1/3 = 66.66% 5 1/6 5 16% 80% 5 1/8 = % 60% 4 1/7 4 14% 56%

12 Lowest Value - Sample Question Explained Or Multiply Vs 5 6 Divide 5 6 by Vs is smaller 5 Vs Vs Vs is smaller. 2 Vs Vs Vs turns into: is the smallest

13 Word Problems - Types Basic arithmetic Work rate Distance, Speed, Time Ratios Percentages (increase/decrease, reverse) Averages

14 Percent= per 100 = value/100 Word Problems Percentages A Bluetooth speaker costs 12. Its price rose by 20% and then by additional 2.4 the day after. What is the total percentage increase in price of this speaker? 1. 25% 2. 35% 3. 40% 4. 45%

15 Word Problems Percentages A Bluetooth speaker costs 12. Its price rose by 20% and then by additional 2.4 the day after. What is the total percentage increase in price of this speaker? 1. 25% 2. 35% 3. 40% 4. 45%

16 Percent= per 100 = value/100 Word Problems Percentages Explained A Bluetooth speaker costs 12. Its price rose by 20% and by additional 2.4 the day after. What is the total percentage increase in price of this speaker? 10% building blocks divide by 10 10% = 12/10 = %=2 10% 20% of 12 = = = = = 40% Or: 1.2 =10% 1.2 4=10% 4=40%!

17 Percentage Quick Tricks 1% and 10% building blocks shift the decimal point to the left 20% of 30 is (2x3)=6, 25% of 40 is 2.5x4 35% of 20 = 20% of 35 Reverse % for price reduction: Original price = Reverse % for price increase: Original price = new price what s left new price what was added

18 Work Rate = Work / Time Word Problems Work Rate 3 machines with equal output build 1 car in 5 hours. If a fourth machine with double the output of a single machine is added, how many hours will it take to build the same car?

19 Word Problems Work Rate 3 machines with equal output build 1 car in 5 hours. If a fourth machine with double the output of a single machine is added, how many hours will it take to build the same car?

20 Work Rate = Work / Time Word Problems Work Rate Explained 3 machines with equal output build 1 car in 5 hours. If a fourth machine with double the output of a single machine is added, how many hours will it take to build the same car? 1 machine does one third of the work: 1/3 Each machine works 5 hours Thus, work rate of one machine = (1/3)of car 5h Fourth machine s work rate = New combined work rate = ( ) + ( ) = = 5 15 = 1 3 which means 1 car in 3 hours! = 1/3 5 = 1 15

21 Word Problems Speed Distance Time Distance = Speed Time *Speed=velocity A spaceship is travelling at a speed that increases by two fold every hour. In 3 hours the spaceship travelled 140 miles. What was the speed of the spaceship during the third hour?

22 Word Problems Speed Distance Time A spaceship is travelling at a speed that increases by two fold every hour. In 3 hours the spaceship travelled 140 miles. What was the speed of the spaceship during the third hour?

23 Distance = Speed Time *Speed=velocity Word Problems Speed Distance Time Explained A spaceship is travelling at a speed that increases by two fold every hour. In 3 hours the spaceship travelled 140 miles. What was the speed of the spaceship during the third hour? Original Speed =? (S) Distance covered in 1 st hour: S 1h Distance in 2 nd hour: 2S 1h Distance in 3 rd hour: 4S 1h 140 = S+2S+4S 140 = 7S S = 20 3 rd hour Speed = 4S = 20 4 = 80mph

24 Avg = (sum of numbers in set) / (# of items in set) Word Problems Averages The average number of weekly working hours of Tom, Helen, and Boris is 34. Boris works 40h on average every week. What is Helen and Tom's average number of weekly working hours?

25 Word Problems Averages The average number of weekly working hours of Tom, Helen, and Boris is 34. Boris works 40h on average every week. What is Helen and Tom's average number of weekly working hours?

26 Avg = (sum of terms in set) / (# of terms in set) Word Problems Averages Explained The average number of weekly working hours of Tom, Helen, and Boris is 34. Boris works 40h on average every week. What is Helen and Tom's average number of weekly working hours? Using the persons' initials as variables, with Boris being substituted with 40, we can write: (T+H+40)/3 = 34 T+H+40 = 34 3 Simplifying 34 3 and subtracting 40: T+H = (30+4) 3-40 T+H = = 62 This is Tom and Helen's sum of ages. And back to finding Tom and Helen s average age: (T+H)/2 = 62/2= 31 hours

27 Word Problems Ratios The number of keynote speakers at the conference constitutes 2/5 of the total number of speakers in the conference. If there are 38 unique keynote talks during the conference, how many speakers are not keynote speakers?

28 Word Problems Ratios The number of keynote speakers at the conference constitutes 2/5 of the total number of speakers in the conference. If there are 38 unique keynote talks during the conference, how many how many speakers are not keynote speakers?

29 Word Problems Ratios Explained The number of keynote speakers at a conference constitutes 2/5 of the total number of speakers in the conference. If there are 38 unique keynote talks during the conference, how many speakers are not keynote speakers? Let S stand for all speakers, K stand for keynote speakers, and R for regular speakers: K = 2/5 S = 38 S = 38 5/2 R = 3/5 S = /(5 2) = 3 19 = 57

30 End of Lesson 4 Note: Grab the PDF with a list of curated Numerical Reasoning practice resources. On to Lesson 5!