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Lesson 4: PILI* Numerical ReasoningSECTION BREAKDOWN, SAMPLE QUESTIONS, TIPS

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Numerical Reasoning Question Types on PILI

• Number series

• Number value

• Word problems


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 ☺


1, 2, 4, 5, 10, ?

1. 15

2. 11

3. 20

4. 12

Number Series Sample Question


1, 2, 4, 5, 10, ?

1. 15

2. 11

3. 20

4. 12

+2or

×2

Number Series - Sample Question Explained

1 2 4 5 10

+1or

×2

+1or

×2

+2or

×2

Rule: +1, ×2, +1, ×2…


Lowest Value

• 1/3

• 1/6

• 2/8

• 2/7

“Which of the following numbers has the lowest value?”

• 0.02

• 2 × 0.1

• 1-0.2

• 2/10+0.5

Only fractions Mixed


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


Memorizing Values, Rules, and FormulasFraction Decimal Percent

½ 0.5 50%

1/3 0.33 33.33%

2/3 0.66 66.66%

¼ 0.25 25%

1/5 0.2 20%

1/6 0.166 16.66%

1/7 0.142 14.2%

1/8 0.125 12.5%

1/9 0.111 11.11%

1/10 0.1 10%

• 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


Lowest Value – Sample Question

• 2/3

• 5/6

• 5/8

• 4/7

Which of the following numbers has the lowest value?


Lowest Value – Sample Question Explained

• 2/3

• 5/6

• 5/8

• 4/7

= 2×1/3 = 66.66%

5×1/6 ≈ 5×16% ≈ 80%

5×1/8 = 5×12.5% ≈ 60%

4×1/7 ≈ 4×14% ≈ 56%

Which of the following numbers has the lowest value?

Using %


Lowest Value - Sample Question Explained

2

3Vs

5

6

Divide 5

6by 2

2

3Vs

2.5

3

2

3is smaller

𝟓

𝟖Vs

𝟒

𝟕

5×7 Vs 4×8

35 Vs 32

4

7is smaller.

2

3Vs

4

7turns into:

2×7 Vs 3×4

14 Vs 12

𝟒

𝟕is the smallest

•2

3

•5

6

•5

8

•4

7

Or Multiply


Word Problems - Types

• Basic arithmetic

• Work rate

• Distance, Speed, Time

• Ratios

• Percentages (increase/decrease, reverse)

• Averages

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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%

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%


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 = £1.2

20%=2×10%

20% of £12 = 1.2×2 = £2.4

£2.4 + £2.4 = £4.8

4.812

×100 = 48012

= 𝟒𝟎%

Or: £1.2 =10%£1.2×4=10%×4=40%!

Percent= per 100 = value/100


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 = new pricewhat’s left

• Reverse % for price increase: Original price = new price

what was added


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?

1. 1

2. 1.5

3. 3

4. 4.5

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?

1. 1

2. 1.5

3. 3

4. 4.5


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=

1/35 =

115

Fourth machine’s work rate = 2 ×115

New combined work rate = (3 ×115 ) + (2 ×

115 )

= 315 +

215 =

515 =

13

which means 1 car in 3 hours!

Work Rate = Work / Time


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?

1. 60

2. 80

3. 50

4. 120

Distance = Speed × Time

*Speed=velocity


Word Problems – Speed Distance Time


In 3 hours the spaceship travelled 140 miles. What was the speed of the spaceship

during the third hour?

1. 60

2. 80

3. 50

4. 120


Word Problems – Speed Distance Time Explained


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 1st hour: S×1hDistance in 2nd hour: 2S×1hDistance in 3rd hour: 4S×1h

140 = S+2S+4S140 = 7SS = 20

3rd hour Speed = 4S = 20×4 = 80mph

Distance = Speed × Time

*Speed=velocity


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?

1. 27.5

2. 31

3. 34

4. 35

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?

1. 27.5

2. 31

3. 34

4. 35


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 = 102-40 = 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

Avg = (sum of terms in set) / (# of terms in set)


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?

1. 95

2. 19

3. 57

4. 63


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?

1. 95

2. 19

3. 57

4. 63


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 = 3×38×5/(5×2) = 3×19 = 57

• Note: Grab the PDF with a list of curated Numerical Reasoning practice

resources.

End of Lesson 4

On to Lesson 5!

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lesson 4: pili* numerical reasoning - 12minprep.com resources/courses... · •note: grab the pdf...

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