Tayarri LCAT
LCAT Math, Problem-Solving and Data Analysis

Percentages for the LCAT: lesson and practice

To solve LCAT percent questions, turn each percent into a multiplier. p% of a number is (p/100) × the number. An increase of p% multiplies by 1 + p/100, and a decrease multiplies by 1 − p/100. Changes in a row multiply together, and to find an original value you divide by the multiplier.

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No calculator on the LCAT. LUMS’s official guidelines say calculators are not allowed, so every practice question here can be solved by hand.

Think in multipliers

SituationMultiply byExample on Rs 2,000
15% of0.15Rs 300
Increase by 15%1.15Rs 2,300
Decrease by 15%0.85Rs 1,700
+20% then −20%1.2 × 0.8 = 0.96Rs 1,920 (4% less)

Percent change

percent change = (new − original) ÷ original × 100
80 → 100: (100 − 80) ÷ 80 × 100 = 25%

Always divide by the starting value. Dividing by 100 in the example gives 20%, a common wrong answer.

Finding the original price

Example

After a 20% discount, a jacket costs Rs 4,000. What was the original price?

0.8 × original = 4,000
original = 4,000 ÷ 0.8 = Rs 5,000

Adding 20% of Rs 4,000 gives Rs 4,800, which is wrong: the 20% was taken from the larger original price.

Two changes in a row

Multiply the multipliers. A 30% increase followed by a 10% decrease is 1.3 × 0.9 = 1.17, a 17% increase, not 20%.

Use Rs 100 as a test value when unsure: 100 → 130 → 117. The numbers show the answer.

Common mistakes

Wrong decimal5% is 0.05, not 0.5.
Dividing by the new valuePercent change always uses the original value.
Adding the percent backTo undo a 20% discount, divide by 0.8. Do not add 20%.
Adding or subtracting percentages+20% then −20% is not zero change; it is a 4% decrease.
Giving the change instead of the new amountRead whether the question wants the increase or the final value.

Sample questions with answers

1. A value changes from 80 to 100. What is the percent increase?
  1. 20%
  2. 25% (correct)
  3. 80%
  4. 125%

20 ÷ 80 × 100 = 25%. Choice A divides by the new value.

2. After a 20% discount, a jacket costs Rs 4,000. What was the original price?
  1. Rs 4,800
  2. Rs 3,200
  3. Rs 5,000 (correct)
  4. Rs 4,020

4,000 ÷ 0.8 = 5,000. Choice A adds 20% of the sale price instead.

3. A price rises by 20% and then falls by 20%. What is the overall change?
  1. No change
  2. 4% decrease (correct)
  3. 4% increase
  4. 40% decrease

1.2 × 0.8 = 0.96, a 4% decrease.

Frequently asked questions

How do you calculate percent change on the LCAT?

Divide the change by the original value and multiply by 100. From 80 to 100, the change is 20 and 20 ÷ 80 × 100 = 25%.

How do you find the original price after a discount?

Divide the sale price by the multiplier. After a 20% discount the multiplier is 0.8, so an Rs 4,000 sale price means an original price of Rs 5,000.

Why is a 20% increase followed by a 20% decrease not zero change?

The second change applies to a larger amount. 1.2 × 0.8 = 0.96, which is a 4% decrease overall.

Is percentages tested on the LCAT?

Yes. It falls under Problem-Solving and Data Analysis, one of the content domains LUMS lists for the LCAT in its official sample questions.

Can I practice this without a calculator?

Yes. Every practice question here can be solved by hand, because calculators are not allowed on the LCAT.

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