IPMAT Indore 2024 · Quantitative Ability · Question 40

IPMAT Indore 2024 previous year question on Fractions and Decimals, with the answer and a step-by-step solution.

Fractions and DecimalsNumber SystemMultiple choiceMedium
The smallest possible number of students in a class if the girls in the class are less than 50% but more than 48% is
  1. A
    25
  2. B
    100
  3. C
    27
  4. D
    200
Pick an option, then check.
Answer & solution

Answer: Option C

Step 1 — state the requirement. With n students and g girls, we need an integer g with

0.48<\frac{g}{n}<0.50 \Rightarrow 0.48\,n<g<0.5\,n

The window has width 0.02n, so for small n it usually contains no integer at all.

Step 2 — test increasing n.

n

window \left( 0.48n, 0.5n \right)

integer inside?

25

\left( 12, 12.5 \right)

no — 12 is excluded (that is exactly 48%)

26

\left( 12.48, 13 \right)

no — 13 is excluded (that is exactly 50%)

27

\left( 12.96, 13.5 \right)

yes, g=13

Step 3 — confirm.

\frac{13}{27}=0.4815\ldots

which is strictly between 0.48 and 0.50 ✔

A check of every n from 2 to 26 confirms none works, so 27 is genuinely the smallest.

Answer: Option 3 — 27

Shortcut. Both bounds are strict — that is the entire question. At n=25 the only candidate is g=12, which is exactly 48%, and at n=26 the only candidate is g=13, which is exactly 50%. Both fail the strict inequalities, which is why the “obvious” answer 25 is wrong.

The structural shortcut: you need a fraction strictly between 12/25 and 1/2. The mediant of two fractions always lies strictly between them:

\frac{12+1}{25+2}=\frac{13}{27}

giving n=27 directly, and the mediant is guaranteed to have the smallest possible denominator between two neighbouring fractions. A genuinely useful tool for this family of questions.

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