CAT 2025 Question Paper | Quant Slot 1

CAT Questions

CAT 2025 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 14 : In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of boys. Then, the minimum possible number of students initially in the class was

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Video Explanation

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Explanatory Answer

Initial Boys \(=5b\)
Initial Girls \(=5g\)

Now calculate the remaining students after people leave:

Girls remaining:
40% left \(\Rightarrow60\%\) remain
Remaining Girls \(=60\%\text{ of }5g=0.6\times5g=3g\)

Boys remaining:
60% left \(\Rightarrow40\%\) remain
Remaining Boys \(=40\%\text{ of }5b=0.4\times5b=2b\)

The remaining girls are 8 more than the remaining boys:
\(3g=2b+8\)
\(2b=3g-8\)
\(\Rightarrow b=\frac{3g-8}{2}\)

Condition on Boys:
There were more than 10 boys initially:
\(5b>10\Rightarrow b>2\)

Integrity Condition:
For \(b=\frac{3g-8}{2}\) to be a whole number, \(3g-8\) must be even.
Since 8 is even, \(3g\) must be even, which means \(g\) must be an even number.

Let's test even values for \(g\) (\(g=2,4,6,\ldots\)):

If \(g=2\):
\(b=\frac{3(2)-8}{2}=-1\)
(Not possible, \(b\) must be positive)

If \(g=4\):
\(b=\frac{3(4)-8}{2}=2\)
(Not possible, because \(b>2\) strictly)

If \(g=6\):
\(b=\frac{3(6)-8}{2}=\frac{10}{2}=5\)
(Valid! \(b=5>2\))

So, the minimum valid integer values are \(g=6\) and \(b=5\).

Initial number of students \(=5b+5g=25+30=55\)

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The answer is '55'

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