Arithmetic

Percentages

Medium

In an examination, the maximum possible score is $N$ while the pass mark is $45\%$ of $N$ . A candidate obtains $36$ marks, but falls short of the pass mark by $68\%$ . Which one of the following is then correct?

$243 \leq N \leq 252$

$N \geq 253$

$201 \leq N \leq 242$

$N \leq 200$

✅ Correct Option: 1

Let's break down what we know:

Maximum possible score: N

Pass mark: 45% of N

Candidate's score: 36 marks

Candidate falls short of pass mark by: 68%

The key insight here is understanding what "falls short by 68%" actually means.

When we say someone "falls short by 68%", it means they achieved only (100% - 68%) = 32% of the required pass mark.

Think of it this way: If you need 100 marks to pass, and you fall short by 68%, you got only 32 marks.

So our candidate achieved 32% of the pass mark.

Since the candidate got 32% of the pass mark:

Pass mark = 45% of N = 0.45N

Candidate's achievement = 32% of pass mark

= 32% of (0.45N)

= 0.32 × 0.45N

= 0.144N

But we know the candidate scored 36 marks, so:

0.144N = 36

$N = 36 ÷ 0.144$

$N = 36 ÷ \tfrac{144}{1000}$

$N = 36 × \tfrac{1000}{144}$

$N = \tfrac{36000}{144} = 250$

Therefore, N = 250

When a problem states someone "falls short by X%", remember:

They achieved (100% - X%) of the target

Set up your equation using this percentage of the target value

This approach works for any similar percentage shortage problems!

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In an examination, the maximum possible score is NNN while the pass mark is 45%45\%45% of NNN. A candidate obtains 363636 marks, but falls short of the pass mark by 68%68\%68%. Which one of the following is then correct?

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CAT Past Year Questions (Topic-Wise)

In an examination, the maximum possible score is $N$ while the pass mark is $45\%$ of $N$ . A candidate obtains $36$ marks, but falls short of the pass mark by $68\%$ . Which one of the following is then correct?