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Pass Marks and Percentage Range

CAT 2019 Slot 1 · Quantitative Ability · Hard · Percentages

This is a hard Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests Percentages. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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?

  1. A.

    N≤200N \le 200

  2. B.

    243≤N≤252243 \le N \le 252

  3. C.

    N≥253N \ge 253

  4. D.

    201≤N≤242201 \le N \le 242

Answer

B

Explanation

Pass mark P=0.45NP = 0.45N. Candidate gets 36 marks, which is 100%−68%=32%100\% - 68\% = 32\% of the pass mark PP. 0.32P=36⇒P=360.32=112.50.32 P = 36 \Rightarrow P = \frac{36}{0.32} = 112.5. 0.45N=112.5⇒N=112.50.45=2500.45 N = 112.5 \Rightarrow N = \frac{112.5}{0.45} = 250. Since 243≤250≤252243 \le 250 \le 252, option B is correct.

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