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CAT 2018 Slot 1 — QA Question 7

PercentageEasy

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?

Answer & solution

Correct answer: 243 ≤ N ≤ 252

  • A

    N ≤ 200

  • B

    201 ≤ N ≤ 242

  • 243 ≤ N ≤ 252

  • D

    N ≥ 253

Solution

Easy

The pass mark is 45%45\% of NN. The candidate's 3636 marks fall short of the pass mark by 68%68\%, so 3636 is the remaining 32%32\% of the pass mark. Write 36=32%36 = 32\% of (45% of N)(45\%\text{ of }N) and solve for NN, then locate the matching range.

1

Interpret "short by 68%68\%". The shortfall is 68%68\% of the pass mark, so 3636 equals (100−68)%=32%(100-68)\% = 32\% of the pass mark.

pass mark=0.45 N⇒ 36=0.32×(0.45 N)\begin{aligned} &\text{pass mark} = 0.45\,N\\ &\Rightarrow\ 36 = 0.32 \times (0.45\,N) \end{aligned}
2

Solve for NN.

36=0.144 N⇒ N=360.144=250\begin{aligned} &36 = 0.144\,N\\ &\Rightarrow\ N = \frac{36}{0.144} = 250 \end{aligned}
3

Match the range. N=250N = 250 satisfies 243≤N≤252243 \le N \le 252.

243≤250≤252  ✓\begin{aligned} &243 \le 250 \le 252 \;\checkmark \end{aligned}
243≤N≤252  ⇒  option (c)\boxed{243 \le N \le 252 \;\Rightarrow\; \text{option (c)}}

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CAT 2018 Slot 1 QA Q7: In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 mar — Solution | TheCATExam