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CAT 2003 Slot 1 — QA Question 14

Simple EquationsEasy
Passage / Data

Answer the following question based on the information given below.

A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1, the south end point of OR to E2, the east endpoint of IR. Traffic moves at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road, and km/hr on all the chord roads.

A test has 50 questions. A student scores 1 mark for a correct answer, −1/3 for a wrong answer, and −1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than

Answer & solution

  • A

    6

  • B

    12

  • 3

  • D

    9

Solution

Let R, W and N be the number of questions with right answers, questions with wrong answers and not attempted questions respectively.

From the conditions given in the question, we have,

R + W + N = 50                      … (i)

R − W/3 − N/6 = 32                … (ii)

Solving equations (i) and (ii), we get,

7R − 242 = W

∴ W will be minimum for R = 35, i.e. W = 3

Hence, option (c).

CAT 2003 Slot 1 QA Q14: A test has 50 questions. A student scores 1 mark for a correct answer, −1/3 for a wrong answer, and &min — Solution | TheCATExam