UPSC Prelims 2014 · CSAT

Question 44: Basic Numeracy

With reference to the figure given below, the number of different routes from S to T without retracing from U and/or V, is

A line diagram of three diamond shapes joined side by side with points S at the far left, U and V at the joints between the diamonds, and T at the far right.

d18

AnswerUPSC’s answer is (d).

The figure is a chain of three sections joined at U and V. From S to U there are three ways: the upper path, the straight line and the lower path. From U to V there are two: the upper or the lower path. From V to T there are three again. Routes multiply across sections: 3 x 2 x 3 = 18. The no-retracing rule means you never go back through U or V.

Why each option is right or wrong

(a) 3 counts only one section's choices.
(b) 6 multiplies only two of the three sections.
(c) 9 multiplies the two three-way sections and misses the middle one.
(d) Right. 3 x 2 x 3 = 18.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2014, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.