UPSC Prelims 2023 · CSAT

Question 46: Basic Numeracy

Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements :

1.The number of possible values of p is 5.
2.The number of possible values of q is 6.

Which of the above statements is/are correct ?

a1 only

b2 only

cBoth 1 and 2

dNeither 1 nor 2

AnswerUPSC’s answer is (c).

pp + qq + rr = 11(p + q + r). For it to end in 0, p + q + r must end in 0. With distinct digits p < q < r, the sum is 10 or 20. Sum 10: (1,2,7), (1,3,6), (1,4,5), (2,3,5). Sum 20: (3,8,9), (4,7,9), (5,6,9), (5,7,8). Values of p: 1, 2, 3, 4, 5, which is 5 values. Values of q: 2, 3, 4, 6, 7, 8, which is 6 values. Both statements are correct.

1. Across the eight triples, p takes the values 1, 2, 3, 4, 5.
2. Across the eight triples, q takes the values 2, 3, 4, 6, 7, 8.

How you could have got this

If you were sure statement 1 is correct, (b) and (d) go: each of them leaves 1 out.
What you needed to know: Across the eight triples, p takes the values 1, 2, 3, 4, 5.
Then, if you were sure statement 2 is correct, (a) goes: it leaves 2 out.
What you needed to know: Across the eight triples, q takes the values 2, 3, 4, 6, 7, 8.

Only (c) is left. This one needs every statement.

Which options go is worked out from UPSC’s key and the options, not by a model.

Why each option is right or wrong

(a) Wrong: statement 2 is also correct (6 values of q).
(b) Wrong: statement 1 is also correct (5 values of p).
(c) Right: p has 5 values and q has 6.
(d) Wrong: both statements are correct.

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

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Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.