2022 CSAT, all questions

UPSC Prelims 2022 · CSAT

Question 8: Basic Numeracy

A bill for ₹1,840 is paid in the denominations of ₹50, ₹20 and ₹10 notes. 50 notes in all are used. Consider the following statements :

  1. 1.25 notes of ₹50 are used and the remaining are in the denominations of ₹20 and ₹10.
  2. 2.35 notes of ₹20 are used and the remaining are in the denominations of ₹50 and ₹10.
  3. 3.20 notes of ₹10 are used and the remaining are in the denominations of ₹50 and ₹20.

Which of the above statements are not correct?

a1 and 2 only
b2 and 3 only
c1 and 3 only
d1, 2 and 3

AnswerUPSC’s answer is (d).

Let the notes be a of ₹50, b of ₹20 and c of ₹10. Then a + b + c = 50 and 50a + 20b + 10c = 1840, which reduce to 4a + b = 134, so b = 134 − 4a and c = 3a − 84. Both must be non-negative, so a lies between 28 and 33, with b at most 22 and c at most 15. Statement 1 needs a = 25, statement 2 needs b = 35, statement 3 needs c = 20: none is possible. The question asks which are not correct, so the answer is all three.

  • 1. Needs 25 notes of ₹50, but a must be at least 28.
  • 2. Needs 35 notes of ₹20, but b is at most 22.
  • 3. Needs 20 notes of ₹10, but c is at most 15 (and 3a = 104 is not a whole number).

How you could have got this

  1. If you were sure statement 1 is not correct, (b) goes: it leaves 1 out.

    What you needed to know: Needs 25 notes of ₹50, but a must be at least 28.

  2. Then, if you were sure statement 2 is not correct, (c) goes: it leaves 2 out.

    What you needed to know: Needs 35 notes of ₹20, but b is at most 22.

  3. Then, if you were sure statement 3 is not correct, (a) goes: it leaves 3 out.

    What you needed to know: Needs 20 notes of ₹10, but c is at most 15 (and 3a = 104 is not a whole number).

Only (d) 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 3 is also incorrect, since c cannot reach 20.
  • (b) Wrong: statement 1 is also incorrect, since a cannot be 25.
  • (c) Wrong: statement 2 is also incorrect, since b cannot be 35.
  • (d) Correct: a must be 28 to 33, so all three statements fail.

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

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Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.