CSAT Solved Papers/ 2021/Q53

2021 CSAT — Q53

Quant Arithmetic & numeracy 2.5 marks Medium

Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store. If Jay bought 33 pens and 55 pencils, and Vijay bought 22 pens and 77 pencils, then which one of the following is correct?

  1. A A pencil costs more than a pen
  2. B The price of a pencil is equal to that of a pen
  3. C The price of a pen is two times the price of a pencil Answer
  4. D The price of a pen is three times the price of a pencil

Worked rationale

Let a pen cost pp and a pencil cost qq. Equal spending gives

3p+5q=2p+7q.3p + 5q = 2p + 7q.

Subtract 2p+5q2p + 5q from both sides:

p=2q.p = 2q.

So a pen costs twice a pencil.

Answer: (c) The price of a pen is two times the price of a pencil.

Why the other options miss

  • A
    the relationship inverted: reads q>pq > p instead of p=2qp = 2q.
  • B
    a cancellation slip: cancels terms incorrectly and lands on p=qp = q.
  • D
    coefficients mis-collected: handles 5q−7q5q-7q wrongly and gets p=3qp = 3q.

Specialist insight

One equation in two unknowns can’t give prices, but it can give a ratio — which is exactly what the question asks. Equate the two expenditures and let the common terms cancel: 3p+5q=2p+7q⇒p=2q3p+5q = 2p+7q \Rightarrow p = 2q. The trap is expecting a numeric price and freezing; instead, read what survives the cancellation. The sign of the surviving relation also kills the “pencil costs more” inversion.

The trap, in one line

3p+5q=2p+7q⇒p=2q3p+5q = 2p+7q \Rightarrow p = 2q: a pen is twice a pencil ⇒\Rightarrow (c).

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