CSAT Solved Papers/ 2025/Q38

2025 CSAT — Q38

Quant Logical & quantitative reasoning 2.5 marks Medium

If $P = +,\ Q = -,\ R = \times,\ S = \div$ , then insert the proper notations between the successive numbers in the equation $60\ \_\ 15\ \_\ 3\ \_\ 20\ \_\ 4 = 20$ :

A SPRQ
B QRPS Answer
C QRSP
D SPQR

Worked rationale

Decode each option into operators (respecting BODMAS: $\times,\div$ before $+,-$ ) and test against $=20$ . The four gaps sit between $60,\ 15,\ 3,\ 20,\ 4$ .

Option (b) QRPS $= -,\ \times,\ +,\ \div$ :

60 - 15 \times 3 + 20 \div 4 = 60 - 45 + 5 = 20. \checkmark

Quick rejection of the rest:

(a) SPRQ $= \div,+,\times,-$ : $60 \div 15 + 3 \times 20 - 4 = 4 + 60 - 4 = 60 \ne 20.$
(c) QRSP $= -,\times,\div,+$ : $60 - 15 \times 3 \div 20 + 4 = 60 - 2.25 + 4 = 61.75 \ne 20.$
(d) SPQR $= \div,+,-,\times$ : $60 \div 15 + 3 - 20 \times 4 = 4 + 3 - 80 = -73 \ne 20.$

Only (b) yields $20$ .

Answer: (b) QRPS.

Why the other options miss

A

ignored the order of operations: a plausible-looking operator string that ignores the BODMAS evaluation, landing on $60$ .
C

an arithmetic slip: shares the correct leading $-,\times$ but mis-places $\div$ before $+$ , giving a non-integer $61.75$ .
D

ignored the order of operations: starts with $\div$ and ends with $\times$ , producing a large negative value, far from the target.

Specialist insight

This is a back-substitution item, not an algebraic one: decode each candidate and evaluate under strict order of operations. The single trap is forgetting BODMAS — every distractor “works” if you read left-to-right, but only (b) survives once $\times$ and $\div$ are done first. Under time pressure, evaluate the multiplicative terms ( $15\times3 = 45$ , $20\div4 = 5$ ) before touching the $+/-$ , and you reach $60 - 45 + 5 = 20$ in one pass.

The trap, in one line

Apply BODMAS: only QRPS gives $60 - 15\times3 + 20\div4 = 60 - 45 + 5 = 20$ .

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