CSAT Solved Papers/ 2021/Q75

2021 CSAT — Q75

Quant Logical & quantitative reasoning 2.5 marks Medium

Joseph visits the club on every $5$ th day, Harsh visits on every $24$ th day, while Sumit visits on every $9$ th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?

A Monday
B Wednesday Answer
C Thursday
D Sunday

Worked rationale

They all meet again after $\operatorname{lcm}(5, 24, 9)$ days. Factorise:

5 = 5,\quad 24 = 2^3\cdot 3,\quad 9 = 3^2 \;\Rightarrow\; \operatorname{lcm} = 2^3\cdot 3^2\cdot 5 = 360.

Now find the weekday $360$ days after Sunday: $360 \bmod 7 = 360 - 357 = 3$ , so the day is $\text{Sunday} + 3 = \textbf{Wednesday}$ .

Answer: (b) Wednesday.

Why the other options miss

A

a remainder slip: takes $360 \equiv 1 \pmod 7$ (a remainder slip) and adds one day.
C

an arithmetic slip: uses $360 \equiv 4 \pmod 7$ or a wrong LCM that shifts the offset.
D

the wrong assumption: assumes the meeting cycle is a whole number of weeks ( $360 \equiv 0$ ), ignoring the $\bmod 7$ remainder.

Specialist insight

Two independent steps, each with a classic trap: the LCM must use the highest power of each prime ( $2^3, 3^2, 5 \to 360$ , not $5\times24\times9$ ), and then the weekday is the remainder mod $7$ ( $360 \equiv 3$ ), not the raw day count. Compute the LCM cleanly, then reduce mod $7$ and step forward from Sunday. The “Sunday” distractor is the bait for anyone who forgets $360$ isn’t a multiple of $7$ .

The trap, in one line

$\operatorname{lcm}(5,24,9) = 360$ , and $360 \equiv 3 \pmod 7$ , so Sunday $+3 =$ Wednesday $\Rightarrow$ (b).

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