CSAT Solved Papers/ 2022/Q49

2022 CSAT — Q49

Quant Data sufficiency 2.5 marks Medium

Consider the Question and two Statements given below:

Question: What is the age of Manisha?

Statement-1: Manisha is $24$ years younger than her mother.

Statement-2: $5$ years later, the ages of Manisha and her mother will be in the ratio $3 : 5$ .

Which one of the following is correct in respect of the Question and the Statements?

A Statement-1 alone is sufficient to answer the Question
B Statement-2 alone is sufficient to answer the Question
C Both Statement-1 and Statement-2 are sufficient to answer the Question Answer
D Both Statement-1 and Statement-2 are not sufficient to answer the Question

Worked rationale

Let Manisha $= M$ , mother $= P$ .

Statement-1 alone ( $P = M + 24$ ): one equation, two unknowns — $M$ not pinned. Insufficient.

Statement-2 alone ( $\tfrac{M+5}{P+5} = \tfrac{3}{5}$ ): one equation, two unknowns — $M$ not pinned. Insufficient.

Both together: substitute $P = M + 24$ into the ratio:

\frac{M+5}{M+29} = \frac{3}{5} \;\Rightarrow\; 5(M+5) = 3(M+29) \;\Rightarrow\; 2M = 62 \;\Rightarrow\; M = 31.

A unique age — both statements are needed.

Answer: (c) Both Statement-1 and Statement-2 are sufficient.

Why the other options miss

A

trusts one statement too far: treats a single age-difference as fixing the age, but one equation in two unknowns can’t pin $M$ .
B

again over-trusts one statement: a future ratio gives a relation between the two ages, not a value, so $M$ stays unpinned.
D

misses that the two statements combine: overlooks that two independent linear relations in $M, P$ solve uniquely.

Specialist insight

Two unknowns ( $M, P$ ) need two independent equations. Statement-1 gives a difference; Statement-2 gives a future ratio — independent, so together they form a $2\times 2$ system with a unique solution. The DS discipline is to count independent constraints versus unknowns, not to solve fully — though the quick solve ( $M = 31$ ) confirms (c).

The trap, in one line

Difference $+$ future-ratio $=$ two independent equations in $M, P$ $\Rightarrow$ unique $M = 31$ $=$ (c).

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