CSAT Solved Papers/ 2021/Q37

2021 CSAT — Q37

Quant Statement validity 2.5 marks Hard

There are two Classes $A$ and $B$ having $25$ and $30$ students respectively. In Class- $A$ the highest score is $21$ and lowest score is $17$ . In Class- $B$ the highest score is $30$ and lowest score is $22$ . Four students are shifted from Class- $A$ to Class- $B$ .

Consider the following statements:

The average score of Class- $B$ will definitely decrease.
The average score of Class- $A$ will definitely increase.

A 1 only Answer
B 2 only
C Both 1 and 2
D Neither 1 nor 2

Worked rationale

Every Class- $A$ score lies in $[17,21]$ ; every Class- $B$ score lies in $[22,30]$ .

Statement 1 (Class- $B$ average): the $4$ incoming students each score at most $21$ , which is below Class- $B$ ’s lowest ( $22$ ). Adding members strictly below the current minimum must pull the mean down. So Class- $B$ ’s average definitely decreases. Correct.

Statement 2 (Class- $A$ average): we are not told which $4$ students leave. If the four highest ( $21$ s) leave, the remaining average falls; if the four lowest ( $17$ s) leave, it rises. The outcome is not forced, so it is not a definite increase. Incorrect.

Answer: (a) 1 only.

Why the other options miss

B

solved the wrong question: assumes the departing students are the weakest, treating a possible increase as definite.
C

missed a case: gets Statement 1 right but overlooks that Class- $A$ ’s change depends on which students leave.
D

solved the wrong question: misses that the incoming four are strictly below Class- $B$ ’s minimum, which forces Statement 1.

Specialist insight

The word “definitely” is the whole question. A claim is definite only if it holds for every admissible scenario. Class- $B$ ’s drop is forced because the entrants ( $\le 21$ ) sit below its floor ( $22$ ) — a guaranteed downward pull. Class- $A$ ’s movement is unknown because the four leavers are unspecified, spanning best-case and worst-case. Separate “always true” from “can be true”: only the former earns the mark.

The trap, in one line

Entrants ( $\le 21$ ) are below $B$ 's min ( $22$ ) so $B$ falls; but $A$ 's leavers are unspecified, so $A$ is undecided $\Rightarrow$ (a).

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