Consider the following: 1. $A + B$ means $A$ is neither smaller nor equal to $B$. 2. $A - B$ means $A$ is not greater than $B$. 3. $A \times B$ means $A$ is not smaller than $B$. 4. $A \div B$ means $A$ is neither greater nor equal to $B$. 5. $A \pm B$ means $A$ is neither smaller nor greater than $B$. Statement: $P \times Q$, $P - T$, $T \div R$, $R \pm S$ Conclusion-1: $Q \pm T$ Conclusion-2: $S + Q$ Which one of the following is correct in respect of the above Statement and the Conclusions?

IAS 2023 — CSAT Reasoning

2023mcqmedium

Consider the following:

$A + B$ means $A$ is neither smaller nor equal to $B$ .
$A - B$ means $A$ is not greater than $B$ .
$A \times B$ means $A$ is not smaller than $B$ .
$A \div B$ means $A$ is neither greater nor equal to $B$ .
$A \pm B$ means $A$ is neither smaller nor greater than $B$ .

Statement: $P \times Q$ , $P - T$ , $T \div R$ , $R \pm S$
Conclusion-1: $Q \pm T$
Conclusion-2: $S + Q$
Which one of the following is correct in respect of the above Statement and the Conclusions?

Official previous-year question

Verified 2 Aug 2026.

Options

AOnly Conclusion-1 follows from the Statement.
BOnly Conclusion-2 follows from the Statement.
CBoth Conclusion-1 and Conclusion-2 follow from the Statement.
DNeither Conclusion-1 nor Conclusion-2 follows from the Statement.

Did you get this right?

Solution

Correct Option (B)

The first step involves translating the given symbolic relationships into standard mathematical inequalities:

$A + B$ signifies $A > B$ (A is neither smaller nor equal to B).
$A - B$ signifies $A \leq B$ (A is not greater than B).
$A \times B$ signifies $A \geq B$ (A is not smaller than B).
$A \div B$ signifies $A < B$ (A is neither greater nor equal to B).
$A \pm B$ signifies $A = B$ (A is neither smaller nor greater than B).

Applying these translations to the provided statement:

$P \times Q$ translates to $P \geq Q$ .
$P - T$ translates to $P \leq T$ .
$T \div R$ translates to $T < R$ .
$R \pm S$ translates to $R = S$ .

Combining these individual inequalities yields the comprehensive relationship:

$Q \leq P \leq T < R = S$

Now, each conclusion is evaluated based on this combined relationship:

Conclusion-1: $Q \pm T$

This conclusion translates to $Q = T$ . From the derived combined statement, we have $Q \leq P \leq T$ , which implies $Q \leq T$ . However, this does not definitively establish that $Q$ must be equal to $T$ . For instance, if $Q=1, P=2, T=3$ , the condition $Q \leq P \leq T$ holds, but $Q \neq T$ . Therefore, Conclusion-1 does not necessarily follow.

Conclusion-2: $S + Q$

This conclusion translates to $S > Q$ . From the combined statement $Q \leq P \leq T < R = S$ , we can deduce that $Q \leq T$ and $T < S$ . If $Q$ is less than or equal to $T$ , and $T$ is strictly less than $S$ , it logically follows that $Q$ must be strictly less than $S$ . Hence, $S > Q$ . Therefore, Conclusion-2 follows from the statement.

Based on this analysis, only Conclusion-2 is valid. Thus, Option (B) is the correct answer.

Incorrect Options:

Options (A), (C), and (D) are incorrect because they do not accurately reflect the validity of the conclusions derived from the given statement.

Option (A) asserts that only Conclusion-1 follows. This is incorrect because Conclusion-1 ( $Q = T$ ) cannot be definitively inferred from the established inequalities.
Option (C) claims that both Conclusion-1 and Conclusion-2 follow. This is incorrect as Conclusion-1 is not a valid deduction.
Option (D) states that neither Conclusion-1 nor Conclusion-2 follows. This is incorrect because Conclusion-2 ( $S > Q$ ) is a direct and valid consequence of the combined statement.

Your note

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Solution

Correct Option (B)

The first step involves translating the given symbolic relationships into standard mathematical inequalities:

$A + B$ signifies $A > B$ (A is neither smaller nor equal to B).
$A - B$ signifies $A \leq B$ (A is not greater than B).
$A \times B$ signifies $A \geq B$ (A is not smaller than B).
$A \div B$ signifies $A < B$ (A is neither greater nor equal to B).
$A \pm B$ signifies $A = B$ (A is neither smaller nor greater than B).

Applying these translations to the provided statement:

$P \times Q$ translates to $P \geq Q$ .
$P - T$ translates to $P \leq T$ .
$T \div R$ translates to $T < R$ .
$R \pm S$ translates to $R = S$ .

Combining these individual inequalities yields the comprehensive relationship:

$Q \leq P \leq T < R = S$

Now, each conclusion is evaluated based on this combined relationship:

Conclusion-1: $Q \pm T$

Conclusion-2: $S + Q$

Based on this analysis, only Conclusion-2 is valid. Thus, Option (B) is the correct answer.

Incorrect Options:

Options (A), (C), and (D) are incorrect because they do not accurately reflect the validity of the conclusions derived from the given statement.

Option (A) asserts that only Conclusion-1 follows. This is incorrect because Conclusion-1 ( $Q = T$ ) cannot be definitively inferred from the established inequalities.
Option (C) claims that both Conclusion-1 and Conclusion-2 follow. This is incorrect as Conclusion-1 is not a valid deduction.
Option (D) states that neither Conclusion-1 nor Conclusion-2 follows. This is incorrect because Conclusion-2 ( $S > Q$ ) is a direct and valid consequence of the combined statement.

IAS 2023 — CSAT Reasoning

Options

Did you get this right?

Solution

Correct Option (B)

Conclusion-1: $Q \pm T$

Conclusion-2: $S + Q$

Incorrect Options:

Your note

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IAS 2023 — CSAT Reasoning

Options

Did you get this right?

Solution

Correct Option (B)

Conclusion-1: $Q \pm T$

Conclusion-2: $S + Q$

Incorrect Options:

Your note

IAS Reasoning in other years

More IAS Reasoning questions

Other CSAT topics for IAS

Comprehension

Maths

Keep practicing Reasoning