325 + 227 is divisible by

IAS 2024 — CSAT Maths

2024mcqmedium

32⁵ + 2²⁷ is divisible by

Official previous-year question

Verified 2 Aug 2026.

Options

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Solution

Correct Option (C)

The given expression is $32^{5} + 2^{27}$ .

First, express 32 as a power of 2: $32 = 2^5$ .
Substitute this into the expression: $(2^5)^5 + 2^{27}$ .
Apply the exponent rule $(a^m)^n = a^{mn}$ : $2^{25} + 2^{27}$ .
Factor out the common term $2^{25}$ : $2^{25}(1 + 2^2)$ .
Simplify the term in the parenthesis: $2^{25}(1 + 4) = 2^{25} \times 5$ .
To demonstrate divisibility by 10, rewrite $2^{25}$ as $2^{24} \times 2^1$ : $2^{24} \times 2 \times 5$ .
This simplifies to $2^{24} \times 10$ .

Since the expression can be written as $2^{24} \times 10$ , it is a multiple of 10 and therefore divisible by 10.

Incorrect Options:

The simplified form of the expression is $2^{25} \times 5$ . This product consists solely of prime factors 2 and 5.

Option A (3): The prime factorization of the expression does not include 3. Therefore, the expression is not divisible by 3.
Option B (7): The prime factorization of the expression does not include 7. Therefore, the expression is not divisible by 7.
Option D (11): The prime factorization of the expression does not include 11. Therefore, the expression is not divisible by 11.

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Solution

Correct Option (C)

The given expression is $32^{5} + 2^{27}$ .

First, express 32 as a power of 2: $32 = 2^5$ .
Substitute this into the expression: $(2^5)^5 + 2^{27}$ .
Apply the exponent rule $(a^m)^n = a^{mn}$ : $2^{25} + 2^{27}$ .
Factor out the common term $2^{25}$ : $2^{25}(1 + 2^2)$ .
Simplify the term in the parenthesis: $2^{25}(1 + 4) = 2^{25} \times 5$ .
To demonstrate divisibility by 10, rewrite $2^{25}$ as $2^{24} \times 2^1$ : $2^{24} \times 2 \times 5$ .
This simplifies to $2^{24} \times 10$ .

Since the expression can be written as $2^{24} \times 10$ , it is a multiple of 10 and therefore divisible by 10.

Incorrect Options:

The simplified form of the expression is $2^{25} \times 5$ . This product consists solely of prime factors 2 and 5.

Option A (3): The prime factorization of the expression does not include 3. Therefore, the expression is not divisible by 3.
Option B (7): The prime factorization of the expression does not include 7. Therefore, the expression is not divisible by 7.
Option D (11): The prime factorization of the expression does not include 11. Therefore, the expression is not divisible by 11.

IAS 2024 — CSAT Maths

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Solution

Correct Option (C)

Incorrect Options:

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IAS 2024 — CSAT Maths

Options

Did you get this right?

Solution

Correct Option (C)

Incorrect Options:

Your note

IAS Maths in other years

More IAS Maths questions

Other CSAT topics for IAS

Comprehension

Reasoning

Keep practicing Maths