JIPMAT 2022 (QA) - Given below are two statements: Statement I : The sum of exponents of prime factors in the prime factorization of 392 is 5. Statement II : The decimal representation 13/2^3 x 5 will terminate after 2 decimal places. In the light of the above statements, choose the correct answer from the options given below: | PYQs + Solutions

JIPMAT 2022

Number System

Miscellaneous

Easy

Given below are two statements:
Statement I : The sum of exponents of prime factors in the prime factorization of 392 is 5.
Statement II : The decimal representation $\frac{13}{2^3 \times 5}$ will terminate after 2 decimal places.
In the light of the above statements, choose the correct answer from the options given below:

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Correct Option: 3

For Statement I:

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392 = 2^3 × 7^2

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Sum of exponents

= 3 + 2 = 5

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Therefore Statement I is true.

For Statement II:

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\frac{13}{2^3 × 5} = \frac{13}{40}

= 0.325

This does not terminate after 2 decimal places.

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Therefore Statement II is false.

Hence, Option 3 is the answer.