# XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

###### XAT Previous Year Paper | XAT QADI Questions | Question 3

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Question 3 : The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2.

What is the product of the squares of the numbers?

1. 48
2. 256
3. 32
4. 16
5. 64

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Let us suppose that the two numbers are ‘a’ and ‘b’
Given that $a^{3}$ + $b^{3}$ = 128
$$frac{1}{a^{3}}$ + $$frac{1}{b^{3}}$ = 2 $\frac{a^{3}+b^{3}}{a^{3} b^{3}}$ = 2 $a^{3} b^{3}$ = 64 $$a b$^{3}$ = 64
ab = 4
$(a b)^{2}$= $a^{2} b^{2}$ = 16
Therefore, the correct answer is 16.

The question is " The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2.

What is the product of the squares of the numbers? "

##### Hence, the answer is '16'

Choice D is the correct answer.

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