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Question

If x and y are integers such that x2=64 and y3=64, which of the following could be true?
I. x=8
II. y=−4
III. x+y=−4

A
I only
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B
II only
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C
I and III only
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D
II and III only
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E
I,II and III
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Solution

The correct option is E I and III only
Given
x2 = 64 and y3 = 64

Possible values of x,
x2 = 64
x = 64
x = 82 or x = (8)2
x = 8 or x = 8

Possible values of y,
y3 = 64
y = 364
y = 343
y = 4

I. x = 8 is True
x = 8 or x = 8

II. y = 4 is False
y = 4

III. x + y = 4 is True
When x = 8,
x + y = 8 + 4 = 12
When x = 8,
x + y = 8 + 4 = 4

Therefore, I and III only are True.

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