Item contains a Question followed by two Statements. Answer each item using the following instructions :

Question: Can the value of (x + y) be determined uniquely?

Statement I: (x + y)⁴ = 256.

Statement II: (x + y)³ < 16.

Question

Question

This question was previously asked in

CDS Elementary Mathematics 16 April 2023 Official Paper

Choose this option if the Question can be answered by one of the Statements alone but not by the other.
Choose this option if the Question can be answered by either Statement alone.
Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
Choose this option if the Question cannot be answered even by using both Statements together.

Answer 1

Calculation:

Statement I: (x + y)4 = 256

(x + y)⁴ = 16⁴

(x + y) = ± 4

So, no unique values of x, and y are possible from this statement alone.

Statement II: (x + y)3 < 16

No unique values of x, and y are possible from this statement alone.

Let's combine both statements

Let x = 4

(4)³ < 16

64 < 16 which is wrong

If x = -4

-64 < 16 which is correct.

So, (x + y) = - 4

∴ Optipon 3 is correct.

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