smrithi.gopal wrote:Is x < y?
(1) Z<Y
(2) Z<X

Can anyone help me to understand why combining both the statements are insufficient?

Source: OG Quantitative Review, 2nd ed.

OA : E

Target question: Is x < y?

Let's jump straight to . . .

Statements 1 and 2 combined
When we combine the two statements, we see that x and y are both greater than z. This, however, does not provide enough information to determine whether x < y
Consider this analogy:
Yanni is older than Zena, and Xerxes is older than Zena. Can we now determine whether or not Yanni is older than Xerxes? No, we don't have enough information to determine that.

Alternatively, consider these two counter-examples that satisfy both statements:
Case a: x = 2, y = 3 and z = 1, x < y
Case b: x = 3, y = 2 and z = 1, x > y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent