If y is an integer such that y

Question

If y is an integer such that y < -3, which of the following expressions must be correct?

I. \(y – y^2 + 12 < 0\)
II. \(y^2 – y – 12 > 0\)
III. \(2y^2 – 3y – 27 > 0\)

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

gmatophobia · Answer

This is a must be true question and the constraint given states y < -3

The first and the second expression is same.

We can evaluate the positive negative nature of the expression and arrive at the answers.

Option E

Harshani · Answer

the answer is e and here my solution using transition points

PTPRO · Answer

For this question, is it not easy to use any value which satisfies y <-3, like -4, and substitute in the 3 equations to check which condition is true?
Or this approach can lead to some error?

Bunuel · Answer

Testing just one value like y = -4 only shows the statement works for that single value. It does not prove that it works for all integers less than -3. A “must be correct” condition must hold for every allowed value, and one test cannot guarantee that.

The risk is simple: y = -4 might satisfy the expression, but another valid value like y = -5 or y = -10 might fail it. That is why relying on a single substitution can lead to a wrong conclusion.

For example, y^2 + 6 y + 5 < 0 is true when -5 < y < -1. It works for y = -4, but if you try y = -5 it fails. This shows why one test point cannot confirm a “must” condition.

Kinshook · Answer

If y is an integer such that y < -3, which of the following expressions must be correct?

I. \(y – y^2 + 12 < 0\)
II. \(y^2 – y – 12 > 0\)
III. \(2y^2 – 3y – 27 > 0\)

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

For this question, is it not easy to use any value which satisfies y <-3, like -4, and substitute in the 3 equations to check which condition is true?
Or this approach can lead to some error?

If y is an integer such that y < -3, which of the following expression

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