Given that | y3 - 14| < 12, which of the following values for y is NOT possible?

Given that | y3 - 14| < 12, which of the foll… | GMAT Sprint

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555-605

Inequalities

Given that $|\frac{y}{3} - \frac{1}{4}| < \frac{1}{2}$ , which of the following values for y is NOT possible?

Answer Choices

Correct answer marked below

-\frac{5}{4}

Correct

-\frac{1}{2}

\frac{3}{4}

\frac{5}{4}

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Explanation

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Official Explanation

Official

To solve

|\frac{y}{3} - \frac{1}{4}| < \frac{1}{2}

, we consider two cases.

Case 1:

\frac{y}{3} - \frac{1}{4} < \frac{1}{2}

leads to

\frac{y}{3} < \frac{1}{2} + \frac{1}{4}

, which simplifies to

\frac{y}{3} < \frac{2 + 1}{4}

\frac{y}{3} < \frac{3}{4}

, giving

y < \frac{9}{4}

.

Case 2:

- (\frac{y}{3} - \frac{1}{4}) < \frac{1}{2}

simplifies to

-\frac{y}{3} + \frac{1}{4} < \frac{1}{2}

, leading to

-\frac{y}{3} < \frac{1}{2} - \frac{1}{4}

, which simplifies to

-\frac{y}{3} < \frac{1}{4}

y > -\frac{3}{4}

.…

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Comments

HarshavMar 6, 2025

thanks for posting

What this question tests

What it tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Common trap

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.

Given that ∣y3−14∣<12|\frac{y}{3} - \frac{1}{4}| < \frac{1}{2}∣3y​−41​∣<21​, which of the following values for y is NOT possible?