If c < 5 and 4x + 2c = 10, which of the follo… | GMAT Sprint

Free Practice Question

PS · Problem Solving

555-605

Algebra

If c < 5 and 4x + 2c = 10, which of the following must be true?

Answer Choices

Correct answer marked below

x > -1

x < 2

x = 2

x < 3

x > 0

Correct

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Explanation

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Official Explanation

Official

We are given that

c < 5

and the equation

4x + 2c = 10

.

Step 1. Solve for

x

First, solve the equation for

x

\begin{aligned} 4x + 2c &= 10 \ 4x &= 10 - 2c \ x &= \frac{10 - 2c}{4} = \frac{5 - c}{2}. \end{aligned}

Step 2. Use the condition

c < 5

Since

c < 5

, then

5 - c > 0.

Dividing both sides by 2 (which is positive) preserves the inequality:

x = \frac{5 - c}{2} > 0.

Thus, we know that

x > 0

.

Step 3. Analyze the Answer Choices

Let's review each option:

(A)

x > 1

x

can be arbitrarily close to 0 if

c

is just below 5 (for example, if

c = 4.9

, then

x \approx \frac{5 - 4.9}{2} = 0.05

). So,

x > 1

is not always true.

(B)

x < 2

:

If

c

is very small (or negative), then

x

becomes large. For example, if

c = -100

, then…

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Comments

MarkétaMar 18, 2025

Amazing

LakshmiMar 31, 2025

thank you for sharing

VugarMar 1, 2025

Thank for sharing!

AmanJan 5, 2025

thank you for sharing

HunterJul 4, 2024

thank you taking time to upload it!

JeremiDec 21, 2024

good question

anindoMay 9

shouldnt option A be 1 and not -1

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.