If 10−yy+2 = y, then y^2 + 4y − 8 = | GMAT Sprint

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PS · Problem Solving

555-605

Algebra

If $\frac{10−y}{y+2} = y$ , then $y^2 + 4y − 8 =$

Answer Choices

Correct answer marked below

-4

Correct

Cannot be determined

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Explanation

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Official Explanation

Official

To solve the equation

\frac{10−y}{y+2} = y

, we first cross-multiply to eliminate the fraction:

10 - y = y(y + 2)

. This simplifies to

10 - y = y^2 + 2y

. Rearranging gives us

y^2 + 3y - 10 = 0

. We can factor this quadratic equation:

(y + 5)(y - 2) = 0

, which gives us the solutions

y = -5

and [m]y =…

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Comments

NeilMar 27, 2025

Thankss

BarborkaApr 7, 2025

Thank you very much!

KabitaMar 15, 2025

thanks!

JonathanJan 5, 2025

can you explain more?

AyushiSep 10, 2024

Greatt

ChinmayaJul 28, 2024

Amazing

VatadeJun 5

Is E a trap here? I almost picked it because the quadratic has two weird roots.

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.

If 10−yy+2=y\frac{10−y}{y+2} = yy+210−y​=y, then y2+4y−8=y^2 + 4y − 8 =y2+4y−8=