If a^2 - 3ab = 72 and a - b = -8, what is the… | GMAT Sprint

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PS · Problem Solving

555-605

Algebra

If $a^2 - 3ab = 72$ and $a - b = -8$ , what is the value of |b|?

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Explanation

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Official Explanation

Official

To solve for |b|, we start with the equations given:

a^2 - 3ab = 72

and

a - b = -8

. From the second equation, we can express

a

in terms of

b

a = b - 8

. Now, we substitute

a

into the first equation:

(b - 8)^2 - 3(b - 8)b = 72

. Expanding this gives us [m](b^2 - 16b + 64) - 3(b^2 - 8b) =…

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Comments

ashrithJan 15, 2025

Thanks for sharingThank you for sharing!!thanks for sharing

aVnavMay 2, 2025

thankss

MannanApr 15, 2025

can you explain more?

AditiApr 25, 2025

can you explain more?

ManasiJul 29, 2024

cheers!

AdvitiyaFeb 5, 2025

Thank for sharing!

ConnieAug 10

wait can someone explain why we can just factor out the a? like i get a^2 - 3ab but then i'm stuck on the next move

GunjeetAug 22

you factor a from both terms so you get a(a-3b). then try to use the second equation somewhere

AkshithSep 29

is this really 555-605? felt more like an easy one to me, the factoring basically gives it away

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 a2−3ab=72a^2 - 3ab = 72a2−3ab=72 and a−b=−8a - b = -8a−b=−8, what is the value of |b|?