What is the largest possible value of c if 4c… | GMAT Sprint

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PS · Problem Solving

505-555

Algebra

What is the largest possible value of $c$ if $4c + (d-10)^2 = 200$ ?

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Explanation

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Official Explanation

Official

To find the largest possible value of

c

, we start with the equation

4c + (d-10)^2 = 200

. We want to isolate

c

. First, we can rearrange the equation:

4c = 200 - (d-10)^2

. The term

(d-10)^2

is always non-negative, so to maximize

c

, we need to…

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Comments

SiddharthJan 22, 2025

thanks!

ChrisFeb 18, 2025

thanks

ChandniMar 28, 2025

Thank for sharing!

KrishanuJan 11, 2025

thank you very much!

ChiamakaDec 27, 2024

thanks

TarushDec 28, 2024

thankss

AntheaMay 10

thanks, this one was quick once you see the square is always positive

YashMay 21

yeah that was the key for me too, took like 20 sec after that

AmelMay 19

wait why is (d-10)^2 just ignored? isn't d unknown too?

SarveshMay 20

it can't be negative, so the biggest c comes from making it as small as possible

TheJun 22

got E but I almost picked D by forgetting to divide at the end lol

ClelioJul 25

pretty easy for algebra, solid warmup before the harder stuff

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.

What is the largest possible value of ccc if 4c+(d−10)2=2004c + (d-10)^2 = 2004c+(d−10)2=200?