If the expression $x^2 â€“ \dfrac{xy}5 + 25$ can be

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sat Nov 30, 2019 6:01 am

If the expression $x^2 - \dfrac{xy}5 + 25$ can be expressed by $(x - 5)^2$, what is the value of $y?$

(A) $0$
(B) $5$
(C) $25$
(D) $50$
(E) $\dfrac5x$

[spoiler]OA=D[/spoiler]

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sat Nov 30, 2019 6:01 am

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by [email protected] » Sat Nov 30, 2019 11:00 am

Hi VJesus12,

We're told that X^2 - (X)(Y)/5 + 25 can be expressed as (X - 5)^2. We're asked for the value of Y. In simple terms, this question asks what value of Y will make the first expression be equal to the second expression.

(X - 5)^2 = X^2 - 10X + 25

Both the "X^2" and the "+25" are accounted for in the first expression, so we need -(X)(Y)/5 to equal - 10X....
thus Y/5 = 10
Y = 50

Final Answer: [spoiler=]D[/spoiler]

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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ktrout2020: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Wed Oct 30, 2019 1:10 pm

If the expression x2âˆ’xy5+25 can be

by ktrout2020 » Sat Nov 30, 2019 1:52 pm

OOpps

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 01, 2019 6:03 am

VJesus12 wrote:If the expression $x^2 - \dfrac{xy}5 + 25$ can be expressed by $(x - 5)^2$, what is the value of $y?$

(A) $0$
(B) $5$
(C) $25$
(D) $50$
(E) $\dfrac5x$

[spoiler]OA=D[/spoiler]

Source: Veritas Prep

GIVEN: (x - 5)Â² = xÂ² - xy/5 + 25
Expand and simplify left side to get: xÂ² - 10x + 25 = xÂ² - xy/5 + 25
Subtract xÂ² from both sides to get: -10x + 25 = -xy/5 + 25
Subtract 25 from both sides to get: -10x = -xy/5
Multiply both sides by 5 to get: -50x = -xy
Divide both sides by x to get: -50 = -y
Solve: y = 50

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Dec 08, 2019 7:11 pm

VJesus12 wrote:If the expression $x^2 - \dfrac{xy}5 + 25$ can be expressed by $(x - 5)^2$, what is the value of $y?$

(A) $0$
(B) $5$
(C) $25$
(D) $50$
(E) $\dfrac5x$

[spoiler]OA=D[/spoiler]

Source: Veritas Prep

(x - 5)^2 = x^2 - 10x + 25

We equate the second terms of each expression, so we have

-10x = -xy/5

-50x = -xy

50 = y

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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