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Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
E
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Difficulty:
55%
(hard)
Question Stats:
63% (01:51) correct
37%
(02:06)
wrong
based on 505
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If x is negative and y is positive, what is the value of x given that \(x^2−8xy+16y^2=49\) ?
A. 4y − 49
B. 49 − 4y
C. −7 − 4y
D. 7 + 4y
E. 4y − 7
A. 4y − 49
B. 49 − 4y
C. −7 − 4y
D. 7 + 4y
E. 4y − 7
19 Nov 2018, 08:12
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Bookmarks
Bunuel
If x is negative and y is positive, what is the value of x given that \(x^2−8xy+16y^2=49\) ?
A. 4y − 49
B. 49 − 4y
C. −7 − 4y
D. 7 + 4y
E. 4y − 7
A. 4y − 49
B. 49 − 4y
C. −7 − 4y
D. 7 + 4y
E. 4y − 7
GIVEN: x² − 8xy + 16y² = 49
Factor left side to get: (x - 4y)(x - 4y) = 49
Or we can write: (x - 4y)² = 49
If SOMETHING² = 49, then either SOMETHING = 7 or SOMETHING = -7
So, EITHER (x - 4y) = 7 OR (x - 4y) = -7
Since x is negative and y is positive, x - 4y = NEGATIVE - 4(POSITIVE) = some negative number
So, it must be the case that x - 4y = -7
Add 4y to both sides to get: x = -7 + 4y
This is the SAME as x = 4y - 7
Answer: E
Cheers,
Brent
General Discussion
gmatdordie
Joined: 13 Nov 2018
Last visit: 02 Jun 2020
Posts: 89
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Given Kudos: 16
Location: India
Schools: Rotman '21 Ivey '21 Queen's Jan20 Intake
GMAT 1: 700 Q51 V32
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19 Nov 2018, 13:16
Kudos
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Bunuel
If x is negative and y is positive, what is the value of x given that \(x^2−8xy+16y2=49\) ?
A. 4y − 49
B. 49 − 4y
C. −7 − 4y
D. 7 + 4y
E. 4y − 7
A. 4y − 49
B. 49 − 4y
C. −7 − 4y
D. 7 + 4y
E. 4y − 7
we have
x^2 -8xy +16y2=49
(x-4y)^2=49
so x-4y=7 or x-4y=-7
as x is negative and y is positive, we will pick
x-4y=-7
or x=4y-7
SO E is correct answer
