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655-705 (Hard)|   Algebra|      
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Bunuel
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If x is negative and y is positive, what is the value of x given that Updated on: 06 Jun 2025, 14:32
Originally posted by Bunuel on 18 Nov 2018, 23:21.
Last edited by Krunaal on 06 Jun 2025, 14:32, edited 1 time in total.
y2 => y^2
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E
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65% (hard)

Question Stats:

62% (01:53) correct 38% (02:04) wrong based on 586 sessions

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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
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E
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BrentGMATPrepNow
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If x is negative and y is positive, what is the value of x given that 19 Nov 2018, 08:12
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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
Show more

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
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If x is negative and y is positive, what is the value of x given that 19 Nov 2018, 13:16
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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
Show more

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
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If x is negative and y is positive, what is the value of x given that 20 Nov 2018, 01:25
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x^2-8xy+16y^2 = 49

(x-4y)^2 = 49

|x-4y| = 7

As x and -4y are both negatives, |x-4y|= 4y-x

So, 4y-x = 7

x= 4y-7

Ans E

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If x is negative and y is positive, what is the value of x given that 18 Jun 2021, 00:22
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Put x = -x in the given equation:

\((-x)^2 - 8 (-x)(y) + 16y^2 = 49\)

=> \(x^2 + 8xy + 16y^2 = 49 \)

=> \(x^2 + 8xy+ (4)y^2 = 7^2 \)

=> \((x + 4y)^2 = 7^2\)

=> x + 4y = 7

=> x = 7 - 4y

Then - x = -7 + 4y or 4y - 7

Answer E
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If x is negative and y is positive, what is the value of x given that 13 Apr 2024, 06:10
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BrentGMATPrepNow

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
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
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­but how do we know |x| is greater than 4y
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If x is negative and y is positive, what is the value of x given that 14 Apr 2024, 02:51
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Carolweszxdrcftvb

BrentGMATPrepNow

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
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
­but how do we know |x| is greater than 4y
Show more
­
From \((x - 4y)^2 = 49\), by taking the square root, we get \(|x - 4y| = 7\). Given that x is negative and y is positive, x - 4y = negative - positive = nehgative, thus \(|x - 4y| = -(x - 4y)\). Therefore, \(|x - 4y| = 7\) transforms into \(-(x - 4y) = 7\), which finally gives \(x = 4y - 7\).

Hope this helps.
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If x is negative and y is positive, what is the value of x given that 22 Jun 2025, 10:36
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