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805+ (Hard)|   Algebra|      
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Bunuel
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If x + y = 7, what is the value of xy(x – y)? 10 Oct 2017, 00:36
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95% (hard)

Question Stats:

30% (02:10) correct 70% (02:10) wrong based on 100 sessions

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If x + y = 7, what is the value of xy(x – y)?

(1) 4xy = 7(x + y)

(2) x^2 = y^2
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D
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Alexey1989x
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If x + y = 7, what is the value of xy(x – y)? Updated on: 11 Oct 2017, 01:27
Originally posted by Alexey1989x on 10 Oct 2017, 02:04.
Last edited by Alexey1989x on 11 Oct 2017, 01:27, edited 1 time in total.
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(1) Since, x+y=7, then substituting corrensponding values in the equation 4xy=7(x+y) we get
xy=49/4
x+y=7
solving
y^2-7y+49/4=0
solving we see that x=y=7/2 and xy(x-y)=0

Sufficient

(2)

x^2=y^2
(x+y)(x-y)=0
Since we know that x+y = 7, then there is only one option for this eqution to hold true x-y=0, thus xy(x-y)=0

Sufficient

Answer D.
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If x + y = 7, what is the value of xy(x – y)? 11 Oct 2017, 01:07
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Alexey1989x
(1) Since, x+y=7, then substituting corrensponding values in the equation 4xy=7(x+y) we get
xy=49/4
x+y=7
solving

y^2-2y+49/4=0
solving we see that x=y=7/2 and xy(x-y)=0

Show more

Hi,

The highlighted part should be 7y.
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If x + y = 7, what is the value of xy(x – y)? 11 Oct 2017, 01:28
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Mo2men
Alexey1989x
(1) Since, x+y=7, then substituting corrensponding values in the equation 4xy=7(x+y) we get
xy=49/4
x+y=7
solving

y^2-2y+49/4=0
solving we see that x=y=7/2 and xy(x-y)=0


Hi,

The highlighted part should be 7y.
Show more


Thank for notice, you're correct!
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If x + y = 7, what is the value of xy(x – y)? 12 Dec 2017, 12:52
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Bunuel
If x + y = 7, what is the value of xy(x – y)?

(1) 4xy = 7(x + y)

(2) x^2 = y^2
Show more

Hi Bunuel
Why answer is B, not D?
Substituting 7*(x+y) = 7*7 = 49 = 4xy (1)
x + y = 7
So, x = 7 - y
Let's put x to equation (1):
4*y*(7-y) = 49
This gives us following results:

y = 3.5 and x = 3.5
So A is sufficient also
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If x + y = 7, what is the value of xy(x – y)? 12 Dec 2017, 20:18
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LeonidK
Bunuel
If x + y = 7, what is the value of xy(x – y)?

(1) 4xy = 7(x + y)

(2) x^2 = y^2

Hi Bunuel
Why answer is B, not D?
Substituting 7*(x+y) = 7*7 = 49 = 4xy (1)
x + y = 7
So, x = 7 - y
Let's put x to equation (1):
4*y*(7-y) = 49
This gives us following results:

y = 3.5 and x = 3.5
So A is sufficient also
Show more

Yes, the OA is D. Edited. Thank you.
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If x + y = 7, what is the value of xy(x – y)? 12 Dec 2017, 23:19
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Bunuel
If x + y = 7, what is the value of xy(x – y)?

(1) 4xy = 7(x + y)

(2) x^2 = y^2
Show more

From Stmnt 1: 4xy = 49

(x+y)^2 - (x-y)^2 = 4xy = 49

Which means (x-y)^2 = 0 or x - y = 0 . Hence, Sufficient.

From Stmnt 2:

(x+y)(x-y) = 0

which means x - y = 0.. Sufficient.
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If x + y = 7, what is the value of xy(x – y)? 23 May 2023, 10:42
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If x + y = 7, what is the value of xy(x – y)?

(1) 4xy = 7(x + y)=7*7=49
Now, \((x+y)^2=7^2…….x^2+y^2+2xy=49\)
Thus, \(x^2+y^2+2xy=4xy=49………x^2+y^2-2xy=0…….(x-y)^2=0…….x-y=0.\)
Therefore, \(xy(x-y)=xy*0=0\)
Sufficient

(2) \(x^2 = y^2……x^2-y^2=0……..(x+y)(x-y)=0……7(x-y)=0\)
Thus, x-y=0 and \(xy(x-y)=xy*0=0\)
Sufficient


D
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