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655-705 Level|   Algebra|      
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BrentGMATPrepNow
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What is the value of xy ? 07 Jul 2022, 08:12
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

56% (02:06) correct 44% (01:46) wrong based on 66 sessions

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What is the value of xy ?

(1) x + y = 7
(2) (x + 1)(y – 1) = 6
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E
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Archit3110
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What is the value of xy ? Updated on: 07 Jul 2022, 11:43
Originally posted by Archit3110 on 07 Jul 2022, 08:50.
Last edited by Archit3110 on 07 Jul 2022, 11:43, edited 2 times in total.
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BrentGMATPrepNow
What is the value of xy ?

(1) x + y = 7
(2) (x + 1)(y – 1) = 6

target value of xy

#1
x+y=7
two unknowns insufficient
#2
xy-x+y-1 = 6
xy-x+y=7
insufficient
from 1 &2
xy=7+x-y
xy=2x
x(y-2)=0
x= 0 ; y=7
x=5;y=2


xy=0 or 10
option E
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BrentGMATPrepNow
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What is the value of xy ? 07 Jul 2022, 09:24
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Archit3110
BrentGMATPrepNow
What is the value of xy ?

(1) x + y = 7
(2) (x + 1)(y – 1) = 6

target value of xy

#1
x+y=7
two unknowns insufficient
#2
xy-x+y-1 = 6
xy-x+y=7
insufficient
from 1 &2
xy=7+x-y
xy=2x
y=2
x=5
xy=10
option C

Close, but there's a slight problem when you went from
xy=2x to y=2
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Archit3110
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What is the value of xy ? 07 Jul 2022, 11:23
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BrentGMATPrepNow

Edited : hope it's fine now :)
BrentGMATPrepNow
Archit3110
BrentGMATPrepNow
What is the value of xy ?

(1) x + y = 7
(2) (x + 1)(y – 1) = 6

target value of xy

#1
x+y=7
two unknowns insufficient
#2
xy-x+y-1 = 6
xy-x+y=7
insufficient
from 1 &2
xy=7+x-y
xy=2x
y=2
x=5
xy=10
option C

Close, but there's a slight problem when you went from
xy=2x to y=2

Posted from my mobile device
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BrentGMATPrepNow
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What is the value of xy ? 07 Jul 2022, 11:41
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Archit3110
BrentGMATPrepNow

Edited : hope it's fine now :)

Not yet.
As you noted, the equation xy=2x has two solutions: x = 0 and y = 2

If x = 0, we can plug this into the equation, x + y = 7, to get 0 + y = 7, which means y = 7. In this case, xy = (0)(7) = 0
If y = 2, we can plug this into the equation, x + y = 7, to get x + 2 = 7, which means x = 5. In this case, xy = (5)(2) = 10

So, there are two different possible values of xy, which means the correct answer is E.
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What is the value of xy ? 07 Jul 2022, 11:45
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I Did a mistake..
It is a good DS trap question

BrentGMATPrepNow

BrentGMATPrepNow
Archit3110
BrentGMATPrepNow

Edited : hope it's fine now :)

Not yet.
As you noted, the equation xy=2x has two solutions: x = 0 and y = 2

If x = 0, we can plug this into the equation, x + y = 7, to get 0 + y = 7, which means y = 7. In this case, xy = (0)(7) = 0
If y = 2, we can plug this into the equation, x + y = 7, to get x + 2 = 7, which means x = 5. In this case, xy = (5)(2) = 10

So, there are two different possible values of xy, which means the correct answer is E.

Posted from my mobile device
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BrentGMATPrepNow
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What is the value of xy ? 08 Jul 2022, 07:48
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BrentGMATPrepNow
What is the value of xy ?

(1) x + y = 7
(2) (x + 1)(y – 1) = 6

Here's another approach....

Target question: What is the value of xy ?

Statement 1: x + y = 7
There are infinitely many pairs of values that satisfy this equation, which means there are infinitely many possible values of xy
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (x + 1)(y – 1) = 6
There are infinitely many pairs of values that satisfy this equation, which means there are infinitely many possible values of xy
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x + y = 7, which we can solve for x to get: x = 7 - y
Statement 2 tells us that (x + 1)(y – 1) = 6
Substitute the x-value from statement 1 to get: (7 - y + 1)(y – 1) = 6
Simplify: (8 - y)(y – 1) = 6
Use FOIL to expand: 8y - 8 - y² + y = 6
Multiply both sides of the equation by -1 to get: -8y + 8 + y² - y = -6
Simplify and set equal to zero: y² - 9y + 14 = 0
Factor: (y - 2)(y - 7) = 0
This means either y = 2 or y = 7.

case i: If y = 2, we can substitute this value into the equation from statement 1 to get x + 2 = 7, which means x = 5. In this case, xy = (5)(2) = 10
case ii: If y = 7, we can substitute this value into the equation from statement 1 to get x + 7 = 7, which means x = 0. In this case, xy = (0)(7) = 0
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E
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