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22 Jul 2022, 07:03
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
48% (01:49) correct
52%
(02:04)
wrong
based on 214
sessions
History
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If \(|x| ≠ |y|\), does \(|xy| = 15\) ?
(1) \((x + 5)(y – 3) = 0\)
(2) \((x + y)^x = y^x\)
(1) \((x + 5)(y – 3) = 0\)
(2) \((x + y)^x = y^x\)
Archit3110
22 Jul 2022, 07:26
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given that
\(|x| ≠ |y|\)
target \(|xy| = 15\)
#1
\((x + 5)(y – 3) = 0\)
x=-5 or y=+3
if x=-5 and y =3 then yes to target or
x=-5 and y = 2,4,5 then to to target
#2
\((x + y)^x = y^x\)
possible when x=0 and y is any integer or fraction value
x=0 , y= 1
( 0+1)^0 = ( 1)^0
1=1
irrespective target would always be 0
sufficient
OPTION B
\(|x| ≠ |y|\)
target \(|xy| = 15\)
#1
\((x + 5)(y – 3) = 0\)
x=-5 or y=+3
if x=-5 and y =3 then yes to target or
x=-5 and y = 2,4,5 then to to target
#2
\((x + y)^x = y^x\)
possible when x=0 and y is any integer or fraction value
x=0 , y= 1
( 0+1)^0 = ( 1)^0
1=1
irrespective target would always be 0
sufficient
OPTION B
BrentGMATPrepNow
24 Jul 2022, 07:11
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BrentGMATPrepNow
Given: \(|x| ≠ |y|\)
Target question: Does \(|xy| = 15\)
Statement 1: \((x + 5)(y – 3) = 0\)
There are infinitely many values of x and y that satisfy statement 1. Here are two:
Case a: \(x = -5\) and \(y = 3\). In this case, the answer to the target question is YES, \(|xy| = 15\)
Case b: \(x = 0\) and \(y = 3\). In this case, the answer to the target question is NO, \(|xy|\) does not equal \(15\)
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: \((x + y)^x = y^x\)
Aside: The equation indirectly tells us that y cannot equal 0.
Why?
If \(y = 0\), then \(y^x = 0^x = 0\), which means our equation becomes \((x + y)^x = 0\), and the only way this can be true is if \((x+y)=0\), which can only happen if \(x = 0\), but we're specifically told that \(|x| ≠ |y|\)
Since y cannot equal 0, we can safely divide both sides of the equation by \(y^x\) to get: \(\frac{(x + y)^x}{y^x} = 1\)
Rewrite the left side of the equation as follows: \((\frac{x + y}{y})^x = 1\)
Finally, we can simplify the fraction as follows: \((\frac{x}{y} + 1)^x = 1\)
At this point, we can see that the only wait for this equation to hold true is if \(x = 0\)
If \(x = 0\), then \(|xy|\) can never equal 15, which means the answer to the target question is NO, \(|xy|\) does not equal \(15\)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
