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Source: Beat The GMAT — Data Sufficiency |
IMO A
If square root (xy) is xy, then xy must be equal to 1 as root(1) = 1. But x and y could be any value. The question is x+y?
A. x = -1/2
As x*y = 1, y = 1/x = -2. x+y value can be found out. Sufficient.
B. y not equal to 0. But many possible values are there to satisy x*y=1. Insufficient.
Please share the OA.
If square root (xy) is xy, then xy must be equal to 1 as root(1) = 1. But x and y could be any value. The question is x+y?
A. x = -1/2
As x*y = 1, y = 1/x = -2. x+y value can be found out. Sufficient.
B. y not equal to 0. But many possible values are there to satisy x*y=1. Insufficient.
Please share the OA.
The question stem: square root xy = xy, therefore xy = x^2 * y^2getso wrote:If square root of xy = xy, what is the value of x + y?
(1) x = -1/2
(2) y is not equal to zero
(1) x = -1/2
subbing in:
(-1/2) * y = (1/2)^2 * y^2
or
-y/2 = y^2/4
or
0 = y^2/4 + y/2
multiplying by 4 to eliminate fractions:
0 = 2y + y^2
factoring out y:
0 = y * (2 + y)
y = 0 or -2
Because we have multiple values for y, this statement is insufficient. The second statement is clearly insufficient because it leaves infinite values for y, and there is no info about x. Together, you know that y is -2 and that x is -1/2.
Apart, insufficient; together, sufficient.
Choose C.
@papgust: you forgot to consider that the equation in the question stem is also satisfied if either of x or y are zero.
Kaplan Teacher in Toronto
Thanks testluv.Testluv wrote:The question stem: square root xy = xy, therefore xy = x^2 * y^2getso wrote:If square root of xy = xy, what is the value of x + y?
(1) x = -1/2
(2) y is not equal to zero
(1) x = -1/2
subbing in:
(-1/2) * y = (1/2)^2 * y^2
or
-y/2 = y^2/4
or
0 = y^2/4 + y/2
multiplying by 4 to eliminate fractions:
0 = 2y + y^2
factoring out y:
0 = y * (2 + y)
y = 0 or -2
Because we have multiple values for y, this statement is insufficient. The second statement is clearly insufficient because it leaves infinite values for y, and there is no info about x. Together, you know that y is -2 and that x is -1/2.
Apart, insufficient; together, sufficient.
Choose C.
@papgust: you forgot to consider that the equation in the question stem is also satisfied if either of x or y are zero.
xy = x^2 * y^2
I made a mistake of cancelling xy, on both sides of xy=x^2*y^2...
Hi Shobha,
cancelling xy on both sides ignores the fact that the equation is also satisfied if either of x or y are zero.
cancelling xy on both sides ignores the fact that the equation is also satisfied if either of x or y are zero.
Kaplan Teacher in Toronto
