ccassel wrote:Hi,
How would you answer this question?
If s=(x+y)^2 and t=(x-y)^2, what is the value of 2^s/2^t?
(1) xy=12
(2) x/y=3
Cheers,
When the bases are the same and we're dividing, we subtract the exponents:
2^s/2^t = 2^(s-t).
Let's determine the value of s-t:
s = (x+y)² = x² + 2xy + y²
t = (x-y)² = x² - 2xy + y²
s-t = (x² + 2xy + y²) - (x² - 2xy + y²) = 4xy.
Thus, 2^(s-t) = 2^(4xy).
Question rephrased: What is the value of xy?
Statement 1: xy = 12.
Sufficient.
Statement 2: x/y = 3.
No way to determine the value of xy.
Insufficient.
The correct answer is
A.
For those not comfortable with the algebra, an easy approach would be to plug in values.
Statement 1: xy = 12.
Let x=4, y=3.
s = (x+y)² = (4+3)² = 49.
t = (x-y)² = (4-3)² = 1.
2^s/ 2^t = 2��/2¹ = 2��.
Let x=6, y=2.
s = (x+y)² = (6+2)² = 64.
t = (x-y)² = (6-2)² = 16.
2^s/ 2^t = 2��/2¹� = 2��.
Since in each case the result is 2��, sufficient.
Statement 2: x/y = 3.
Let x=3, y=1.
s = (x+y)² = (3+1)² = 16.
t = (x-y)² = (3-1)² = 4.
2^s/ 2^t = 2¹�/2� = 2¹².
Let x=6, y=2.
s = (x+y)² = (6+2)² = 64.
t = (x-y)² = (6-2)² = 16.
2^s/ 2^t = 2��/2¹� = 2��.
Since in the first case the result is 2¹² and in the second case the result is 2��, insufficient.
The correct answer is
A.
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