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if 0<x<y, what is (x+y)^2/(x-y)^2?

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Source: — Data Sufficiency |

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by [email protected] » Sun Apr 10, 2016 9:03 am
Hi ceh232,

This question is based around a couple of Algebra patterns: Classic Quadratics.

We're told that 0 < X < Y, which means that we're dealing with positive numbers only. We're asked for the value of (X+Y)^2 / (X-Y)^2.

To start, we can rewrite the given question:

[X^2 + 2XY + Y^2] / [X^2 - 2XY + Y^2] = ?

By looking at the question in this way, we might find it easier to answer...

1) X^2 + Y^2 = 3XY

With this Fact, we can substitute in 3XY for "X^2 + Y^2" in the question...

[3XY + 2XY] / [3XY - 2XY]

Then we can combine "like terms" and simplify:

[5XY] / [XY] = 5/1 = 5. We now have the answer to the given question (and it's the ONLY answer).
Fact 1 is SUFFICIENT

2) XY = 3

With this fact, we can also substitute in a value, but we still don't know what X^2 or Y^2 actually equals. We end up with...

[X^2 + 2(3) + Y^2] / [X^2 - 2(3) + Y^2] = ?

Without those values, the answer to the question changes (TESTing X=1, Y=3 and X=1.5, Y=2 will give you two different results).
Fact 2 is INSUFFICIENT

Final Answer: A

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by OptimusPrep » Thu Apr 14, 2016 7:45 pm
ceh232 wrote:if 0<x<y, what is value of (x+y)^2/(x-y)^2?

1) x^2 + y^2 = 3xy
2) xy = 3

Can somebody explain the correct answer for this question?
(a) statement 1 is sufficient
Given: 0<x<y
Required: (x+y)^2/(x-y)^2 = ?
Or (x^2 + y^2 +2xy)/(x^2 + y^2 - 2xy) = ? - (i)

Statement 1: x^2 + y^2 = 3xy
On substituting the values in (i)
(3xy + 2xy) / (3xy - 2xy) = 5xy / xy = 5
Sufficient

Statement 2:
xy = 3
On substituting the values in (i)
(x^2 + y^2 +6)/(x^2 + y^2 - 6)
This cannot be solved ahead.
Insufficient.

Correct Option: A
Does this help?
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by Matt@VeritasPrep » Fri Apr 15, 2016 1:29 pm
S1::
(x + y)² / (x - y)² =>

(x² + 2xy + y²) / (x² - 2xy + y²)

We know x² + y² = 3xy, so we can sub that in

(3xy + 2xy) / (3xy - 2xy) =>

5xy/1xy =>

5

So we've got that value after all!
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