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x and y positive ---GMAT Prep

by rommysingh » Wed Aug 12, 2015 5:39 pm
Are x and y both positive?
a. 2x - 2y = 1
b. x�y > 1

OA C

I tried solving ---
1) x-y = 1/2(we have several cases Not Sufficient)
2) x/y > 0 (both + or -) not sufficient

eq 1+2

x = 1/2+y
substituting value

1/2 +y / y >0
1/2 + y > 0
1/2y > 0
y is positive and since y is positive case 2 is true when both are +ive hence sufficient...
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by Brent@GMATPrepNow » Wed Aug 12, 2015 6:12 pm
Are x and y both positive?
1) 2x - 2y =1
2) x/y >1
Target question: Are x and y both positive?

Statement 1: 2x - 2y = 1
There are several pairs of numbers that satisfy this condition. Here are two:
Case a: x = 1 and y = 0.5, in which case x and y are both positive
Case b: x = -0.5 and y = -1, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x/y > 1
This tells us that x/y is positive. This means that either x and y are both positive or x and y are both negative. Here are two possible cases:
Case a: x = 4 and y = 2, in which case x and y are both positive
Case b: x = -4 and y = -2, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2
Statement 1 tells us that 2x - 2y = 1.
Divide both sides by 2 to get: x - y = 1/2
Solve for x to get x = y + 1/2

Now take the statement 2 inequality (x/y > 1) and replace x with y + 1/2 to get:
(y + 1/2)/y > 1
Rewrite as: y/y + (1/2)/y > 1
Simplify: 1 + 1/(2y) > 1
Subtract 1 from both sides: 1/(2y) > 0
If 1/(2y) is positive, then y must be positive.

Statement 2 tells us that either x and y are both positive or x and y are both negative.
Now that we know that y is positive, it must be the case that x and y are both positive
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Matt@VeritasPrep » Sun Aug 16, 2015 9:57 pm
Let's explore some possibilities here.

1:: 2x - 2y = 1, or x - y = 1/2, or x = y + 1/2.

This tells us that x > y, but it isn't insufficient.

2:: This has TWO possibilities: (a) if y is positive, x > y; (b) if y is negative, x < y. This is also insufficient.

Together, we know that x > y, since it's the only thing that satisfies BOTH equations. This means case (a) from S2 is true, so y > 0 and x > y, meaning that x > y > 0, and both x and y are positive. Success!
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