Are X and Y both positive.

Question

Are X and Y both positive ? (1) 2x - 2y = 1 (2) x / y > 1

GMATGuruNY · Answer

rppala90 wrote:Are X and Y both positive ?

(1) 2x - 2y = 1
(2) x / y > 1

Statement 1: 2x-2y = 1.
2(x-y) = 1.
x-y = 1/2.
x = y + 1/2.
It's possible that y=1/2 and x=1.
It's possible that y=0 and x=1/2.
Since in the first case x and y are both positive and in the second case x and y are not both positive, insufficient.

Statement 2: x/y > 1.
It's possible that x=2 and y=1, since 2/1 > 1.
It's possible that x=-2 and y=-1, since (-2)/(-1) > 1.
Since in the first case x and y are both positive and in the second case x and y are not both positive, insufficient.

Statements 1 and 2 combined:
Statement 1: x = y + 1/2.
Statement 2: x/y > 1.
Substituting for x in the inequality:
(y + 1/2)/y > 1.
1 + 1/(2y) > 1.
1/(2y) > 0.
Thus, y>0.
Since y>0 and x = y + 1/2, we know that x>1/2.
Sufficient.

The correct answer is C.

First take-away:
The approach above combined two techniques: algebra and plugging in values.
Many DS questions are best solved using a combination of these two techniques.

Second take-away:
Given an equation with 2 variables (such as x = y + 1/2) and an inequality with the same 2 variables (such as x/y > 1), use the equation to substitute for one of the variables in the inequality.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

prateek_guy2004 · Answer

GMATGuruNY wrote:rppala90 wrote:Are X and Y both positive ? (1) 2x - 2y = 1 (2) x / y > 1 Statement 1: 2x-2y = 1. 2(x-y) = 1. x-y = 1/2. x = y + 1/2. It's possible that y=1/2 and x=1. It's possible that y=0 and x=1/2. Since in the first case x and y are both positive and in the second case x and y are not both positive, insufficient. Statement 2: x/y > 1. It's possible that x=2 and y=1, since 2/1 > 1. It's possible that x=-2 and y=-1, since (-2)/(-1) > 1. Since in the first case x and y are both positive and in the second case x and y are not both positive, insufficient. Statements 1 and 2 combined: Statement 1: x = y + 1/2. Statement 2: x/y > 1. Substituting for x in the inequality: (y + 1/2)/y > 1. 1 + 1/(2y) > 1. 1/(2y) > 0. Thus, y>0. Since y>0 and x = y + 1/2, we know that x>1/2. Sufficient. The correct answer is C. First take-away: The approach above combined two techniques: algebra and plugging in values. Many DS questions are best solved using a combination of these two techniques. Second take-away: Given an equation with 2 variables (such as x = y + 1/2) and an inequality with the same 2 variables (such as x/y > 1), use the equation to substitute for one of the variables in the inequality. Awesome Explanation Thanks GmatguruNy

gmatboost · Answer

Just wanted to add a quick thought: When you see x/y > 1 (or anything else that says x/y is positive) you should immediately think: x and y have the same sign.

Brent@GMATPrepNow · Answer

rppala90 wrote:Are X and Y both positive ?

(1) 2x - 2y = 1
(2) x / y > 1

Statement 1: 2x-2y = 1.
2(x-y) = 1.
x-y = 1/2.
x = y + 1/2.
It's possible that y=1/2 and x=1.
It's possible that y=0 and x=1/2.
Since in the first case x and y are both positive and in the second case x and y are not both positive, insufficient.

Statement 2: x/y > 1.
It's possible that x=2 and y=1, since 2/1 > 1.
It's possible that x=-2 and y=-1, since (-2)/(-1) > 1.
Since in the first case x and y are both positive and in the second case x and y are not both positive, insufficient.

Statements 1 and 2 combined:
Statement 1: x = y + 1/2.
Statement 2: x/y > 1.
Substituting for x in the inequality:
(y + 1/2)/y > 1.
1 + 1/(2y) > 1.
1/(2y) > 0.
Thus, y>0.
Since y>0 and x = y + 1/2, we know that x>1/2.
Sufficient.

The correct answer is C.

First take-away:
The approach above combined two techniques: algebra and plugging in values.
Many DS questions are best solved using a combination of these two techniques.

Second take-away:
Given an equation with 2 variables (such as x = y + 1/2) and an inequality with the same 2 variables (such as x/y > 1), use the equation to substitute for one of the variables in the inequality.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Are X and Y both positive.

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER