GMATPrep 6
This topic has expert replies
- akhilsuhag
- Master | Next Rank: 500 Posts
- Posts: 351
- Joined: Mon Jul 04, 2011 10:25 pm
- Thanked: 57 times
- Followed by:4 members
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Statement 1: 2x-2y = 1.Are X and Y both positive ?
(1) 2x - 2y = 1
(2) x / y > 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
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
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: Are x and y both positive?Are x and y both positive?
1) 2x - 2y =1
2) x/y >1
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