If x and y are both positive integers, how much greater is x than y?
(1) x + y = 20
(2) x = y^2
The OA is C.
How can I use both statements together to get an answer? Experts, may you help me?
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If x and y are both positive integers, how much greater is x
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Jay@ManhattanReview
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We have to find out the value of x - y.Vincen wrote:If x and y are both positive integers, how much greater is x than y?
(1) x + y = 20
(2) x = y^2
The OA is C.
How can I use both statements together to get an answer? Experts, may you help me?
(1) x + y = 20
Certainly insufficient. If, for example, x = 1 and y = 19, then x - y = 18; however, if x = 2 and y = 18, then x - y = 16. No unique value. Insufficient.
(2) x = y^2
Certainly insufficient.
(1) and (2) combined:
y^2 + y = 20
y^2 + y - 20 = 0
y^2 + 5y - 4y - 20 = 0
y(y+5) -4(y+5)=0
(y+5)(y-4)=0
=> y = -5 or 4.
Since y is positive, y = 4.
=> x = y^2 = 4^2 = 16
=> x - y = 16 - 4 = 12. Sufficient.
The correct answer: C
Hope this helps!
-Jay
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
_________________
Manhattan Review GMAT Prep
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GMAT/MBA Expert
-
Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
We have to find out the value of x - y.Vincen wrote:If x and y are both positive integers, how much greater is x than y?
(1) x + y = 20
(2) x = y^2
The OA is C.
How can I use both statements together to get an answer? Experts, may you help me?
(1) x + y = 20
Certainly insufficient. If, for example, x = 1 and y = 19, then x - y = 18; however, if x = 2 and y = 18, then x - y = 16. No unique value. Insufficient.
(2) x = y^2
Certainly insufficient.
(1) and (2) combined:
y^2 + y = 20
y^2 + y - 20 = 0
y^2 + 5y - 4y - 20 = 0
y(y+5) -4(y+5)=0
(y+5)(y-4)=0
=> y = -5 or 4.
Since y is positive, y = 4.
=> x = y^2 = 4^2 = 16
=> x - y = 16 - 4 = 12. Sufficient.
The correct answer: C
Hope this helps!
-Jay
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
_________________
Manhattan Review GMAT Prep
Locations: New York | New Delhi | Seoul | Cairo | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
