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Algebra - DS

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by GMATGuruNY » Wed Nov 16, 2011 10:27 am
shankar.ashwin wrote:If x^2+5y = 49, is y an integer?

1) 1 < x < 4
2) x^2 is an integer.
y = (49 - x²)/5.

Both statements are satisfied by x=2 and by x=√2.
If x=2, then y = (49 - 2²)/5 = 9.
If x=√2, then y = (49 - (√2)²)/5 = 47/5.
Since in the first case y is an integer and in the second case y is not an integer, INSUFFICIENT.

The correct answer is E.
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by rijul007 » Wed Nov 16, 2011 10:27 am
x^2+5y = 49
y = (49 - x^2)/5

Statement 1
1<x<4
we cannot say anything about y

Insufficient

Statement 2
x^2 is an integer
y could either be an integer or in decimel


Insufficient


Combining both
value of x = 2 or 3

x = 2
y = 49-4/5 = 9 (Integer)

x = 3
y = 49-9/5 = 8 (integer)


Option C
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by rijul007 » Wed Nov 16, 2011 10:31 am
GMATGuruNY wrote:
Both statements are satisfied by x=2 and by x=√2.
If x=2, then y = (49 - 2²)/5 = 9.
If x=√2, then y = (49 - (√2)²)/5 = 47/5.
Since in the first case y is an integer and in the second case y is not an integer, INSUFFICIENT.

The correct answer is E.

can u please explain how you got x=2 and x=√2..

thank you...
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by rijul007 » Wed Nov 16, 2011 10:43 am
Got it ..

Option E
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by GMATGuruNY » Wed Nov 16, 2011 10:45 am
rijul007 wrote:
GMATGuruNY wrote:
shankar.ashwin wrote:
Both statements are satisfied by x=2 and by x=√2.
If x=2, then y = (49 - 2²)/5 = 9.
If x=√2, then y = (49 - (√2)²)/5 = 47/5.
Since in the first case y is an integer and in the second case y is not an integer, INSUFFICIENT.

The correct answer is E.

can u please explain how you got x=2 and x=√2..

thank you...
Let x=2.
Statement 1: 1 < x < 4
1 < 2 < 4.
Satisfied.
Statement 2: x² is an integer
2² = 4.
Satisfied.

Let x =√2 ≈ 1.4.
Statement 1: 1 < x < 4
1 < √2 < 4.
Satisfied.
Statement 2: x² is an integer
(√2)² = 2.
Satisfied.

Always note how a problem is restricted and how it isn't.
There is no requirement that x be an integer here.
Last edited by GMATGuruNY on Wed Nov 16, 2011 10:56 am, edited 1 time in total.
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by rijul007 » Wed Nov 16, 2011 10:54 am
GMATGuruNY wrote:
rijul007 wrote:
GMATGuruNY wrote:
shankar.ashwin wrote:
Both statements are satisfied by x=2 and by x=√2.
If x=2, then y = (49 - 2²)/5 = 9.
If x=√2, then y = (49 - (√2)²)/5 = 47/5.
Since in the first case y is an integer and in the second case y is not an integer, INSUFFICIENT.

The correct answer is E.

can u please explain how you got x=2 and x=√2..

thank you...
Let x=2.
Statement 1: 1 < x < 4
1 < 2 < 4.
Satisfied.
Statement 2: x² is an integer
2² = 4.
Satisfied.

Let x =√2 ≈ 1.4.
Statement 1: 1 < x < 4
1 < √2 < 4.
Satisfied.
Statement 2: x² is an integer
(√2)² = 2.
Satisfied.

Always note how problem is restricted and how it isn't.
There is no requirement that x be an integer here.

I failed to think of all the possible cases.. jsut assumed that if x^2 is an integer then x will always be an integer ..

Thanks Mitch
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by ariz » Thu Nov 17, 2011 2:42 pm
rijul007 wrote:
I failed to think of all the possible cases.. jsut assumed that if x^2 is an integer then x will always be an integer ..

Thanks Mitch
Same here. I always miss the dreaded square root...
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