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Integers

by sivaelectric » Mon Jun 06, 2011 10:45 pm
If x is an integer, is y an integer?
1) (4X+4Y)/2 = 6
2) (3X+6Y)/3 = 5
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by Frankenstein » Mon Jun 06, 2011 10:52 pm
Hi,
From(1): 2x+2y=6 => x+y=3 =>y = 3-x(integer)
Sufficient
From(2): x+2y=5=>y=(5-x)/2. Integer if x is odd and not an integer if x is even
Insufficient

Hence, A
Last edited by Frankenstein on Mon Jun 06, 2011 11:10 pm, edited 1 time in total.
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by cans » Mon Jun 06, 2011 11:07 pm
a)x+y=3
if x is an integer, y is also an integer
Sufficient
b)x+2y=5
2y is integer. (if 2y is even, then y is integer. if 2y=odd, then y is not)
Insufficient
IMO A
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by smackmartine » Mon Jun 06, 2011 11:24 pm
IMO A

given :x --> int , Asked: y int?

1) 4(x+y)/2 =6
x+y = 3
if x is integer , y has to integer to get 3, an integer.
Sufficient.

2) 3(x+2y)/3 =5

x+2y=5

now if x is 3 and y is 1 , (3)+(2*1)is 5 (y is integer)
also if x = 2 and y = 1.5 , (2)+(2*1.5) is 5 (y is not an integer)

so insufficient.
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by Anurag@Gurome » Tue Jun 07, 2011 6:23 am
sivaelectric wrote:If x is an integer, is y an integer?
1) (4X+4Y)/2 = 6
2) (3X+6Y)/3 = 5
Statement 1: (4x + 4y)/2 = 6 --> y = (12 - 4x)/4 = (3 - x)
Hence, y is also an integer.

Sufficient

Statement 2: (3x + 6y)/3 = 5 --> y = (15 - 3x)/6 = (5 - x)/2
We don't know whether (5 - x) is divisible by 2 or not.

Not sufficient

The correct answer is A.
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by kruthika » Wed Jun 08, 2011 12:43 am
IMO A
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by Brent@GMATPrepNow » Thu Oct 10, 2019 5:28 am
sivaelectric wrote:If x is an integer, is y an integer?
1) (4X+4Y)/2 = 6
2) (3X+6Y)/3 = 5
Target question: Is y an integer?

Given: x is an integer

Statement 1: (4x + 4y)/2 = 6
Multiply both sides by 2 to get: 4x + 4y = 12
Divide both sides by 4 to get: x + y = 3
Since x is an INTEGER and 3 is an INTEGER, we can rewrite the above equation as INTEGER + y = INTEGER
From this, we can conclude that y must be an integer
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (3x + 6y)/3 = 5
Multiply both sides by 3 to get: 3x + 6y = 15
Divide both sides by 3 to get: x + 2y = 5
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 2, in which case y IS an integer
Case b: x = 2 and y = 1.5, in which case y is NOT an integer
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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