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Manhattan GMAT Number Properties Question

by G_Rug » Thu Apr 25, 2013 3:37 pm
Is the integer x odd?

1) 2(y+x) is an odd integer
2) 2y is an odd integer


I don't agree with the book's answer. Here's my approach:

1) SUFF. Looking at statement 1, it is clear that y and/or x are fractions, and they add to a fraction with an odd number in the numerator (i.e. 1/2 + 2/2 = 3/2, multiplied by 2 will yield 3). Given that the question already suggests that x is an integer ("is the integer x odd?"), y must be the fraction. This means x is an even number (2,4,6,8), so that the sum of y and x yield an odd number in the numerator. This is sufficient to answer the question.

2) INSUFF. 2y tells nothing about x

I come up with A, but the book says it's E. Can anyone tell me where I went wrong?? Thanks.
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by Brent@GMATPrepNow » Thu Apr 25, 2013 3:51 pm
G_Rug wrote:Is the integer x odd?

1) 2(y+x) is an odd integer
2) 2y is an odd integer
Target question: Is the integer x odd?

Statement 1: 2(y+x) is an odd integer
There are several pairs of values that meet this condition. Here are two:
Case a: x = 3 and y = 0.5 in which case integer x is odd
Case b: x = 2 and y = 0.5 in which case integer x is even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2y is an odd integer
No information about x so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Statement 1 says that 2(y+x) is an odd integer
In other words, 2y + 2x is odd
Statement 2 says that 2y is some odd #.
When we combine this with statement 1, we get: some odd # + 2x is odd
If x is an integer, then 2x is always even, which means some odd # + 2x will ALWAYS be odd, regardless of whether or not x is odd.
So, the combined statements are NOT SUFFICIENT

To demonstrate this, consider these two conflicting cases:
Case a: x = 3 and y = 0.5 in which case integer x is odd
Case b: x = 2 and y = 0.5 in which case integer x is even

Answer = E

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by Brent@GMATPrepNow » Thu Apr 25, 2013 3:56 pm
G_Rug wrote:Is the integer x odd?

1) 2(y+x) is an odd integer
2) 2y is an odd integer


I don't agree with the book's answer. Here's my approach:

1) SUFF. Looking at statement 1, it is clear that y and/or x are fractions, and they add to a fraction with an odd number in the numerator (i.e. 1/2 + 2/2 = 3/2, multiplied by 2 will yield 3). Given that the question already suggests that x is an integer ("is the integer x odd?"), y must be the fraction. This means x is an even number (2,4,6,8), so that the sum of y and x yield an odd number in the numerator. This is sufficient to answer the question.
The problem with your solution is above, in blue. We cannot conclude that x is even based on statement 1.
Consider these cases:
Case a: x = 3 and y = 0.5 (here, 2(y+x) is an odd integer and x is odd)
Case b: x = 2 and y = 0.5 (here, 2(y+x) is an odd integer and x is even)

IMPORTANT: In your example, you show that 1/2 + 2/2 = 3/2, multiplied by 2 will yield 3
Here, y = 0.5 and x = 1, so in your example, x is not even (as you suggest)

Cheers,
Brent
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by GMATGuruNY » Fri Apr 26, 2013 5:12 am
G_Rug wrote:Is the integer x odd?

1) 2(y+x) is an odd integer
2) 2y is an odd integer
This is an EVEN VS. ODD question.
Make the problem more concrete by testing one ODD value for x and one EVEN value for x.
Note that the ONLY CONSTRAINT in the question stem is that x is an integer.

Statement 1: 2(y+x) = odd
Case 1: x=1 and 2(y+x) = 3
2(y+1) = 3
2y + 2 = 3
y = 1/2.
Since 2y = 2(1/2) = 1, this case also satisfies statement 2.

Case 2: x=0 and 2(y+x) = 3
2(y+0) = 3
2y = 3
y = 3/2.
Since 2y = 2(3/2) = 3, this case also satisfies statement 2.

Case 1 satisfies both statements, as does Case 2.
Since in the first case x=1 (odd), and in the second case x=0 (even), the two statements combined are INSUFFICIENT.

The correct answer is E.
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by ella willius » Fri Apr 26, 2013 12:45 pm
If X And Y Are Integers Greater Than 1 Is X A Multiple Of Y (1) 3y^2 + 7 Y = X. sufficient or not ?
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by Brent@GMATPrepNow » Fri Apr 26, 2013 12:54 pm
ella willius wrote:If X And Y Are Integers Greater Than 1 Is X A Multiple Of Y (1) 3y^2 + 7 Y = X. sufficient or not ?
Asking whether x is a multiple of y is the same as asking whether x = (y)(some integer)
For example, 12 is a multiple of 3 because 12 = (3)(4)

Given: x = 3y^2 + 7y
Factor to get x = y(3y + 7)
In other words: x = y(some integer)
So, it MUST be the case that x is a multiple of y. (The statement is SUFFICIENT)

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