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Math Expert V
Joined: 02 Sep 2009
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Is the integer x odd?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 66% (01:42) correct 34% (01:35) wrong based on 207 sessions

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Is the integer x odd?

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

Kudos for a correct solution.

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Is the integer x odd?  [#permalink]

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Bunuel wrote:
Is the integer x odd?

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

Kudos for a correct solution.

Statement 1:
Converts to 2y + 2x = odd integer. Well how come that 2*y + 2*x equals something odd? Usually if you multiply with an even integer, the result is always even. Since x is an integer, the term 2x is even. Therefore statement 1 says 2x = even and 2y must be odd. Still x can be any number even or odd which satisfies the statement. Thus insufficient.

Statement 2:
Nothing about x. > IS.

1+2 together: Statement 2 does not provide new information. Clearly insufficient.

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Re: Is the integer x odd?  [#permalink]

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Statement 1:
Question doesn't say anything about y. y can be integer or non-integer but x is only integer. For the expression to be odd y should be 1/2, 3/2, 5/2....
taking y=1/2; x can be anything 2,3 (even or odd)

Not sufficient.

Statement 2:

Insufficient information.
Not sufficient

Taking both 1 & 2 still we can not say anything about x.

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Re: Is the integer x odd?  [#permalink]

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1
Is the integer x odd?

(1) 2(y+ x) is an odd integer.
y could equal 1/2 and x could equal 1. x is odd
y could equal -1/2 and x could equal 2. x is even
insufficient

(2) 2y is an odd integer.
nothing about x is indicated.
insufficient

Together, using the example from (1), the statements are both insufficient

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Re: Is the integer x odd?  [#permalink]

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Bunuel wrote:
Is the integer x odd?

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

Kudos for a correct solution.

Question : Is the integer x odd?

Statement 1: 2(y+ x) is an odd integer
i.e. (y+x) is a decimal number of the type 1.5 or 2.5 or 3.5 etc
i.e. for y=0.5, x may be 1(odd) or 2(even) or 3 etc

Hence, NOT SUFFICIENT

Statement 2: 2y is an odd integer.
i.e. y = 0.5 or 1.5 etc
No information about x and no relation of y with x
Hence, NOT SUFFICIENT

Combining the two statements
i.e. for y=0.5, x may be 1(odd) or 2(even) or 3 etc

Hence, NOT SUFFICIENT

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Re: Is the integer x odd?  [#permalink]

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Is the integer x odd?

(1) 2(y+ x) is an odd integer. - Lets take y=3/2 and y= 2 or 3 -> For both the values of x, 2(y+ x) is an odd integer. Not Sufficient.
(2) 2y is an odd integer. - Lets take y=3/2. But no information of x. Not Sufficient.

1+2 -> y = 3/2, but x can be either even or odd. Not Sufficient.

Thanks,
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Math Expert V
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Re: Is the integer x odd?  [#permalink]

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Bunuel wrote:
Is the integer x odd?

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

Kudos for a correct solution.

1) stat 1 tells us that y is a fraction with odd numerator and 2 in denminator and x , an integer , can take any value.. insuff
2) stat 2 also tells us the same info about y as stat 1 does.. insuff
combined nothing new.. insuff
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Is the integer x odd?  [#permalink]

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1
The other way to look at the question is to start from statement 2

2) clearly insufficient. But the second statement there considering the first one at the same time is a clue, how the question is conceived, that the answer is C or E

Now combining the two statements we do have : 2y + 2x = Odd ---> 2y = odd -----> Odd + 2x = Odd.

To have an odd number 2x must be or 1 (i.e. 3+2=5) or could be zero (3+0=3) that is even.

So we do have to values for X = 1 or zero.

E wins. 30 seconds approach

regards
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Math Expert V
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Re: Is the integer x odd?  [#permalink]

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Bunuel wrote:
Is the integer x odd?

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

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

(1) INSUFFICIENT: 2(y + x) is an odd integer. How is it possible that 2 multiplied by something could yield an odd integer? The value in the parentheses must not be an integer itself. For example, the decimal 1.5 times 2 yields the odd integer 3. List some other possibilities:

2(y + x) = 1, 3, 5, 7, 9, etc.
(y + x) = 1/2, 3/2, 5/2, 7/2, 9/2, etc.

You know that x is an integer, so y must be a fraction in order to get such a fractional sum. Say that y = 1/2. In that case, x = 0, 1, 2, 3, 4, etc. Thus, x can be either odd (“yes”) or even (“no”).

(2) INSUFFICIENT: This statement tells you nothing about x. If 2y is an odd integer, this implies that y = odd/2 = 1/2, 3/2, 5/2, etc.

(1) AND (2) INSUFFICIENT: Statement (2) fails to eliminate the case you used in Statement (1) to determine that x can be either odd or even. Thus, you still cannot answer the question with a definite yes or no.

But, just to combine the statements another way,
Statement (1) says that 2(y + x) = 2y + 2x = an odd integer.
Statement (2) says that 2y = an odd integer. By substitution, odd + 2x= odd, so 2x = odd - odd = even.
2x would be even regardless of whether x is even or odd.

The correct answer is (E).
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Re: Is the integer x odd?  [#permalink]

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_________________ Re: Is the integer x odd?   [#permalink] 12 Apr 2019, 13:26
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