Is the integer x odd?

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.

Answer E.

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

Answer: Option

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

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,
Kudos Please.

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

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).

First and Foremost imp thing :-
x is integer (given in the ques)

2(y+x) always even if x and y both integers. Since x is integer so y is fraction but nothing can be judged whether x is even or odd so S1 is insufficient
as nothing given in S2 about x so S2 is insufficient

now combining S1 and S2 since 2y is odd here odd+2x = even which is possible only when x is not integer thus negating the data set

hence both statements cannot jusitfy the answer together also so E is the answer

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