If x and y are consecutive odd integers such that x

Question

If x and y are consecutive odd integers such that x < y, what is the value of y + x?

(1) The product of xy is negative.
(2) The sum x + y is the square of an integer

sudish · Answer

The question states that x and y are consecutive odd integers such that x < y.
We are asked to find the value of 'x+y'.
Let's look at the given statements.

Statement 1 says that the product of x and y is negative.
If the odd integers x and y are both positive, their product will be positive. (E.g. 3 and 5, 19 and 21, etc)
Similarly, if x and y are both negative, their product will still be positive. (-1 and -3, -13 and -15, etc)
Hence, the only possible numbers which satisfy the given condition are 1 and -1 i.e. one negative and other positive number. Here x = -1 and y = 1 since x < y.
1 and -1 are consecutive odd integers such that their product is -1 which is negative.
Hence we can find the sum of these 2 odd integers as -1 +1 = 0.
Hence this statement by itself is sufficient.

Statement 2 says that the sum x + y is the square of an integer.
Let's consider a few examples which satisfy this condition.
Let x = 1 and y = 3. Their sum = 1+3 = 4 (which is the square of 2 or -2)
If x = 7 and y = 9, then their sum 7+9 = 16 is the square of 4 or -4.
We see that there can be a number of possible combinations of numbers which satisfy this condition.
Hence, this statement by itself is insufficient.

As statement 1 is sufficient and statement 2 is not, the correct answer is option A.

Hope this helps

Bunuel · Answer

If x and y are consecutive odd integers such that x < y, what is the value of y + x?

(1) The product of xy is negative. x and y have the opposite signs. Consecutive odd integers to have the opposite signs one must be equal to -1 and another to 1, so their sum is -1+1=0. Sufficient.

(2) The sum x + y is the square of an integer. If x=-1 and y=1, then -1+1=0^2 but if x=1 and y=3, then x+y=2^2. Not sufficient.

Answer: a.

earnit · Answer

two consecutive odd integers x and y can be (2n+1) and (2n+3) respectively.

Now given (1) the product is negative. The only way for a product of two integers to be negative is if one of them is negative while the other isn't. 
Given the consecutive nature, only -1,1 satisfies for x and y.

Therefore Option (1) is sufficient alone.

Now given (2) Sum of x and y is the square of an integer. So x and y can be 1,3 as well as 7,9. Their respective sums (4 and 16) are squares of 2 and 4.
SO insufficient for a conclusive answer.

Therefore, Option 1 alone is sufficient to answer.
 Answer:A

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: oddconsecutives_explanation(1).png

BrentGMATPrepNow · Answer

Target question :    What is the value of y + x?

Given : x and y are consecutive odd integers such that x < y

Statement 1 : The product of xy is negative  
In order for the product xy to be NEGATIVE, it must be the case that one value is POSITIVE and one value of NEGATIVE.
Since x and y are CONSECUTIVE ODD integers, it must be the case that x = -1 and y = 1 
This is the ONLY way to satisfy statement 1. 
If x = -1 and y = 1, then  x + y = (-1) + 1 = 0 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : The sum x + y is the square of an integer. 
There are several values of x and y that satisfy statement 2. Here are two: 
 Case a : x = 1 and y = 3. Notice that x + y = 1 + 3 = 4, and 4 IS the square of an integer (4 = 2²) In this case, the answer to the target question is  x + y = 4 
 Case b : x = 7 and y = 9. Notice that x + y = 7 + 9 = 16, and 16 IS the square of an integer (16 = 4²) In this case, the answer to the target question is  x + y = 16 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

bumpbot · Answer

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If x and y are consecutive odd integers such that x < y

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