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03 Dec 2011, 13:30
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Difficulty:
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Question Stats:
74% (01:36) correct
26%
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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
(1) The product of xy is negative.
(2) The sum x + y is the square of an integer
sudish
Joined: 09 Sep 2011
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Schools: CBS '15 (D) Ross '15 (D) Anderson '15 (D) Johnson '15 (WL) ISB '14 (D) Kellogg '15 (D) Olin '15 (WA$) McDonough '15 (M)
GMAT 1: 710 Q49 V38
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03 Dec 2011, 13:51
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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
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
19 Sep 2012, 16:09
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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.
(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.
