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

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Magoosh GMAT Instructor
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If x and y are consecutive odd integers such that x < y [#permalink]

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19 Sep 2012, 13:38
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35% (medium)

Question Stats:

70% (02:10) correct 30% (01:19) wrong based on 149 sessions

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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.

See the answer and a full video explanation here.
http://gmat.magoosh.com/questions/880
[Reveal] Spoiler: OA

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Re: If x and y are consecutive odd integers such that x < y [#permalink]

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19 Sep 2012, 16:09
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.

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Re: If x and y are consecutive odd integers such that x < y [#permalink]

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19 Sep 2012, 20:48
mikemcgarry wrote:
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.

See the answer and a full video explanation here.
http://gmat.magoosh.com/questions/880

(1) xy is negative only if one number is negative and the other is positive. (-1) and (1) is the only possibility. Thus. SUFFICENT
(2) x + y = s^2

Try (-1) + (1) = 0, is equal to 0^2
Try (1) + (3) = 4, is equal to 2^2, Thus, INSUFFICIENT

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Re: If x and y are consecutive odd integers such that x < y [#permalink]

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20 Sep 2012, 00:11
mikemcgarry wrote:
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.

See the answer and a full video explanation here.
http://gmat.magoosh.com/questions/880

(1) Obviously one integer must be negative and the other one positive. Being both odd, the only possibility is -1 and 1.
Sufficient.

(2) There are infinitely many pairs of consecutive integers for which their sum is a square of an integer.
If $$x$$ and $$y$$ are consecutive odd integers, $$x<y$$, then between them there is a unique even integer $$2k$$, where $$2k=(x+y)/2.$$
$$x=2k-1$$ and $$y=2k+1.$$ Their sum is $$4k$$ and necessarily $$4k=n^2$$, or $$2k=n^2/2.$$

So, take any even integer $$n$$, then $$\frac{n^2}{2}-1$$ and $$\frac{n^2}{2}+1$$ are two consecutive odd integers.
Tor example, 1 and 3, 7 and 9, 17 and 19, 31 and 33,...

Not sufficient.

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Re: If x and y are consecutive odd integers such that x < y [#permalink]

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16 May 2013, 11:31
mikemcgarry wrote:
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.

See the answer and a full video explanation here.
http://gmat.magoosh.com/questions/880

Consecutive odd integers and product is negative => -1 and 1

stmt 2: nope wrong, can't get any particular value.

so A
Re: If x and y are consecutive odd integers such that x < y   [#permalink] 16 May 2013, 11:31
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