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

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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If x and y are consecutive odd integers such that x < y  [#permalink]

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19 Sep 2012, 12:38
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Difficulty:

35% (medium)

Question Stats:

70% (01:36) correct 30% (01:46) wrong based on 194 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

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Mike McGarry
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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, 15:09
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, 19:48
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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19 Sep 2012, 23:11
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, 10:31
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
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Re: If x and y are consecutive odd integers such that x < y  [#permalink]

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03 Oct 2017, 13:39
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.
Just by picking numbers: -1*-3 =3 ; 1*3 = 3. Only number that does this is -1*1 (with zero in the middle) is negative. so SUFF.

(2) The sum x + y is the square of an integer.-3+(-1) = -4. But -4 cannot be square of any integer. 3+1 = is sq of 2. 1 + (-1)
= 0; which is not square of anything. So different answers.

Re: If x and y are consecutive odd integers such that x < y &nbs [#permalink] 03 Oct 2017, 13:39
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