## If w + z = 28

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### If w + z = 28

by ektamatta » Mon Jul 28, 2008 1:08 pm
7.If w + z = 28, what is the value of wz ?
(1) w and z are positive integers.
(2) w and z are consecutive odd integers.

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by ricky » Mon Jul 28, 2008 3:13 pm
IMO B

(i) z and w are positive..NOT SUFFICIENT

(ii)Let w = x then z = x+2

x+x+2= 28 =>x=13

w=13, z= 15 or z=13, w= 15.But we just need wz, which will be same anyway...SUFFICIENT

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### why dont we consider negative odd integers

by sweet83 » Mon Mar 09, 2009 7:28 pm
the problem does not state when the consecutive odd integers are negative or positive. if we consider negative odd integers, then should'nt the answer be C?

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### Re: why dont we consider negative odd integers

by [email protected] » Mon Mar 09, 2009 7:38 pm
sweet83 wrote:the problem does not state when the consecutive odd integers are negative or positive. if we consider negative odd integers, then should'nt the answer be C?

If they were negative, then they couldn't add to positive 28

To examine (2) algebraically, we might let x be the smaller odd # and let x+2 be the larger odd #

We know that x + (x+2) = 28
We can solve this for x (x=13), which means the 2 numbers are 13 and 15
SUFFICIENT.

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by sweet83 » Mon Mar 09, 2009 8:24 pm
ok makes sense.

thanks so much!!!

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by cramya » Mon Mar 09, 2009 8:35 pm
Ricky's solution is good.

Another way to look at B would be the sum of any 2 consecutive integers or odd integers or even integers is always unique. Therefore we know we can find the two numbers and hence their product.

SUFF

Regards,
CR

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### Re: If w + z = 28

by [email protected] » Mon Jul 05, 2021 4:47 am
ektamatta wrote:
Mon Jul 28, 2008 1:08 pm
7.If w + z = 28, what is the value of wz ?
(1) w and z are positive integers.
(2) w and z are consecutive odd integers.
Solution:

Question Stem Analysis:

We need to determine the value of wz, given that the sum of w and z is 28.

Statement One Alone:

Statement one alone is not sufficient. For example, if w = 1 and z = 27, then wz = 27. However, if w = 14 and z = 14, then wz = 196.

Statement Two Alone:

Statement two alone is sufficient since the only consecutive odd integers that add up to 28 are 13 and 15. Therefore, regardless of whether w = 13 and z = 15 OR w = 15 and z = 13, we have wz = 195.