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If w + z = 28, what is the value of wz?

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If w + z = 28, what is the value of wz  [#permalink]

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Updated on: 22 Mar 2013, 12:19
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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

Originally posted by GMAThirst on 22 Mar 2013, 09:14.
Last edited by Bunuel on 22 Mar 2013, 12:19, edited 1 time in total.
Edited the question.
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Re: if w + Z = 28, what is the value of wz  [#permalink]

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22 Mar 2013, 11:13
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No problemo!

Just to clarify one thing. Two consecutive odd numbers adding up to 28 must be 13 and 15, but if the numbers get unwieldy, such as w+z = 280, just divide the sum by 2 and then take the numbers on either side. In other words, the two numbers need to average out to that, so it would be 139 and 141 in this example. Obviously, since this is the GMAT, the numbers will lead you to an even integer so you can take the odd ones on either side.

This is the same principle for dividing by 3 or any other number, you just need to divide by the number of terms. Ex: w + x + z = 279. What are the 3 consecutive odd integers that form w, x and z: 279 /3 = 93. The three odd numbers would be 91, 93 and 95, so that they average out to 93.

Hope this helps on questions like this when the numbers aren't so easy to spot!
-Ron
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Re: if w + Z = 28, what is the value of wz  [#permalink]

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22 Mar 2013, 10:21
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GMAThirst wrote:
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

Hi GMAThirst, let's examine these statements one at a time:

1. w and z are positive integers.
We know that both must be positive, so this eliminates 30 and -2, but it could be 1 and 27, 2 and 26, 3 and 25, etc. All of which have different products (1x27=27, 2x26=52, etc) A is insufficient on its own

2. w and z are consecutive odd integers
This would have to be 13 and 15. No other positive consecutive odd integers would add up to 28. Statement A makes us wonder about negative numbers, what about -13 and -15? Well they would add up to -28, which isn't the same as +28, so they're out as possibilities. What about other negative consecutive odd integers? Nothing is ever going to give you anything other than a negative number, so no negative numbers could work here. Statement 2 is thus sufficient on its own, with no need to bring in statement #1. (w*z must be either 13*15 or 15*13, either way giving the answer of 195 by commutativity)

Hope this helps!
-Ron
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Re: If w + z = 28, what is the value of wz  [#permalink]

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18 Jul 2013, 23:47
Quote:
(1) w and z are positive integers
(2) w and z are consecutive odd integers

I understand why statment 2 alone is sufficent in this example, but what if we were told that "w + z = $$|28|$$" would that mean the answer is C as statment 2 in itself is insufficent (w and z could be -15, -13 or 13, 15) but with statment 1 we can solve the stem (since only 13 and 15 are left).

Have I understood it correctly?
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Re: If w + z = 28, what is the value of wz  [#permalink]

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19 Jul 2013, 00:02
aeglorre wrote:
Quote:
(1) w and z are positive integers
(2) w and z are consecutive odd integers

I understand why statment 2 alone is sufficent in this example, but what if we were told that "w + z = $$|28|$$" would that mean the answer is C as statment 2 in itself is insufficent (w and z could be -15, -13 or 13, 15) but with statment 1 we can solve the stem (since only 13 and 15 are left).

Have I understood it correctly?

No. |28|=28, so w + z = |28| is the same as w + z = 28.

Guess, you meant: |w + z| = 28. Now, if the question were: "|w + z| = 28, what is the value of wz?", the correct answer would still be B. From |w + z| = 28 and w and z are consecutive odd integers, it follows that the integers can be 13 and 15 OR -13 and -15. In any case wz = 195.

Hope it's clear.
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If w + z = 28, what is the value of wz?  [#permalink]

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13 Jan 2014, 00:58
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1
SOLUTION:

If w + z = 28, what is the value of wz?

(1) w and z are positive integers. Many values are possible for w and z, for example: (1, 27), (2, 26), (3, 25), ... Not sufficient.

(2) w and z are consecutive odd integers. So, we have that 28 is the sum of two consecutive odd integers: x+(x+2)=28 (where x is an odd integer) --> x=13. So, either w=13 and z=15 OR w=15 and z=13. In any case, wz=13*15. Sufficient.

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Re: If w + z = 28, what is the value of wz?  [#permalink]

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13 Jan 2014, 01:23
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Hello...
Statement A : not suff. If w,z were positive is the only known condition, then there are numerous values for w and z such that w+ z =28 ; eg. (1,27); (3,25), (2,26) etc.
Statement B:
w and z are consecutive odd integers so,
lets take w=2k-1 and z=2k+1
Thus w+z= 4k= 28 and wz=4k^2 - 1
Two possible sets for w,z i.e (15,13) or (13,15) both have the same product ---> Sufficient

Thus B
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Re: If w + z = 28, what is the value of wz?  [#permalink]

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14 Jan 2014, 11:10
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

Statement 1) w and z are +ve integers. w can be 1 and z can be 27 or w can be 2 and z can be 26. so in each case wz changes. Hence Not sufficient.

Statement 2) As w and z are consecutive odd integers, then w can be either 13 or 15 and z can be 15 or 13. In either case wz is same same.
Hence Sufficient.

Hence Option B)
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Re: If w + z = 28, what is the value of wz?  [#permalink]

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14 Jan 2014, 13:37
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Option 1 will lead to multiple answers for ex: W =27,z=1 then WZ=27 or W=15,Z=13 then WZ= 195. Answer will not Statement A

Option 2 :

Given W and Z are consecutive odd interger then W and Z can be written as W= 2n+1 and Z=2n+3 OR Z= 2n+1 and W=2n+3 (by using definition of Odd number)
Also from problem statement W+ Z = 28 => 2n+1 + 2n+3 = 28
Solving for n , we get n = 6
W= (2*6)+1=13
Z=(2*6)+3 =15

OR

Z= (2*6)+1=13
W=(2*6)+3 =15
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Re: If w + z = 28, what is the value of wz?  [#permalink]

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15 Jan 2014, 01:39
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(1) Option 1 can lead to many possibilities: ex., w=1 & z=27 or w=13 & z=15...
Insufficient;
(2) Since w and z are consecutive odd integers, we can find out quite easily that the 2 possible numbers should be -1 and +1 of the middle number(14).

Alternative approach, especially when the sum is big, is by assuming (2n+1) as the 1st consecutive odd integer and (2n+3) as the 2nd consecutive odd integer.

2n+1+2n+3=28;
4n=24;
=> n=6;

The 1st consecutive odd integer is 2(6)+1 = 13;
The 2nd consecutive odd integer is 2(6)+3 = 15;

Ans is (B).
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Re: If w + z = 28, what is the value of wz?  [#permalink]

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24 Apr 2017, 03:30
Bunuel wrote:
SOLUTION:

If w + z = 28, what is the value of wz?

(1) w and z are positive integers. Infinitely many values are possible for w and z, for example: ..., (-1, 29), (0, 28), (1, 27), ... Not sufficient.

(2) w and z are consecutive odd integers. So, we have that 28 is the sum of two consecutive odd integers: x+(x+2)=28 (where x is an odd integer) --> x=13. So, either w=13 and z=15 OR w=15 and z=13. In any case, wz=13*15. Sufficient.

I thought that you would need to know that both are not negative to ensure that they add up to 28.. thoughts?
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Re: If w + z = 28, what is the value of wz?  [#permalink]

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24 Apr 2017, 03:38
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schak wrote:
Bunuel wrote:
SOLUTION:

If w + z = 28, what is the value of wz?

(1) w and z are positive integers. Infinitely many values are possible for w and z, for example: ..., (-1, 29), (0, 28), (1, 27), ... Not sufficient.

(2) w and z are consecutive odd integers. So, we have that 28 is the sum of two consecutive odd integers: x+(x+2)=28 (where x is an odd integer) --> x=13. So, either w=13 and z=15 OR w=15 and z=13. In any case, wz=13*15. Sufficient.

I thought that you would need to know that both are not negative to ensure that they add up to 28.. thoughts?

There is no other solution exist for w + z = 28 and w and z are consecutive odd integers, other than 13 and 15.
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