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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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New post 13 Jan 2014, 01:58
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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.

Data Sufficiency
Question: 35
Category: Arithmetic Arithmetic operations
Page: 155
Difficulty: 600


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

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New post 13 Jan 2014, 01:58
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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.

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

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New post 13 Jan 2014, 02:23
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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 :-D
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Re: If w+ z = 28, what is the value of wz?  [#permalink]

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New post 14 Jan 2014, 12:10
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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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New post 14 Jan 2014, 14:37
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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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New post 15 Jan 2014, 02:39
1
(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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New post 17 Jan 2014, 04:52
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.

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

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New post 17 Jan 2014, 05:42
[quote="Bunuel"]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 I is insufficient
w = 14 , z = 14 OR w = 15, z = 13

Statement II is sufficient
(w)+(w+2) = 28
w = 13 and z = 15 OR opposite
The only possible way it can happen if the pair is 15 and 13.
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Re: If w+ z = 28, what is the value of wz?  [#permalink]

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New post 24 Apr 2017, 04:30
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.

Answer: B.



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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New post 24 Apr 2017, 04:38
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.

Answer: B.



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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Re: If w+ z = 28, what is the value of wz? &nbs [#permalink] 24 Apr 2017, 04:38
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