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If w+ z = 28, what is the value of wz? [#permalink]
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13 Jan 2014, 01:58
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: If w+ z = 28, what is the value of wz? [#permalink]
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13 Jan 2014, 01:58
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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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=2k1 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, 12:10
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Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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, 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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15 Jan 2014, 02:39
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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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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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17 Jan 2014, 05:42
[quote="Bunuel"] The Official Guide For GMAT® Quantitative Review, 2ND EditionIf 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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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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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?
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