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If a, b, x, y, and z are nonnegative integers and 2^a – 2^b = (3^x)(2^
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25 Apr 2016, 04:06
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If a, b, x, y, and z are nonnegative integers and \(2^a – 2^b = (3^x)(2^y)(7^z)\), what is the value of xyz? (1) \(a – b = 3\) (2) \(yz > 0\)
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Re: If a, b, x, y, and z are nonnegative integers and 2^a – 2^b = (3^x)(2^
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25 Apr 2016, 06:07
Bunuel wrote: If a, b, x, y, and z are nonnegative integers and 2^a – 2^b = (3^x)(2^y)(7^z), what is the value of xyz?
(1) a – b = 3 (2) yz > 0 Hi Nonnegative would mean O or positive integers.. \(2^a – 2^b = (3^x)(2^y)(7^z)\).. lets see the statements (1) a – b = 3\(2^a – 2^b = (3^x)(2^y)(7^z)\).. \(2^b(2^{ab} – 1) = (3^x)(2^y)(7^z)\).. \(2^b(2^3 – 1) = (3^x)(2^y)(7^z)\).. \(2^b*7 = (3^x)(2^y)(7^z)\).. so clearly 3^x=1, since there is no 3 on LHS.. OR x=0..now irrespective of what y and z are, xyz will remain 0.. Suff.. Otherwise we get b=y, z=1 and x=0 (2) yz > 0Just tells us that y and z are not 0 nothing about x or the numeric values of y and z.. Insuff A
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Re: If a, b, x, y, and z are nonnegative integers and 2^a – 2^b = (3^x)(2^
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27 Oct 2018, 10:35
Ans: A Let us start with analyzing the equation: Since all are nonnegative numbers, a>b. Which makes the question2^b * (2^(ab) – 1) = 3^x * 2^y * 7^z
Let us consider Statement 1: ab=3 Substituting gives us> 2^b * (2^3  1) = 2^b * 7 So we get x=0, y=b and z=1, which gives xyz = 0. Thus statement 1 is sufficient.
Now statement 2: yz>0 This statement tells us that y and z both are not zero, but it tells us nothing about x. If ab=3, we get x=0 and thus xyz = 0. But if ab=6, we get x=2, y=b and z=1. Since we do not know b, we can not calculate the value of xyz. Thus, Statement 2 is insufficient.
A is the answer.




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Re: If a, b, x, y, and z are nonnegative integers and 2^a – 2^b = (3^x)(2^
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27 Oct 2018, 10:05
If a, b, x, y, and z are non negative integers and \(2^a — 2^b = (3^x)(2^y)(7^Z)\). what is the value of xyz? 1) ab=3 2) yz > O Weekly Quant Quiz #6 Question No 2
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Re: If a, b, x, y, and z are nonnegative integers and 2^a – 2^b = (3^x)(2^
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27 Oct 2018, 10:29
ab = 3 is insufficient yz>0 is insufficient since there is no information about x.
2^a2^b = 2^b(2^ab  1) = 2^b * 7^1 ; x=0, z= 1, y=b... IMO E?



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Re: If a, b, x, y, and z are nonnegative integers and 2^a – 2^b = (3^x)(2^
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24 Dec 2018, 09:16
gmatbusters wrote: If a, b, x, y, and z are non negative integers and \(2^a — 2^b = (3^x)(2^y)(7^Z)\). what is the value of xyz? 1) ab=3 2) yz > O Weekly Quant Quiz #6 Question No 2 ________________ Merged topics.
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Re: If a, b, x, y, and z are nonnegative integers and 2^a – 2^b = (3^x)(2^
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25 Dec 2018, 01:05
Bunuel wrote: If a, b, x, y, and z are nonnegative integers and \(2^a – 2^b = (3^x)(2^y)(7^z)\), what is the value of xyz?
(1) \(a – b = 3\)
(2) \(yz > 0\) from 1: 2^b(2^ab 1 )= 3^x*2^y*7^z given ab=3 2^b(7)=3^x*2^y*7^z 3^x=1 or say x=0 so xyz= 0 sufficeint from 2 yz>0 no relation given in terms of a,b,x so in sufficeint IMO A




Re: If a, b, x, y, and z are nonnegative integers and 2^a – 2^b = (3^x)(2^
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25 Dec 2018, 01:05






