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If a, b, x, y, and z are non negative integers and [m]2^a — 2^b = (3^x

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If a, b, x, y, and z are non negative integers and [m]2^a — 2^b = (3^x  [#permalink]

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New post 27 Oct 2018, 09:05
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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) a-b=3
2) yz > O

Weekly Quant Quiz #6 Question No 2


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Re: If a, b, x, y, and z are non negative integers and [m]2^a — 2^b = (3^x  [#permalink]

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New post 27 Oct 2018, 09:35
Ans: A
Let us start with analyzing the equation:
Since all are non-negative numbers, a>b. Which makes the question--2^b * (2^(a-b) – 1) = 3^x * 2^y * 7^z

Let us consider Statement 1:
a-b=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 a-b=3, we get x=0 and thus xyz = 0.
But if a-b=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 non negative integers and [m]2^a — 2^b = (3^x  [#permalink]

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New post 27 Oct 2018, 09:29
a-b = 3 is insufficient
yz>0 is insufficient since there is no information about x.

2^a-2^b = 2^b(2^a-b - 1) = 2^b * 7^1 ; x=0, z= 1, y=b...
IMO
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Re: If a, b, x, y, and z are non negative integers and [m]2^a — 2^b = (3^x &nbs [#permalink] 27 Oct 2018, 09:29
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