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If 3^x*4^y = 177,147 and x y = 11, then x =? A) Undefined B) 0 C) 1
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22 Jul 2022, 06:30
22 Jul 2022, 06:30
Expert Reply
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Question Stats:
85% (01:23) correct
14% (01:26) wrong based on 14 sessions
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If \((3^x)(4^y) = 177,147\) and \(x – y = 11\), then \(x =\) ?
A) Undefined
B) 0
C) 11
D) 177,136
E) 177,158
A) Undefined
B) 0
C) 11
D) 177,136
E) 177,158
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 3^x*4^y = 177,147 and x y = 11, then x =? A) Undefined B) 0 C) 1
[#permalink]
22 Jul 2022, 06:46
22 Jul 2022, 06:46
2
Carcass wrote:
If \((3^x)(4^y) = 177,147\) and \(x – y = 11\), then \(x =\) ?
A) Undefined
B) 0
C) 11
D) 177,136
E) 177,158
A) Undefined
B) 0
C) 11
D) 177,136
E) 177,158
Notice that, since 177,147 is ODD, it is not a multiple of 4.
This means that y MUST equal zero.
If y = 0 AND we know that x - y = 11, we can conclude that x = 11
Answer: C
Cheers,
Brent
Re: If 3^x*4^y = 177,147 and x y = 11, then x =? A) Undefined B) 0 C) 1
[#permalink]
23 Jul 2022, 01:50
23 Jul 2022, 01:50
2
Since 177,147 is ODD, it is not a multiple of 4.
This means that y MUST equal zero.
If y = 0 AND we know that x - y = 11, we can conclude that x = 11
Hence Answer Choice C
An alternative approach to solve this question could be to use the cyclicity of units digits of the power of 3, but only after figuring out that 4^y has to be odd. The cyclicity of unit digits of 3 is 3,9,7 and 1. Since the number we have is a number ending with 7, the power should be of the form 4k+3 and this also points us towards the fact that x=11.
The correct answer option is C.
This means that y MUST equal zero.
If y = 0 AND we know that x - y = 11, we can conclude that x = 11
Hence Answer Choice C
An alternative approach to solve this question could be to use the cyclicity of units digits of the power of 3, but only after figuring out that 4^y has to be odd. The cyclicity of unit digits of 3 is 3,9,7 and 1. Since the number we have is a number ending with 7, the power should be of the form 4k+3 and this also points us towards the fact that x=11.
The correct answer option is C.
