If 6^xâˆ’3[6^(xâˆ’4)]=1293(36^y), what is the value of x, in

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hazelnut01: Master | Next Rank: 500 Posts; Posts: 157; Joined: Sat Nov 19, 2016 5:34 amFollowed by: 4 members; Thanked: 2 times

by hazelnut01 » Fri May 05, 2017 9:17 pm

If 6^xâˆ’3[6^(xâˆ’4)]=1293(36^y), what is the value of x, in terms of y?

(A) y
(B) y+4
(C) y-4
(D) 2y+4
(E) 2y-4

Source : Math Revolution
OA=D

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Source: Beat The GMAT — Problem Solving | Fri May 05, 2017 9:17 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Fri May 05, 2017 10:58 pm

ziyuenlau wrote:If 6^xâˆ’3[6^(xâˆ’4)]=1293(36^y), what is the value of x, in terms of y?

(A) y
(B) y+4
(C) y-4
(D) 2y+4
(E) 2y-4

Source : Math Revolution
OA=D

6^x-3[6^(x-4)]=1293(36^y)

= 2^x.3^x - 3.2^(x-4).3^(x-4) = 3.431.6^(2y)

= 2^x.3^x - 2^(x-4).3^(x-3) = 3^(2y+1).2^(2y).431

= 2^(x-4).3^(x-3).[2^4.3^3 - 1] = 3^(2y+1).2^(2y).431

= 2^(x-4).3^(x-3).431 = 3^(2y+1).2^(2y).431

= 2^(x-4).3^(x-3). = 3^(2y+1).2^(2y)

=> x-4 = 2y; equating the exponents of 2

=> x = 2y + 4

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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