If $ (3^x)(2^x)=6^y,$ which of the following must be true?

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Wed Nov 13, 2019 8:03 am

If $ (3^x)(2^x)=6^y,$ which of the following must be true?

A. $x = 2y$
B. $2x = y$
C. $x = y^2$
D. $x^2 = y$
E. $x = y$

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Wed Nov 13, 2019 8:03 am

nitink: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Thu Oct 11, 2018 9:10 am

by nitink » Wed Nov 13, 2019 10:38 am

Using the equation : (ab)^x = a^x . b ^x

it is clear that to get 6 , on the LHS 2 and 3 must be multiplied, so 6 ^ x = 6 ^ y,

so, x= y

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Nov 16, 2019 10:37 am

Hi Vincen,

This question involves a specific Exponent Rule, but you don't actually need to know the rule to answer it - you can TEST VALUES.

IF...
X = 2, then....
(3^2)(2^2) = 6^Y
(9)(4) = 36 = 6^Y
Y = 2

So Y = 2 when X = 2. There's only one answer that matches...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Nov 17, 2019 7:04 pm

Vincen wrote:If $ (3^x)(2^x)=6^y,$ which of the following must be true?

A. $x = 2y$
B. $2x = y$
C. $x = y^2$
D. $x^2 = y$
E. $x = y$

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

Simplifying, we have:

6^x = 6^y

x = y

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Nov 18, 2019 5:24 am

Vincen wrote:If $ (3^x)(2^x)=6^y,$ which of the following must be true?

A. $x = 2y$
B. $2x = y$
C. $x = y^2$
D. $x^2 = y$
E. $x = y$

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

Another approach is to find values of x and y that satisfy the equation (3^x)(2^x)=6^y
For example, it COULD be the case that x =2 and y = 2, since (3^2)(2^2)=6^2

Since it could be the case that x =2 and y = 2, we can now test each answer choice by plugging in x =2 and y = 2
A. 2 = 2(2) NOT TRUE
B. 2(2) = 2 NOT TRUE
C. 2 = 2^2 NOT TRUE
D. 2^2 = 2 NOT TRUE
E. 2 = 2 TRUE!!!

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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