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

[Vincen]

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

[nitink]

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

[[email protected]]

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

[Scott@TargetTestPrep]

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

[Brent@GMATPrepNow]

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