BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

\(\dfrac{(6.804)^6\cdot(1.701)^{-13}}{2^{19}\cdot(3.402)^{-7}}=\)

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Tue Jul 28, 2020 9:01 pm

Re: \(\dfrac{(6.804)^6\cdot(1.701)^{-13}}{2^{19}\cdot(3.402)^{-7}}=\)

by terminator12 » Thu Jul 30, 2020 5:53 pm
Let 1.701 be x

Hence, the equation becomes:
\(\frac{\left(4x\right)^6\cdot\left(2x\right)^7}{2^{19}\cdot x^{13}}\)

We see the powers of 2 and x cancel off in numerator and denominator and we remain with 1

Hence, answer is B.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: \(\dfrac{(6.804)^6\cdot(1.701)^{-13}}{2^{19}\cdot(3.402)^{-7}}=\)

by Scott@TargetTestPrep » Sun Aug 02, 2020 8:49 am
M7MBA wrote: ↑
Thu Jul 30, 2020 11:37 am
 \(\dfrac{(6.804)^6\cdot(1.701)^{-13}}{2^{19}\cdot(3.402)^{-7}}=\)

A. \(0.8502\)
B. \(1.000\)
C. \(1.7010\)
D \(3.402\)
E. \(6.804\)

[spoiler]OA=B[/spoiler]

Solution:

Notice that 1.701 is exactly half of 3.402, let’s simplify (1.701)^(-13)/(3.402)^(-7) first:

(1.701)^(-13)/(2 x 1.701)^(-7) = (1.701)^(-13)/(2^(-7) x 1.701^(-7)) = (1.701)^(-6)/2^(-7)

So, we have:

[(6.804)^6 x (1.701)^(-6)]/[2^19 x 2^(-7)]

Now, also notice that 6.804 is exactly 4 times of 1.701, we have:

[(4 x 1.701)^6 x (1.701)^(-6)]/[2^19 x 2^(-7)]

[4^6 x (1.701)^6 x (1.701)^(-6)]/[2^12]

[4^6]/[2^12] = (2^2)^6/2^12 = 2^12/2^12 = 1

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

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

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1