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Manager  Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 89
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40

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7 00:00

Difficulty:   55% (hard)

Question Stats: 64% (02:14) correct 36% (02:33) wrong based on 255 sessions

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$$\frac{6.804^6*1.701^{-13}}{2^{19}*3.402^{-7}}$$.

A. .8502
B. 1.000
C. 1.7010
D 3.402
E. 6.804

Originally posted by tonebeeze on 06 Oct 2010, 10:05.
Last edited by Bunuel on 09 Oct 2013, 01:08, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 64275
Re: MGMAT CAT exponents problem  [#permalink]

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2
tonebeeze wrote:
Can you please walk me through simplifying this exponents problem. Thanks

(6.804)^6 (1.701)^-13
_________________________ =

(2)^19 (3.402)^-7

a. .8502
b. 1.000
b. 1.7010
c. 3.402
d. 6.804

$$\frac{6.804^6*1.701^{-13}}{2^{19}*3.402^{-7}}=\frac{(2^2*1.701)^6}{2^{19}*(2*1.701)^{-7}*1.701^{13}}=\frac{2^{12}*1.701^6*(2*1.701)^{7}}{2^{19}*1.701^{13}}=\frac{2^{12}*1.701^6*2^7*1.701^{7}}{2^{19}*1.701^{13}}=\frac{2^{19}*1.701^{13}}{2^{19}*1.701^{13}}=1$$.

Please do check the questions when posting and use formating for such formulas (writing-mathematical-symbols-in-posts-72468.html).
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Intern  Joined: 30 Aug 2010
Posts: 10
Re: MGMAT CAT exponents problem  [#permalink]

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5
the hardest thing here is to discern that:

2*1.701=3.402
4*1.701=6.804

In order to save time and avoid making mistakes by re-writing decimals, 3.402 can be substituted with '2x' and 6.804 with 4x. Therefore, the initial formula is quite simplified:

$$\frac{(4x)^6*x^-13}{2^19*(2x)^-7}$$

Afterwards, it takes 20 seconds to arrive to the final result
##### General Discussion
GMAT Tutor P
Joined: 24 Jun 2008
Posts: 2120
Re: MGMAT CAT exponents problem  [#permalink]

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1
tonebeeze wrote:
Can you please walk me through simplifying this exponents problem. Thanks

(6.806)^6 (1.701)^-13
_________________________ =

(2)^9 (3.402)^-7

a. .8502
b. 1.000
b. 1.7010
c. 3.402
d. 6.804

I'm sure the question must have $$(6.804)^6$$ in the numerator; otherwise you won't have much simplification. I also suspect that the denominator should have a 2^19 in it, instead of 2^9; otherwise you won't get one of the five answer choices. With those changes, then if you notice that 3.402 = 2(1.701), and that 6.804 = (2^2)(1.701), we can factor out 2's in order to cancel:

$$\frac{(6.804)^6 (1.701)^{-13}}{(2^{19})(3.402)^{-7}} = \frac{(2^2)^6(1.701)^6 (1.701)^{-13}}{(2^{19})(2^{-7})(1.701)^{-7}} = \frac{(2^{12})(1.701)^{-7}}{(2^{12})(1.701)^{-7}} = 1$$
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VP  Joined: 06 Sep 2013
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1
tonebeeze wrote:
Can you please walk me through simplifying this exponents problem. Thanks

(6.806)^6 (1.701)^-13
_________________________ =

(2)^9 (3.402)^-7

a. .8502
b. 1.000
b. 1.7010
c. 3.402
d. 6.804

Question is wrong. Please correct. Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 64275

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jlgdr wrote:
tonebeeze wrote:
Can you please walk me through simplifying this exponents problem. Thanks

(6.806)^6 (1.701)^-13
_________________________ =

(2)^9 (3.402)^-7

a. .8502
b. 1.000
b. 1.7010
c. 3.402
d. 6.804

Question is wrong. Please correct. Thanks

Edited the original post. Thank you.
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Manager  Joined: 26 Sep 2013
Posts: 181
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41

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I realized something when looking at this one: they would never have you doing the kind of calculations that would lead to those long decimals. I figured it had to be B based simply on the fact that they rarely if ever have you calculating out that far past the decimal point.
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Re-writing the equation in the powers of 1.701 & 2 :

2^12 . 1.701^6 . 1.701^ -13

Divide by

2^19 . 2^ -7 . 1.701^-7

Manager  Joined: 07 Feb 2015
Posts: 59

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igormkd wrote:
the hardest thing here is to discern that:

2*1.701=3.402
4*1.701=6.804

In order to save time and avoid making mistakes by re-writing decimals, 3.402 can be substituted with '2x' and 6.804 with 4x. Therefore, the initial formula is quite simplified:

$$\frac{(4x)^6*x^-13}{2^19*(2x)^-7}$$

Afterwards, it takes 20 seconds to arrive to the final result

How are you even supposed to know that 2*1.701 = 3.402??? I'm supposed to hand-multiply that out on the test?
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_________________ Re: (6.804)^6*(1.701)^-13/(2)^19*(3.402)^-7   [#permalink] 29 Apr 2019, 14:05

# (6.804)^6*(1.701)^-13/(2)^19*(3.402)^-7   