GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 03:15

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If 0.845 is an approximate solution for the equation 10^x=7, which

Author Message
TAGS:

### Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
If 0.845 is an approximate solution for the equation 10^x=7, which  [#permalink]

### Show Tags

Updated on: 11 Mar 2019, 04:41
00:00

Difficulty:

(N/A)

Question Stats:

59% (02:53) correct 41% (02:52) wrong based on 37 sessions

### HideShow timer Statistics

GMATH practice exercise (Quant Class 3)

If 10^0.845 is approximately equal to 7, which of the following fractions is closest to the solution of the equation 7^(x+2) = 70?

(A) 29/211
(B) 19/107
(C) 31/169
(D) 43/211
(E) 53/211

P.S.: we thank kgmat12 for the question stem wording improvement!

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Originally posted by fskilnik on 08 Mar 2019, 08:33.
Last edited by fskilnik on 11 Mar 2019, 04:41, edited 1 time in total.
Manager
Joined: 21 Feb 2019
Posts: 125
Location: Italy
Re: If 0.845 is an approximate solution for the equation 10^x=7, which  [#permalink]

### Show Tags

08 Mar 2019, 10:53
2
$$10^x = 7$$

$$10 = 7^\frac{1}{x}$$

Now, let's look for the second one:

$$7^x * 7^2 = 7 * 10$$

$$7^x * 7 = 10$$

Compare:

$$x + 1 = \frac{1}{x}$$

Remember that $$\frac{1}{x} = \frac{1}{0.845}$$

Hence $$x = \frac{1 - 0.845}{0.845} = \frac{155}{845} = \frac{31}{169}$$

_________________
If you like my post, Kudos are appreciated! Thank you.

MEMENTO AUDERE SEMPER
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If 0.845 is an approximate solution for the equation 10^x=7, which  [#permalink]

### Show Tags

08 Mar 2019, 11:21
fskilnik wrote:
GMATH practice exercise (Quant Class 3)

If 0.845 is an approximate solution for the equation 10^x = 7, which of the following fractions is closest to the solution of 7^(x+2) = 70?

(A) 29/211
(B) 19/107
(C) 31/169
(D) 43/211
(E) 53/211
Very nice, lucajava! Kudos and thanks for joining!

Let me present our official solution:

$${10^{0.845}} \cong 7$$

$${7^{x + 2}} = 70$$

$$?\,\, \cong x$$

$${7^{x + 2}} = 7 \cdot 10\,\,\,\,\, \Rightarrow \,\,\,\,\,{7^{x + 1}} = 10\,\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {{7^{x + 1}}} \right)^{0.845}} = {10^{0.845}}\,\, \cong \,\,\,7$$

$${7^{0.845\left( {x + 1} \right)}} = {7^1}\,\,\,\, \Rightarrow \,\,\,\,\,x = {{1000} \over {845}} - 1 = {{155} \over {845}} = {{31} \over {169}}\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{C}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Intern
Joined: 24 Dec 2018
Posts: 4
Re: If 0.845 is an approximate solution for the equation 10^x=7, which  [#permalink]

### Show Tags

10 Mar 2019, 18:03
1
The question is confusing. The same variable x is used twice and has two different values?
Should we expect Qs like this on the exam?
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If 0.845 is an approximate solution for the equation 10^x=7, which  [#permalink]

### Show Tags

10 Mar 2019, 18:16
kgmat12 wrote:
The question is confusing. The same variable x is used twice and has two different values?
Should we expect Qs like this on the exam?

Hi, kgmat12 !

Thinking twice, I believe you are right. I mean, although the question stem (seems to me) perfectly understandable ("x" is a dummy variable), I guess GMAT´s wording would be (better and) something like that:

If 10^0.845 is approximately equal to 7, which of the following fractions is closest to the solution of the equation 7^(x+2) = 70?

(I have changed the question stem of this problem in our course, also. Thanks and kudos for the contribution!)

Regards and success in your studies,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: If 0.845 is an approximate solution for the equation 10^x=7, which   [#permalink] 10 Mar 2019, 18:16
Display posts from previous: Sort by