If 0.845 is an approximate solution for the equation 10^x =

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Fri Mar 08, 2019 7:17 am

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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

Answer: [spoiler]_____(C)__[/spoiler]

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Source: Beat The GMAT — Problem Solving | Fri Mar 08, 2019 7:17 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

If 0.845 is an approximate solution for the equation 10^x =

by fskilnik@GMATH » Fri Mar 08, 2019 10:10 am

fskilnik@GMATH 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

$${10^{0.845}} \cong 7$$
$${7^{x + 2}} = 70$$
$$?\,\, \cong x\,\,\,\,\,\,$$

$${7^{x + 2}} = 7 \cdot 10\,\,\,\,\, \Rightarrow \,\,\,\,\,{7^{x + 1}} = 10\,\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {{7^{x + 1}}} \right)^{0.845}} = {10^{0.845}}\,\, \cong \,\,\,7$$
$${7^{0.845\left( {x + 1} \right)}} = {7^1}\,\,\,\, \Rightarrow \,\,\,\,\,x = {{1000} \over {845}} - 1 = {{155} \over {845}} = {{31} \over {169}}\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{C}} \right)$$

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

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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