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Let A=2^50, B=3^30, and C=4^20. Which of the following is tr

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by Max@Math Revolution » Sun Nov 25, 2018 11:26 pm

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[Math Revolution GMAT math practice question]

Let A=2^50, B=3^30, and C=4^20. Which of the following is true?

A. A < B < C
B. A < C < B
C. B < A < C
D. B < C < A
E. C < B < A
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by fskilnik@GMATH » Mon Nov 26, 2018 3:55 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

Let A=2^50, B=3^30, and C=4^20. Which of the following is true?

A. A < B < C
B. A < C < B
C. B < A < C
D. B < C < A
E. C < B < A
$$?\,\,\,:\,\,\,A\,,\,\,B\,\,,\,\,C\,\,\,{\rm{increasing}}\,\,{\rm{order}}\,$$
$$\left. \matrix{
A = {2^{50}} = {\left( {{2^5}} \right)^{10}} = {32^{10}} \hfill \cr
B = {3^{30}} = {\left( {{3^3}} \right)^{10}} = {27^{10}}\,\,\, \hfill \cr
C = {4^{20}} = {\left( {{4^2}} \right)^{10}} = {16^{10}} \hfill \cr} \right\}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,C < B < A\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\rm{E}} \right)$$

This solution follows 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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by Max@Math Revolution » Wed Nov 28, 2018 12:19 am
=>

A = 2^50 = (2^5)^10 = (32)^10
B = 3^30 = (3^3)^10 = (27)^10
C = 4^20 = (4^2)^10 = (16)^10

Thus, (16)^10 < (27)^10 < (32)^10 and C < B < A.

Therefore, the answer is E.
Answer: E
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