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Let A=2^50, B=3^30, and C=5^20. Which of the following is true?

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Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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New post 19 Feb 2018, 23:38
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A
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C
D
E

Difficulty:

  45% (medium)

Question Stats:

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[GMAT math practice question]

Let \(A=2^{50,} B=3^{30}\), and \(C=5^{20}\). Which of the following is true?

A. A<B<C
B. A<C<B
C. C<A<B
D. B<C<A
E. C<B<A

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Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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New post 20 Feb 2018, 02:48
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MathRevolution wrote:
[GMAT math practice question]

Let \(A=2^{50,} B=3^{30}\), and \(C=5^{20}\). Which of the following is true?

A. A<B<C
B. A<C<B
C. C<A<B
D. B<C<A
E. C<B<A


HCF of \(50\), \(30\) & \(20\) is \(10\), so arrange the numbers to the power of \(10\) to get a clear picture

\(A=2^{50}=(2^5)^{10}=32^{10}\)

\(B=3^{30}=(3^3)^{10}=27^{10}\)

\(C=5^{20}=(5^2)^{10}=25^{10}\)

Clearly, \(A>B>C\)

Option E
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Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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New post 20 Feb 2018, 02:46
MathRevolution wrote:
[GMAT math practice question]

Let \(A=2^{50,} B=3^{30}\), and \(C=5^{20}\). Which of the following is true?

A. A<B<C
B. A<C<B
C. C<A<B
D. B<C<A
E. C<B<A



Unconventional method

No of digits in A= 2^50 = 50 log 2 ( here log 2 is of the base 10 ) = 50 x 0.3010 = 15.xx = 15 + 1 = 16 digits
No of digits in B = 3^30 = 30 log 3 = 30 x .4771 = 14.xx = 14 +1 = 15 digits
No of digits in C = 5^20 = 20 log 5 = 20 x 0.69 = 13.xx = 14 digits

Now greater the digits greater the number ( in positive numbers)

thus C<B<A / A > B>C

(E) imo


PS- don't try this on the gmat if you are not sure of Log values :)
I'm sure there are other ways to solve this but this was the only method I could think of
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Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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New post 20 Feb 2018, 02:50
Hatakekakashi wrote:
MathRevolution wrote:
[GMAT math practice question]

Let \(A=2^{50,} B=3^{30}\), and \(C=5^{20}\). Which of the following is true?

A. AB. AC. CD. BE. C


Unconventional method

No of digits in A= 2^50 = 50 log 2 ( here log 2 is of the base 10 ) = 50 x 0.3010 = 15.xx = 15 + 1 = 16 digits
No of digits in B = 3^30 = 30 log 3 = 30 x .4771 = 14.xx = 14 +1 = 15 digits
No of digits in C = 5^20 = 20 log 5 = 20 x 0.69 = 13.xx = 14 digits

Now greater the digits greater the number ( in positive numbers)

thus C B>C

(E) imo


PS- don't try this on the gmat if you are not sure of Log values :)
I'm sure there are other ways to solve this but this was the only method I could think of


hi Hatakekakashi

Truly unconventional :-D :-D

I am sure hardly anyone of us would remember log values at this age ;) ;)
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Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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New post 20 Feb 2018, 02:51
Bunuel :-> Similar Que

https://gmatclub.com/forum/let-a-5-30-b ... fl=similar

Let A=2^50, B=3^30, and C=5^20. Which of the following is true?

A=32^10, B=27^10 & C=25^10

E. C
A. AB. AC. CD. BE. C_________________

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Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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New post 20 Feb 2018, 02:54
niks18 wrote:

hi Hatakekakashi

Truly unconventional :-D :-D

I am sure hardly anyone of us would remember log values at this age ;) ;)



haha :D well that's true

but squares 1-50
cubes 1 - 15
0 is not positive
log 1 to 5
1 is not prime

i do remember these things most of the times
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Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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New post Updated on: 20 Feb 2018, 06:55
MathRevolution wrote:
[GMAT math practice question]

Let \(A=2^{50,} B=3^{30}\), and \(C=5^{20}\). Which of the following is true?

A. A<B<C
B. A<C<B
C. C<A<B
D. B<C<A
E. C<B<A


We can write as -
\(A = (1024)^{5}, B = (729)^{5}, C = (625)^{5}

Hence, A>B>C\)
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Originally posted by rahul16singh28 on 20 Feb 2018, 06:47.
Last edited by rahul16singh28 on 20 Feb 2018, 06:55, edited 1 time in total.
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Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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New post 20 Feb 2018, 06:50
rahul16singh28 wrote:
MathRevolution wrote:
[GMAT math practice question]

Let \(A=2^{50,} B=3^{30}\), and \(C=5^{20}\). Which of the following is true?

A. A<B<C
B. A<C<B
C. C<A<B
D. B<C<A
E. C<B<A


We can write as -
\(A = (1024)^{50}, B = (729)^{5}, C = (625)^{5}

Hence, A>B>C\)


1024^5 you mean?

Posted from my mobile device

Posted from my mobile device
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Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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New post 20 Feb 2018, 07:39
Hatakekakashi wrote:
rahul16singh28 wrote:
MathRevolution wrote:
[GMAT math practice question]

Let \(A=2^{50,} B=3^{30}\), and \(C=5^{20}\). Which of the following is true?

A. A<B<C
B. A<C<B
C. C<A<B
D. B<C<A
E. C<B<A


We can write as -
\(A = (1024)^{50}, B = (729)^{5}, C = (625)^{5}

Hence, A>B>C\)


1024^5 you mean?

Posted from my mobile device

Posted from my mobile device


1024^5 you mean?

(2^10)^5=1024^5
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Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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New post 22 Feb 2018, 01:10
=>

If we wish to compare these numbers, we need to either make their bases the same or make their exponents the same. In this case, it is easiest to make all exponents the same as follows:
\(A=2^{50} = (2^5)^{10} = 32^{10}\)
\(B=3^{30} = (3^3)^{10} = 27^{10}\)
\(C=5^{20} = (5^2)^{10} = 25^{10}\)

Since \(32 > 27 > 25\), we must have \(A > B > C\).

Therefore, the answer is E.

Answer: E
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Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true? &nbs [#permalink] 22 Feb 2018, 01:10
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