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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Let A=2^50, B=3^30, and C=5^20. Which of the following is true?

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Math Revolution GMAT Instructor V
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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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Difficulty:   45% (medium)

Question Stats: 58% (01:28) correct 42% (01:50) wrong based on 99 sessions

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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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5
1
1
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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GMAT 1: 710 Q49 V36 Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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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

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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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  I am sure hardly anyone of us would remember log values at this age  Director  V
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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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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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Current Student P
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GMAT 1: 710 Q49 V36 Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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niks18 wrote:

hi Hatakekakashi

Truly unconventional  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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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, 07:47.
Last edited by rahul16singh28 on 20 Feb 2018, 07:55, edited 1 time in total.
Current Student P
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GMAT 1: 710 Q49 V36 Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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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
Director  V
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Location: India
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GPA: 3.35
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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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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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=>

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.

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GMAT 1: 680 Q44 V38 Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?  [#permalink]

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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

We can write this as (2^5)^10 , (3^3)^10, (5^2)^10 --> A= 32^10, B= 27^10, C= 25^10
From this we can see that C<B<A Re: Let A=2^50, B=3^30, and C=5^20. Which of the following is true?   [#permalink] 20 Apr 2019, 22:41
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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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