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# Which of the following expressions has the largest value?

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Math Expert
Joined: 02 Sep 2009
Posts: 54369
Which of the following expressions has the largest value?  [#permalink]

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23 Jun 2015, 23:29
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Difficulty:

5% (low)

Question Stats:

81% (01:08) correct 19% (01:13) wrong based on 224 sessions

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Which of the following expressions has the largest value?

A. $$(3^4)^{13}$$

B. $$((3^{30})^{12})^{\frac{1}{10}}$$

C. $$3^{30}+3^{30}+3^{30}$$

D. $$4*3^{51}$$

E. $$(3^{100})^{\frac{1}{2}}$$

Kudos for a correct solution.

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Re: Which of the following expressions has the largest value?  [#permalink]

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23 Jun 2015, 23:41
1
D

a: 3^52
b:3^36
c:3^31
d:4*3^51
e:3^50

Between a and d - A: 3*3^51 D: 4*3^51, hence D>A.
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Re: Which of the following expressions has the largest value?  [#permalink]

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24 Jun 2015, 02:40
Simplifying all the options we get the following

A) 3^52
B) 3^36
C) 3^31
D) 3^52 + 3^51
E) 3^50

Answer: D
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Re: Which of the following expressions has the largest value?  [#permalink]

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24 Jun 2015, 10:21
Arranging Option we get
A = (3^51)*3
B=3^ 30*12/10=3^12*3=3^36
C= 3^31
D = (3^51)*4
E = 3^50
Option B & C are too small to be compared, A>E now final comparison between A and D. and D >A
Hence answer is D
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Re: Which of the following expressions has the largest value?  [#permalink]

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25 Jun 2015, 10:21
Bunuel wrote:
Which of the following expressions has the largest value?

A. $$(3^4)^{13}$$

B. $$((3^{30})^{12})^{\frac{1}{10}}$$

C. $$3^{30}+3^{30}+3^{30}$$

D. $$4*3^{51}$$

E. $$(3^{100})^{\frac{1}{2}}$$

Kudos for a correct solution.

Let us reduce the options to the powers of 3
A=3^52
B=3^36
C=3^31
D=4*3^51
E=3^20

Between A and D, A=(3^51)*3 and D=(3^51)*4
Answer D
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Re: Which of the following expressions has the largest value?  [#permalink]

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26 Jun 2015, 07:28
Bunuel wrote:
Which of the following expressions has the largest value?

A. $$(3^4)^{13}$$

B. $$((3^{30})^{12})^{\frac{1}{10}}$$

C. $$3^{30}+3^{30}+3^{30}$$

D. $$4*3^{51}$$

E. $$(3^{100})^{\frac{1}{2}}$$

Kudos for a correct solution.

A -> 3^52
B -> 3^36
c -> 3^91
D -> (3+1) 3^51 = 3^52 + 3^51
E -> 3^50

Between 3^91 and 3^52 + 3^51 i think 3^52 + 3^51 is bigger. Hence Option D
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Re: Which of the following expressions has the largest value?  [#permalink]

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26 Jun 2015, 08:13
I will go with D. Needs bit of rearrangement.
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Joined: 24 Aug 2017
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Re: Which of the following expressions has the largest value?  [#permalink]

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25 Aug 2017, 00:02
i know this seems like a dumb question but how do you get 3^30 +3^30+3^30 = 3^31?
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Posts: 54369
Re: Which of the following expressions has the largest value?  [#permalink]

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25 Aug 2017, 00:04
lunarchick wrote:
i know this seems like a dumb question but how do you get 3^30 +3^30+3^30 = 3^31?

$$3^{30} +3^{30}+3^{30} = 3*3^{30}=3^{30+1}=3^{31}$$.

Hope it's clear.
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Re: Which of the following expressions has the largest value?  [#permalink]

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25 Aug 2017, 00:10
Bunuel
thank you so much. I feel so foolish...it was so easy
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Re: Which of the following expressions has the largest value?  [#permalink]

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28 Aug 2017, 08:29
Each option can be simplified as power of 3

A) 3^52
B) 3^36
C) 3^31
D) 3^52 + 3^51
E) 3^50
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Re: Which of the following expressions has the largest value?   [#permalink] 28 Aug 2017, 08:29
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# Which of the following expressions has the largest value?

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