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# What is the largest value?

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Senior CR Moderator
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What is the largest value?  [#permalink]

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12 Dec 2016, 08:40
2
6
00:00

Difficulty:

95% (hard)

Question Stats:

23% (02:23) correct 77% (01:57) wrong based on 94 sessions

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What is the largest value?

A. $$81^8$$

B. $$27^{11}$$

C. $$6^{19}$$

D. $$2^{49}$$

E. $$5^{22}$$

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What is the largest value?  [#permalink]

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Updated on: 14 Dec 2016, 03:06
4
4
A) $$81^8 = (3^4)^8 = 3^{32}$$

B) $$27^{11} = (3^3)^{11} = 3^{33}$$

C) $$6^{19} = 2^{19}*3^{19}$$

$$2^3 < 3^2 ------- 6^{19} < 2*(3^2)^6*3^{19}= 2* 3^{12}*3^{19} = 2*3^{31}$$

$$3^{32} > 2*3^{31} > 6^{19}$$

D) $$2^{49}$$ same logic $$(2^3)^{16}*2 < (3^2)^{16}*2 = 3^{32}*2$$

$$3^{33} > 2*3^{32} > 2^{49}$$

E) $$5^{22}$$

$$5^2 < 3^3$$

$$(5^2)^{11} < (3^3)^{11} = 3^{33}$$

Originally posted by vitaliyGMAT on 12 Dec 2016, 09:29.
Last edited by vitaliyGMAT on 14 Dec 2016, 03:06, edited 5 times in total.
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Re: What is the largest value?  [#permalink]

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12 Dec 2016, 09:33
1
nguyendinhtuong wrote:
What is the largest value?

A. $$81^8$$

B. $$27^{11}$$

C. $$6^{19}$$

D. $$2^{49}$$

E. $$5^{22}$$

(A) $$81^8 = 3^{32}$$

(B) $$27^{11} = 3^{33}$$

(C) $$6^{19} = 3^{19}*2^{19}$$

(D) $$2^{49} = ( 3 - 1 )^{49}$$

(E) $$5^{22} = ( 3 + 2 )^{22}$$

Largest value among the given options is the one with the highest power of 3, that's (B) $$27^{11}$$
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Re: What is the largest value?  [#permalink]

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12 Mar 2019, 20:52
Your logic seems Incorrect, Can you explain this.

3^4 =81

(3+k)^3 = can be bigger than 81 or smaller depending upon k .

Coz (3+4)^3 = 243 and 243 > 81 but (3+2)^3 = 125 i.e greater than 81 or (3+1)^3 = 64 i.e < 81

Abhishek009 wrote:
nguyendinhtuong wrote:
What is the largest value?

A. $$81^8$$

B. $$27^{11}$$

C. $$6^{19}$$

D. $$2^{49}$$

E. $$5^{22}$$

(A) $$81^8 = 3^{32}$$

(B) $$27^{11} = 3^{33}$$

(C) $$6^{19} = 3^{19}*2^{19}$$

(D) $$2^{49} = ( 3 - 1 )^{49}$$

(E) $$5^{22} = ( 3 + 2 )^{22}$$

Largest value among the given options is the one with the highest power of 3, that's (B) $$27^{11}$$

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Re: What is the largest value?   [#permalink] 12 Mar 2019, 20:52
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