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What is the largest value?

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What is the largest value?  [#permalink]

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New post 12 Dec 2016, 08:40
2
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

25% (02:18) correct 75% (02:00) wrong based on 130 sessions

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What is the largest value?  [#permalink]

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New post Updated on: 14 Dec 2016, 03:06
5
6
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) \(5^{22}\)

\(5^2 < 3^3\)

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

Hence answer B.

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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New post 12 Dec 2016, 09:33
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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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New post 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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