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16 Nov 2021, 07:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
27% (02:02) correct
73%
(01:53)
wrong
based on 133
sessions
History
Date
Time
Result
Not Attempted Yet
What is the largest value?
A. \(81^8\)
B. \(27^{11}\)
C. \(6^{19}\)
D. \(2^{49}\)
E. \(5^{22}\)
A. \(81^8\)
B. \(27^{11}\)
C. \(6^{19}\)
D. \(2^{49}\)
E. \(5^{22}\)
17 Nov 2021, 18:31
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Bunuel
A - 3^32
B - 3 ^33
C - 3^19 * 2 ^19
2 ^ 19 = (2^3)^6 * 2
= (9-1)^6 * 2
Now 9^6 * 2 itself is less than 3^13. So the expression (9-1)^6 * 2
is definitely less than 3^13. Option C is less than 3 ^32
D - 2^49
= 8 ^ 16 * 2
= (9-1) ^16 * 2
9 ^ 16 = 3 ^32
(9-1) ^16 * 2 will be definitely less than 3 ^33
E - 5 ^22 = 25 ^11 = (27 - 2) ^11 less than 3 ^33
Option B
18 Nov 2021, 04:38
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Bunuel
Compare similar terms in terms of base or power
B and E: \(27^{11} \ \ and \ \ 5^{22}=25^{11}\)..........Clearly B is greater
A and B: \(27^{11}=3^{33} \ \ and \ \ 81^{8}=3^{32}\)..........Again B is greater
A and D: \(81^{8}=9^{16} \ \ and \ \ 2^{49}=2^{48}*2=8^{16}*2\)
Is \(9^{16}>8^{16}*2?.......\frac{9}{8}^16>2.......1.1^{16}>2...yes\)..........Again B is greater than D
A and D: \(27^{11}=3^{33} \ \ and \ \ 6^{19}=2^{19}*3^{19}\)
Is \(3^{33}>2^{19}*3^{19}......3^{14}>2^{19}.......9^7>8^6*2...yes\)..........Again B is greater
B
