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27 Jun 2022, 19:15
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B
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Difficulty:
55%
(hard)
Question Stats:
68% (02:05) correct
32%
(02:00)
wrong
based on 318
sessions
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Date
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Not Attempted Yet
If \(a=3^3*2^9\), \(b= 3^6 *7^3\), \(c = 2^6*5^3\), which of the following is true?
A. \(c>b>a\)
B. \(b>a>c\)
C. \(a>c>b\)
D. \(b>c>a\)
E. \(c>a>b\)
A. \(c>b>a\)
B. \(b>a>c\)
C. \(a>c>b\)
D. \(b>c>a\)
E. \(c>a>b\)
27 Jun 2022, 19:32
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Given
a = 3^3 * 2^9 = 27 * 2^9 = (27 * 2^3) * 2^6 = (27 * 8) * 2^6 = 216 * 2^6
b = 3^6 * 7^3 = 343 * 3^6
c = 2^6 * 5^3 = 125 * 2^6
Now comparing b to c we see that b = 343 * 3^6 and c = 125 * 2^6. We see that term 343 in b is greater than 125 in c and also term 3^6 is greater than term 2^6. So it is clear that b>c
Similarly comparing a to b we see that a = 216 * 2^6 and b = 343 * 3^6. From this also we clearly see that term 343 in b is greater than 216 in a and term 3^6 in b is also greater than 2^6 in a. So clearly b>a
Thus combining we have, b>a>c
Hence answer choice B
a = 3^3 * 2^9 = 27 * 2^9 = (27 * 2^3) * 2^6 = (27 * 8) * 2^6 = 216 * 2^6
b = 3^6 * 7^3 = 343 * 3^6
c = 2^6 * 5^3 = 125 * 2^6
Now comparing b to c we see that b = 343 * 3^6 and c = 125 * 2^6. We see that term 343 in b is greater than 125 in c and also term 3^6 is greater than term 2^6. So it is clear that b>c
Similarly comparing a to b we see that a = 216 * 2^6 and b = 343 * 3^6. From this also we clearly see that term 343 in b is greater than 216 in a and term 3^6 in b is also greater than 2^6 in a. So clearly b>a
Thus combining we have, b>a>c
Hence answer choice B
BhavyaJha
Joined: 24 Mar 2021
Last visit: 15 Sep 2022
Posts: 11
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Location: India
Schools: S.P.Jain Institute (A)
GMAT 1: 610 Q46 V28
03 Jul 2022, 09:01
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