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If a=3^3*2^9, b= 3^6 *7^3, c = 2^6*5^3, which of the following is true

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Tuck School Moderator
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If a=3^3*2^9, b= 3^6 *7^3, c = 2^6*5^3, which of the following is true  [#permalink]

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New post 18 Feb 2019, 07:17
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (02:08) correct 34% (01:49) wrong based on 32 sessions

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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

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Re: If a=3^3*2^9, b= 3^6 *7^3, c = 2^6*5^3, which of the following is true  [#permalink]

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New post 18 Feb 2019, 07:41
1
PeepalTree wrote:
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


\(a=3^3*2^9, b= 3^6 *7^3, c = 2^6*5^3\)

Comparing a and b

\(a/b = 2^9 / 3^3*7^3 = 512 / (27*343)\)

i.e. a < b (Options C and E ARE OUT)



Comparing a and c

\(a/c = 3^3*2^3 / 5^3 = 27*8 /125\)

i.e. a > c (Options A and D ARE OUT)

Answer: Option B
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Re: If a=3^3*2^9, b= 3^6 *7^3, c = 2^6*5^3, which of the following is true  [#permalink]

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New post 18 Feb 2019, 14:22
2
You can instantly see that b > c, because the exponents are identical in b and c, but the bases are larger in b. So only B or D could be right, and to decide between them, we just need to work out whether a > c or c > a.

a = 2^9 * 3^3
c = 2^6 * 5^3

Divide both by 2^6:

a/2^6 = 2^3 * 3^3 = 6^3
c/2^6 = 5^3

so clearly a > c.
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Re: If a=3^3*2^9, b= 3^6 *7^3, c = 2^6*5^3, which of the following is true   [#permalink] 18 Feb 2019, 14:22
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