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19 Nov 2015, 17:43
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D
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Difficulty:
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Question Stats:
73% (01:56) correct
27%
(01:53)
wrong
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QUANT 4-PACK SERIES Problem Solving Pack 4 Question 3 If a, b and c are consecutive...
If a, b and c are consecutive positive integers and a < b < c, then what is the minimum possible value of
\(\frac{3^{2bc}}{3^{2ab}}\)
A) 81
B) 2,187
C) 3,300
D) 6,561
E) 19,683
48 Hour Window Answer & Explanation Window
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OA, and explanation will be posted after the 48 hour window closes.
This question is part of the Quant 4-Pack series
Scroll Down For Official Explanation
If a, b and c are consecutive positive integers and a < b < c, then what is the minimum possible value of
\(\frac{3^{2bc}}{3^{2ab}}\)
A) 81
B) 2,187
C) 3,300
D) 6,561
E) 19,683
48 Hour Window Answer & Explanation Window
Earn KUDOS! Post your answer and explanation.
OA, and explanation will be posted after the 48 hour window closes.
This question is part of the Quant 4-Pack series
Scroll Down For Official Explanation
19 Nov 2015, 18:28
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If a, b and c are consecutive positive integers and a < b < c, then what is the minimum possible value of
\(3^{2bc}\) / \(3^{2ab}\)
A) 81
B) 2,187
C) 3,300
D) 6,561
E) 19,683
assume a=1, b=2, c=3 for minimum possible value
the equation then becomes \(3^{12}\) / \(3^{4}\)
=\(3^{8}\)
calculating only for the units digit to save time, we can then see that 1 is the last units digit of \(3^{8}\)
Answer: D
\(3^{2bc}\) / \(3^{2ab}\)
A) 81
B) 2,187
C) 3,300
D) 6,561
E) 19,683
assume a=1, b=2, c=3 for minimum possible value
the equation then becomes \(3^{12}\) / \(3^{4}\)
=\(3^{8}\)
calculating only for the units digit to save time, we can then see that 1 is the last units digit of \(3^{8}\)
Answer: D
ENGRTOMBA2018
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23 Nov 2015, 09:26
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EMPOWERgmatRichC
\(\frac {3^{2bc}}{3^{2ab}} = ?\) ---> \(\frac {3^{2bc}}{3^{2ab}} = 3^{2bc-2ab} = 3^{2b(c-a)}\)and as a,b,c are consecutive integers, c-a will always be = 2.
Thus, \(3^{2b(c-a)} = 3^{4b}\) and as all 3 a,b,c are POSITIVE integers, minimum value of a=1, making b =2 ---> \(3^{4b} = 3^8 = 65\)61. D is the correct answer.
