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06 Sep 2019, 10:55
Kudos
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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:
35%
(medium)
Question Stats:
65% (01:32) correct
35%
(01:28)
wrong
based on 103
sessions
History
Date
Time
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Not Attempted Yet
Is the product of the three nonzero numbers a, b, and c divisible by 81?
(1) The product of the three numbers a, b, and c is a multiple of 27.
(2) None of the three numbers a, b, and c is divisible by 9.
(1) The product of the three numbers a, b, and c is a multiple of 27.
(2) None of the three numbers a, b, and c is divisible by 9.
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09 Sep 2019, 00:56
Kudos
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(1) The product of the three numbers a, b, and c is a multiple of 27.
If the numbers are 1,2,27 - abc is not divisible by 81
If the numbers are 1,3,27 - abc is divisible by 81
1 is insufficient
(2) None of the three numbers a, b, and c is divisible by 9.
If none of the three numbers is divisible by 9, abc is not divisible by
If abc is divisible by 81, then abc must be divisible by 9
Therefore we can conclude that abc is not divisible by 81
2 is sufficient
Answer is (B)
If the numbers are 1,2,27 - abc is not divisible by 81
If the numbers are 1,3,27 - abc is divisible by 81
1 is insufficient
(2) None of the three numbers a, b, and c is divisible by 9.
If none of the three numbers is divisible by 9, abc is not divisible by
If abc is divisible by 81, then abc must be divisible by 9
Therefore we can conclude that abc is not divisible by 81
2 is sufficient
Answer is (B)
03 Mar 2020, 03:42
Kudos
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Bunuel
Solution
Step 1: Analyse Question Stem
• a, b, and c are non-zero numbers.
We need to find, whether the product of a, b, and c is divisible by 81 or not.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The product of the three numbers a, b, and c is a multiple of 27.
- • \(a*b*c = 27*n\), where n is an integer.
• If n is a multiple of 3, then \(27*n\) is divisible by 81.
• If n is not a multiple of 3, then \(27*n\) is not divisible by 81.
Statement 2: None of the three numbers a, b, and c is divisible by 9.
- • Since none of the numbers are divisible by 9, we need to check if one or two or all integers are divisible by 3, will that make the product divisible by 81 or not.
- o Best case, if all these are divisible by 3, then we can say that \(abc = 3*3*3*x\) , where x is an integer, which is not a multiple of 3.
- The maximum power of 3 which the product of number a, b, and c can contain is 3.
