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08 Sep 2019, 18:48
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
73% (02:36) correct
27%
(02:38)
wrong
based on 276
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[GMAT math practice question]
\(a, b\) and \(c\) are different positive integers between \(1\) and \(9\), inclusive. The \(5\)-digit integer \(ababc\) is a multiple of \(12\), and the \(2\)-digit number \(ab\) is equal to \(c^2\). What is the value of the \(3\)-digit number \(abc\)?
\(A. 164\)
\(B. 255\)
\(C. 366\)
\(D. 497\)
\(E. 648\)
\(a, b\) and \(c\) are different positive integers between \(1\) and \(9\), inclusive. The \(5\)-digit integer \(ababc\) is a multiple of \(12\), and the \(2\)-digit number \(ab\) is equal to \(c^2\). What is the value of the \(3\)-digit number \(abc\)?
\(A. 164\)
\(B. 255\)
\(C. 366\)
\(D. 497\)
\(E. 648\)
08 Sep 2019, 18:55
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=>
Since \(c^2=ab\), the possibilities for \(a, b\) and \(c\) are given by \(4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64\) and \(9^2=81.\)
So, the possible values of \(ababc\) are \(16164, 25255, 36366, 49497, 64648\) and \(81819.\)
Since \(ababc\) is a multiple of \(12\), \(ababc\) is both a multiple of \(3\) and a multiple of \(4\). \(16164\) and \(64648\) are the only multiples of \(4\) in the list of values of \(ababc,\) because their last two digits are multiples of \(4\). Of these, only \(16164\) is a multiple of \(3\), since the sum of its digits is \(18\), which is a multiple of \(3.\)
Therefore, \(abc\) is \(164\), and A is the answer.
Answer: A
Since \(c^2=ab\), the possibilities for \(a, b\) and \(c\) are given by \(4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64\) and \(9^2=81.\)
So, the possible values of \(ababc\) are \(16164, 25255, 36366, 49497, 64648\) and \(81819.\)
Since \(ababc\) is a multiple of \(12\), \(ababc\) is both a multiple of \(3\) and a multiple of \(4\). \(16164\) and \(64648\) are the only multiples of \(4\) in the list of values of \(ababc,\) because their last two digits are multiples of \(4\). Of these, only \(16164\) is a multiple of \(3\), since the sum of its digits is \(18\), which is a multiple of \(3.\)
Therefore, \(abc\) is \(164\), and A is the answer.
Answer: A
General Discussion
08 Sep 2019, 18:56
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MathRevolution
Given:
1. \(a, b\) and \(c\) are different positive integers between \(1\) and \(9\), inclusive.
2. The \(5\)-digit integer \(ababc\) is a multiple of \(12\), and the \(2\)-digit number \(ab\) is equal to \(c^2\).
Asked: What is the value of the \(3\)-digit number \(abc\)?
\(A. 164\)
16=c^2
ababc =
16164
Is a multiple of 3&4=12
\(B. 255\)
\(C. 366\)
\(D. 497\)
\(E. 648\)
IMO A
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