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a, b and c are different positive integers between 1 and 9,

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a, b and c are different positive integers between 1 and 9,

by Max@Math Revolution » Sun Sep 08, 2019 5:26 pm
[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
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by Max@Math Revolution » Sun Sep 08, 2019 5:28 pm
=>

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
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