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Is the four-digit positive integer a,bc6 divisible by 4?

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Is the four-digit positive integer a,bc6 divisible by 4?

by Max@Math Revolution » Tue Mar 26, 2019 11:55 pm

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[GMAT math practice question]

Is the four-digit positive integer a,bc6 divisible by 4?

1) ac is an odd number
2) bc is an even number
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Mar 28, 2019 11:08 pm

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The number a,bc6 is divisible by 4 precisely when c is an odd number.
Condition 1) tells us that both a and c are odd numbers. Thus, condition 1) is sufficient.

Condition 2)
If a = 1, b = 2, c = 1, then 1216 is divisible by 4 and the answer is 'yes'.
If a = 1, b = 1, c = 2, then 1126 is not divisible by 4 and the answer is 'no'.
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

Therefore, A is the answer.
Answer: A
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by deloitte247 » Wed Apr 03, 2019 1:06 pm

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For statement 1: ac is an odd number.
So, if c= odd number, then a,bc6 is divisible by 4
If c = 1, then c6 =16 => divisible by 4
If c = 3, then c6 = 36 => divisible by 4
If c = 5, then c6 = 56 => divisible by 4
Hence, statement 1 is sufficient

For statement 2: bc is an even number
if c = 2, then c6 = 26 => not divisible by 4
if c = 4, then c6 = 46 => not divisible by 4
if c = 6, then c6 = 66 => not divisible by 4
Therefore, statement 2 is not sufficient

Conclusively, option A is the correct answer to this question.
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