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# If x is a 5-digit integer, abc,de, is it divisible by 4? 1) d is an e

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6517
GMAT 1: 760 Q51 V42
GPA: 3.82
If x is a 5-digit integer, abc,de, is it divisible by 4? 1) d is an e  [#permalink]

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02 Nov 2017, 00:08
00:00

Difficulty:

25% (medium)

Question Stats:

77% (00:59) correct 23% (01:00) wrong based on 65 sessions

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[GMAT math practice question]

If x is a 5-digit integer, abc,de, is it divisible by 4?

1) d is an even number.
2) e is an even number.

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Re: If x is a 5-digit integer, abc,de, is it divisible by 4? 1) d is an e  [#permalink]

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02 Nov 2017, 08:35
MathRevolution wrote:
[GMAT math practice question]

If x is a 5-digit integer, abc,de, is it divisible by 4?

1) d is an even number.
2) e is an even number.

any digit number will be div by 4 if the LAST two digits are div by 4

so abcde will be div by 4 if de is div by 4....

1) d is an even number.
d is 2... 24 is div but 22 is not
insuff

2) e is an even number.
e is 4.... 24 is div but 34 is NOT
insuff

combined
22 is not div but 44 is
insuff

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6517
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x is a 5-digit integer, abc,de, is it divisible by 4? 1) d is an e  [#permalink]

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05 Nov 2017, 17:21
=>
Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

We can check the divisibility by 4 with the last two digits. The last two digit number is 10d + e. Since we have 2 variables and 0 equation, C is most likely to be the answer.
Condition 1) & 2)
d = 2, e = 4 ➔ 24 is divisible by 4.
d = 4, e = 4 ➔ 44 is not divisible by 4.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer, hence using 1) and 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.
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Re: If x is a 5-digit integer, abc,de, is it divisible by 4? 1) d is an e &nbs [#permalink] 05 Nov 2017, 17:21
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