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# If a is an integer, is a-b an integer?

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Math Revolution GMAT Instructor
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If a is an integer, is a-b an integer? [#permalink]

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25 Oct 2017, 01:18
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Difficulty:

35% (medium)

Question Stats:

70% (00:47) correct 30% (01:06) wrong based on 57 sessions

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[GMAT math practice question]

If a is an integer, is a-b an integer?

1) 95 is a factor of a
2) b is 20 percent of a
[Reveal] Spoiler: OA

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If a is an integer, is a-b an integer? [#permalink]

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25 Oct 2017, 01:25
Statement 1: Nothing mentioned about $$b$$. Insufficient

Statement 2: implies $$b=0.2a$$

therefore $$a-b=a-0.2a=0.8a$$, if $$a$$ is a multiple of $$5$$ then $$a-b$$ will be integer otherwise it will not be an integer. Insufficient

Combining 1 & 2 we know $$a$$ is a multiple of $$5$$, hence $$a-b$$ is an integer. Sufficient

Option C

Last edited by niks18 on 25 Oct 2017, 03:29, edited 3 times in total.

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Re: If a is an integer, is a-b an integer? [#permalink]

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25 Oct 2017, 01:25
1
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Option C

From st1 we don’t have much info. Hence insufficient
From st2 we have b=a/5 i.e b will be an integer if a is divisible by 5. But we don’t have a value.
Combining we have a is divisible by 5 and hence b is also an integer. This stands good for negative integer values also

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If a is an integer, is a-b an integer? [#permalink]

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25 Oct 2017, 03:24
We need to figure out whether "b" is an integer
(2) if a=1 then b =0,2
a-b=0,8 (not an integer)
a=5 then b=1
a-b=4 (integer)
(1) + (2)
95 = 5 * 19 * k, so "a" is at least equal to 95

b= 1/5 * a=1/5 * 5*19*k, hence "b" is an integer and a-b is an integer

Option C

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Re: If a is an integer, is a-b an integer? [#permalink]

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27 Oct 2017, 00:27
=>
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.

Under the condition that a is an integer, if a – b is an integer, b is an integer. Thus, the question asks if b is an integer.

Since we have 2 variables and 0 equation, C is most likely to be the answer.
Condition 1) & 2)
b = 95 * (20/100) = 95 / 5 = 19.
Both conditions are sufficient.
Thus, C is the answer as expected.

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 con 1) and con 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 con 1) and con 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 a is an integer, is a-b an integer?   [#permalink] 27 Oct 2017, 00:27
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