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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6810
GMAT 1: 760 Q51 V42
GPA: 3.82
If a is an integer, is a-b an integer?  [#permalink]

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25 Oct 2017, 01:18
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:03) correct 31% (01:16) wrong based on 88 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

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Joined: 25 Feb 2013 Posts: 1220 Location: India GPA: 3.82 If a is an integer, is a-b an integer? [#permalink] ### Show Tags Updated on: 25 Oct 2017, 03:29 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 Originally posted by niks18 on 25 Oct 2017, 01:25. Last edited by niks18 on 25 Oct 2017, 03:29, edited 3 times in total. Senior Manager Joined: 17 Oct 2016 Posts: 318 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: If a is an integer, is a-b an integer? [#permalink] ### Show Tags 25 Oct 2017, 01:25 1 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 Posted from my mobile device Posted from my mobile device _________________ Help with kudos if u found the post useful. Thanks Manager Joined: 05 Dec 2016 Posts: 243 Concentration: Strategy, Finance GMAT 1: 620 Q46 V29 If a is an integer, is a-b an integer? [#permalink] ### Show Tags 25 Oct 2017, 03:24 We need to figure out whether "b" is an integer (1) no information about "b" (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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6810 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If a is an integer, is a-b an integer? [#permalink] ### Show Tags 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. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Joined: 26 Mar 2013
Posts: 1998
If a is an integer, is a-b an integer?  [#permalink]

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Updated on: 02 Aug 2018, 18:07
MathRevolution wrote:
[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

If b is integer....... then a-b =Integer

The questions rephrased: Is b integer?

1) 95 is a factor of a

Insufficient

2) b is 20 percent of a

$$b=\frac{20}{100}*a$$= $$\frac{1}{5}*a$$

Let a =1........b is Not integer integer......Answer is No

Let a = 5.........b is integer....Answer is Yes

Insufficient

Combine 1 & 2

From 1, a is multiple of 5 so It divides by 5 evenly ......b is integer........Answer is always Yes.

Originally posted by Mo2men on 02 Aug 2018, 11:48.
Last edited by Mo2men on 02 Aug 2018, 18:07, edited 2 times in total.
Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
If a is an integer, is a-b an integer?  [#permalink]

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02 Aug 2018, 17:30
1
Mo2men wrote:
MathRevolution wrote:
[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

If b is integer....... then a-b =Integer

The questions rephrased: Is b integer?

1) 95 is a factor of a

Insufficient

2) b is 20 percent of a

$$b=\frac{20}{100}*a$$= $$\frac{2}{10}*a$$

Let a =10........b is integer......Answer is Yes

Let a = 5.........b is not integer....Answer is NO

Insufficient

Combine 1 & 2

From 1, a is multiple of 5 so It can't divide by 10 evenly ......b is not integer........Answer is always No.

Hi Mo2men

Your assumption for a is incorrect. a cannot be 5 or 10 because 95 is a factor of a. So a=95k, for some integer k. Also b=2/10*a=1/5*a. This will make b an integer

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Joined: 26 Mar 2013
Posts: 1998
Re: If a is an integer, is a-b an integer?  [#permalink]

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02 Aug 2018, 18:04
niks18 wrote:
Mo2men wrote:
MathRevolution wrote:
[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

If b is integer....... then a-b =Integer

The questions rephrased: Is b integer?

1) 95 is a factor of a

Insufficient

2) b is 20 percent of a

$$b=\frac{20}{100}*a$$= $$\frac{2}{10}*a$$

Let a =10........b is integer......Answer is Yes

Let a = 5.........b is not integer....Answer is NO

Insufficient

Combine 1 & 2

From 1, a is multiple of 5 so It can't divide by 10 evenly ......b is not integer........Answer is always No.

Hi Mo2men

Your assumption for a is incorrect. a cannot be 5 or 10 because 95 is a factor of a. So a=95k, for some integer k. Also b=2/10*a=1/5*a. This will make b an integer

Posted from my mobile device

Thanks niks18

I was thinking of statement 1 while solving statement 2. But at least i arrived into the right solution. Nice coincidence. Do you agree?

I will amend my post soon.
Re: If a is an integer, is a-b an integer? &nbs [#permalink] 02 Aug 2018, 18:04
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