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# If the greatest common factor of positive integers A and B is 20, what

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Math Expert
Joined: 02 Sep 2009
Posts: 50619
If the greatest common factor of positive integers A and B is 20, what  [#permalink]

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28 Apr 2016, 00:07
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Difficulty:

55% (hard)

Question Stats:

64% (02:08) correct 36% (02:26) wrong based on 85 sessions

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If the greatest common factor of positive integers A and B is 20, what is the value of A – B?

(1) The least common multiple of A and B is 400.
(2) A = 80

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7035
If the greatest common factor of positive integers A and B is 20, what  [#permalink]

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29 Apr 2016, 01:31
1
2
Bunuel wrote:
If the greatest common factor of positive integers A and B is 20, what is the value of A – B?

(1) The least common multiple of A and B is 400.
(2) A = 80

Just to remember => Product of two numbers = GCF*LCM..

lets see the statements-

(1) The least common multiple of A and B is 400.

there are possiblities of different values of A and B..
so AB = 20*400 = 8000
a) A=20 , B = 400
GCF = 20 and LCM = 400
b) A=80 , B = 100
GCF = 20 and LCM = 400
other two
c) B=20 , A = 400
GCF = 20 and LCM = 400
d) B=80 , A = 100
GCF = 20 and LCM = 400

we will get different values for A-B
Insuff

(2) A = 80
Insuff

Combined..
There is ONLY one set of values which fits in
A=80 and B=100
A-B = -20
Suff
_________________

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

GMAT online Tutor

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Joined: 11 Sep 2015
Posts: 3122
Re: If the greatest common factor of positive integers A and B is 20, what  [#permalink]

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31 Oct 2017, 10:38
Top Contributor
Bunuel wrote:
If the greatest common factor of positive integers A and B is 20, what is the value of A – B?

(1) The least common multiple of A and B is 400.
(2) A = 80

Target question: What is the value of A – B?

Given: The greatest common factor of positive integers A and B is 20

Statement 1: The least common multiple of A and B is 400
USEFUL RULE: (greatest common factor x and y)(least common multiple of x and y) = xy
So, (greatest common factor A and B)(least common multiple of A and B) = AB
Replace values to get: (20)(400) = AB
In other words, AB = 8000
Is knowing the value of AB enough to determine the value of A - B?
No.
There are several values of A and B that satisfy statement 1 (and the given information). Here are two:
Case a: A = 20 and B = 400, in which case A - B = 20 - 400 = -380
Case b: A = 400 and B = 20, in which case A - B = 400 - 20 = 380
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: A = 80
There's no information about B, so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that AB = 8000
Statement 2 tells us that A = 80
This means that B = 100
So, A - B = 80 - 100 = -20
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: If the greatest common factor of positive integers A and B is 20, what &nbs [#permalink] 31 Oct 2017, 10:38
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