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When a and b are positive integers, what is the greates

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by Max@Math Revolution » Thu Apr 19, 2018 1:40 am

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[GMAT math practice question]

When a and b are positive integers, what is the greatest common divisor of a + b and a + 100?

1) a = 100
2) b = 99
Last edited by Max@Math Revolution on Thu Apr 19, 2018 9:56 pm, edited 1 time in total.
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Apr 19, 2018 2:49 am
Max@Math Revolution wrote:[GMAT math practice question]

When a and b are positive integers, what is the greatest common divisor of a + b and a + 100?

1) a = 100
2) b = 99
Consecutive integers are COPRIMES: they share no factors other than 1.

Statement 1: a=100, implying that a+100 = 100+100 = 200
Case 1: b=100, with the result that a+b = 100+100 = 200
The GCF for the value in blue (200) and Case 1 (200) is 200.
Case 2: b=101, with the result that a+b = 100+101 = 201
Since 200 and 201 are consecutive integers, the GCF for the value in blue (200) and Case 2 (201) is 1.
Since the GCF can be different values, INSUFFICIENT.

Statement 2: b=99, implying that a+b = a+99
Since a+99 and a+100 are consecutive integers, they share no factors other than 1.
Thus, their GCF = 1.
SUFFICIENT.

The correct answer is B.
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by Max@Math Revolution » Sun Apr 22, 2018 5:20 pm
=>
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.


Condition 1)
If a = 100, and b = 98, the greatest common divisor of a + b and a + 100 is 2.
If a = 100, and b = 99, the greatest common divisor of a + b and a + 100 is 1.
Thus, condition 1) is not sufficient as it does not yield a unique solution.

Condition 2)
a + b = a + 99 and a + 100 are consecutive integers. Therefore, their greatest common divisor is 1.
Thus, condition 2) is sufficient.


Therefore, the answer is B.
Answer: B
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