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If x and y are positive integers, is xy a multiple of 8?

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If x and y are positive integers, is xy a multiple of 8?

by Vincen » Fri Sep 22, 2017 10:06 am

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If x and y are positive integers, is xy a multiple of 8?

(1) The greatest common divisor of x and y is 10
(2) The least common multiple of x and y is 100

The Official Answer is C.

Why we need both statements to solve the question? I don't know how to use it both together. I need some help please.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Sep 22, 2017 2:30 pm

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Vincen wrote:If x and y are positive integers, is xy a multiple of 8?

(1) The greatest common divisor of x and y is 10
(2) The least common multiple of x and y is 100
Target question: Is xy a multiple of 8?

Statement 1: The greatest common factor of x and y is 10
There are several values of x and y that satisfy statement 1. Here are two:
case a: x=10 and y=10. Here, xy=100, which means xy is NOT a multiple of 8
case b: x=10 and y=20. Here, xy=200, which means xy IS a multiple of 8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The least common multiple of x and y is 100
There are several values of x and y that satisfy statement 2. Here are two:
case a: x=1 and y=100. Here, xy=100, which means xy s NOT a multiple of 8
case b: x=2 and y=100. Here, xy=200, which means xy IS a multiple of 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 & 2
There's a nice rule that says:
If x and y are positive integers, then (GCF of x and y)(LCM of x and y)=xy
(aside: whenever a question mentions the LCM and the GCF, be sure to consider the above rule)
Statement 1 says the GCF of x and y is 10
Statement 2 says the LCM of x and y is 100
So, from our handy rule, xy = (10)(100) = 1,000, which means xy IS a multiple of 8
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

So, the answer is C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by masoom j negi » Thu Dec 20, 2018 2:35 am

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Statement 1. The greatest common divisor of x and y is 10.
The value of x,y could be 10,10 and 10,20. We get different results in both the cases. Hence, Insufficient.
Statement 2. The LCM of x and y is 100.
The value of x,y could be 1,100 or 10,100. We get different results in both the cases. Hence, Insufficient.
Statement 1 & 2 together.
We know, LCM x HCF = xy.
So, xy = 1000 i.e. a multiple of 8. Hence, sufficient
Hence, c is the answer.
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