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30 Oct 2016, 04:07
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
63% (01:37) correct
37%
(01:53)
wrong
based on 713
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of x?
1) The Greatest Common Factor of 90 and x is 30
2) The Least Common Multiple of 90 and x is 900
1) The Greatest Common Factor of 90 and x is 30
2) The Least Common Multiple of 90 and x is 900
10 Mar 2022, 06:54
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interceptor77
Target question: What is the value of x?
Statement 1: The Greatest Common Factor of 90 and x is 30
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 30
Case b: x = 60
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The Least Common Multiple of 90 and x is 900
There are several values of x that satisfy statement 2. Here are two:
Case a: x = 900
Case b: x = 300
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
There's a nice rule that says:
(greatest common divisor of x and y)(least common multiple of x and y) = xy
So, for this question, we get: (greatest common divisor of 90 and x)(least common multiple of 90 and x) = 90x
Substitute values: (30)(900) = 90x
Divide both sides of the equation by 90 to get: (30)(10) = x
Evaluate: x = 300
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
30 Oct 2016, 05:51
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damybox
When considering (1) and (2) together you can apply the most important property of LCM and GCD: for any positive integers \(a\) and \(b\), \(a*b=GCD(a,b)*LCM(a,b)\). According to this 90x=30*900 --> x=300.
