Data Sufficiency

BTGmoderatorDC wrote: ↑

Wed Mar 09, 2022 6:21 pm

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


OA C

Source: Veritas Prep

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