BTGmoderatorDC wrote:If a and b are two positive numbers, what is the product of a and b?
1) The LCM of a and b is 16
2) The GCD of a and b is 4
Target question: What is the value of ab?
Statement 1: The LCM of a and b is 16
Let's TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 1 and b = 16 (the LCM of 1 and 16 is 16). In this case, the answer to the target question is
ab = (1)(16) = 16
Case b: a = 2 and b = 16 (the LCM of 2 and 16 is 16). In this case, the answer to the target question is
ab = (2)(16) = 32
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The GCD of a and b is 4
Let's TEST some more values.
Case a: a = 4 and b = 4 (the GCD of 4 and 4 is 16). In this case, the answer to the target question is
ab = (4)(4) = 16
Case b: a = 4 and b = 12 (the GCD of 4 and 12 is 16). In this case, the answer to the target question is
ab = (4)(12) = 48
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
--------ASIDE----------------------
There's a nice rule that says:
(greatest common divisor of x and y)(least common multiple of x and y) = xy
Example: x = 10 and y = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above
rule, since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------
Statement 1 tells us that the LCM of a and b is 16
Statement 2 tells us that the GCD of a and b is 4
So, the product ab = (16)(4) = 64
So, the answer to the target question is
ab = 64
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
