carcass
If a and b are positive integers, what is the value of the product ab ?
(1) The least common multiple of a and b is 48
(2) The greatest common factor of a and b is 4
Target question: What is the value of the product ab? Statement 1: The least common multiple of a and b is 48 Let's TEST some numbers.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 1 and b = 48. In this case,
ab = (1)(48) = 48Case b: a = 2 and b = 48. In this case,
ab = (2)(48) = 96Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The greatest common factor (aka divisor) of a and b is 4Let's TEST some numbers (again).
There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 8 and b = 4. In this case,
ab = (8)(4) = 32Case b: a = 4 and b = 4. In this case,
ab = (4)(4) = 16Since 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) = xyExample: 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! ----------------------
When we apply the above
rule, we get: (4)(48) = ab
So,
ab = 192Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C