[email protected] wrote:If x and Y are integers and
2 < x < y, does y = 16?
1) The greatest common factor (GCF) of x and y is 2
2) The least common multiple (LCM) of x and y is 48
Target question: Does y = 16?
Statement 1: The greatest common factor (GCF) of x and y is 2
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 2 and y = 16, in which case
y does equal 16
Case b: x = 2 and y = 4, in which case
y does not equal 16
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The least common multiple (LCM) of x and y is 48
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 3 and y = 16, in which case
y does equal 16
Case b: x = 12 and y = 48, in which case
y does not equal 16
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: Whenever we see a question involving GCF and LCM, we should recall the following rule:
(the GCF of x and y)(the LCM of x and y) = xy
Plug in statements to get: (2)(48) = xy
So, we know that
xy = 96 AND we know that
2 < x < y
Start checking pairs of values (there aren't many) such that
xy = 96 AND
2 < x < y:
x = 3 and y = 32 (does not satisfy statements 1 or 2)
x = 4 and y = 24 (does not satisfy statements 1 or 2)
x = 6 and y = 16 (YES, satisfies statements 1 and 2)
x = 8 and y = 12 (does not satisfy statements 1 or 2)
Now that we've checked all possible values for x and y, we can see that
y must equal 16
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
