Problem Solving

teejaycrown wrote:if x and y are positive integers what is the value of x and y

1. The greatest common factor of x and y is 10
2. The LCM of x and y is 180

(1) The greatest common factor of x and y is 10.
If x = 10, y = 10, then GCF of x and y = 10. Here xy = 10 * 10 = 100
If x = 10, y = 30, then GCF of x and y = 10. Here xy = 10 * 30 = 300
No definite answer; NOT sufficient.

(2) The LCM of x and y is 180.
If x = 10, y = 180, then LCM of x and y = 180. Here xy = 10 * 180 = 1800
If x = 1, y = 180, then LCM of x and y = 180. Here xy = 1 * 180 = 180.
No definite answer; NOT sufficient.

Combining (1) and (2), x * y = (GCF of x and y )* (LCM of x and y) {Property of LCM and GCF}
So, xy = 10 * 180 = 1800; SUFFICIENT.

The correct answer is C.

teejaycrown wrote:if x and y are positive integers what is the value of x and y

1. The greatest common factor of x and y is 10
2. The LCM of x and y is 180

Hey teejaycrown,

I believe you wrote down the target question incorrectly. If should be . . .

Target question: What is the value of xy?

Statement 1: The greatest common factor of x and y is 10
case a: x=10 and y=10. Here, xy=100
case b: x=10 and y=20. Here, xy=200
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The least common multiple of x and y is 180
case a: x=1 and y=180. Here, xy=180
case b: x=2 and y=180. Here, xy=360
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 & 2
There's a nice rule that says:
If x and y are positive integers, then (GCF of x and y)(LCM of x and y)=xy
(aside: whenever a question mentions the LCM and the GCF, be sure to consider the above rule)
Statement 1 says the GCF of x and y is 10
Statement 2 says the LCM of x and y is 180
So, from our handy rule, xy = (10)(180) = 1800
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

So, the answer is C

Cheers,
Brent