If x and y are positive, what is the value of y ?
(1) xy is the square of an integer.
(2) 600 percent of x equals 200 percent of y.
Target question: What is the value of y?
Given: x and y are positive
Statement 1: xy is the square of an integer.
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 1. Here xy = (1)(1) = 1, which is the square of an integer. In this case
y = 1
Case b: x = 2 and y = 2. Here xy = (2)(2) = 4, which is the square of an integer. In this case
y = 2
Since we cannot answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: 600 percent of x equals 200 percent of y.
So, 6x = 2y
Divide both sides by 2 to get: 3x = y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 3. In this case
y = 3
Case a: x = 2 and y = 6. In this case
y = 6
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that xy is the square of an integer.
Statement 2 tells us that 3x = y
Take statement 1 and replace y with 3x to get: x(3x) is the square of an integer.
In other words, 3x² is the square of an integer.
There are several values of x that satisfy this condition. Here are two:
Case a: x = √3. This means 3x² = 3(√3)² = 9, and 9 is the square of an integer. From statement 2, if x = √3, then
y = 3√3.
Case b: x = 4√3. This means 3x² = 3(4√3)² = 36, and 36 is the square of an integer. From statement 2, if x = 4√3, then
y = 12√3.
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
