BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:42 pm
If x and y are positive integers, what is the value of x?
1) 3x + 2y = 12
2) |9x² + 30xy + 25y²| = 21²
Answer:
D
Source:
www.gmatprepnow.com
Target question: What is the value of x?
Given: x and y are positive integers
Statement 1: 3x + 2y = 12
Some students will see this equation with 2 variables and automatically conclude that there are infinitely many solutions, in which case, statement 1 is not sufficient.
Under most conditions, this conclusion would be correct. However, in this question, we have the given condition that x and y are
positive integers, which severely limits the possible solutions.
In fact, there is only ONE pair of positive integers that satisfy the equation: x = 2 and y = 3.
So, we can be certain that
x = 2
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: |9x² + 30xy + 25y²| = 21²
First factor the part inside the absolute value to get: |(3x + 5y)²| = 21²
This means that EITHER (3x + 5y)² = 21² OR (3x + 5y)² = -(21²)
We can quickly dismiss the second case, (3x + 5y)² = -(21²), since (3x + 5y)² must be greater than or equal to zero. So, it could never equal -(21²)
So, what about (3x + 5y)² = 21²?
This means that either 3x + 5y = 21 or 3x + 5y = -21
If x and y are both positive, we know that 3x + 5y will be positive, which means there are no solutions to the equation 3x + 5y = -21
What about the equation 3x + 5y = 21?
Under the restriction that x and y are POSITIVE INTEGERS, there is only ONE pair of positive integers that satisfy the equation: x = 2 and y = 3.
So, once again, we can be certain that
x = 2
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
