ahmedshafea wrote:What is the value of x?
(1) 2x - 5y + 6 = 12
(2) 8x - (4x + 10y) + 27 = 39
Target question: What is the value of x?
Statement 1: 2x - 5y + 6 = 12
Subtract 6 from both sides to get: 2x - 5y = 6
Since we have one equation with 2 variables, there are infinitely many solutions.
In other words, x can have infinitely many values, which means statement 1 is NOT SUFFICIENT.
ASIDE: If you're not 100% convinced that there are infinitely many solutions, you can always
test some values
There are several values of x and y that satisfy the equation 2x - 5y = 6. Here are two:
Case a: x = 3 and y = 0, in which case
x = 3
Case b: x = 8 and y = 2, in which case
x = 8
Statement 2: 8x - (4x + 10y) + 27 = 39
Subtract 27 from both sides to get: 8x - (4x + 10y) = 12
Expand: 8x - 4x - 10y = 12
Simplify: 4x - 10y = 12
Here we have another equation with 2 variables, which means there are infinitely many solutions.
In other words, x can have infinitely many values, which means statement 2 is NOT SUFFICIENT.
Statements 1 and 2 combined
Statement 1 tells us that 2x - 5y = 6
Statement 2 tells us that 4x - 10y = 12
IMPORTANT: the two equations above are EQUIVALENT equations.
If we take the equation 4x - 10y = 12 and divide both sides by 2 we get the EQUIVALENT equation 2x - 5y = 6
Since the two statements provide the
same information, and since each statement alone is NOT SUFFICIENT, we can conclude that the COMBIEND statements are NOT SUFFICIENT
Answer:
E
Cheers,
Brent
