One way to solve this question is by counter-example.agni_h1 wrote:If x^2 + 5y = 49 . Is y an integer ?
(1) 1<x<4
(2) x^2 is an integer
I selected C. But the correct answer is E.
Please help.
Statement 1: 1<x<4
Here, we can see that if x=2, then y is an integer. So, when x=2 the answer to the target question is YES.
At this point, we can see that most other values of x (other than x=3) will mean that y is not an integer. However, before we choose a value for x, let's take a quick look at statement 2: x^2 is an integer.
Notice that the first value for x we chose (x=2) is an integer when squared. So, this value of x satisfies statements 1 and 2.
If we can find another value of x that satisfies both statements and that value of x is such that y is not an integer (i.e., the answer to the target question is NO), then we can solve this question very quickly.
Notice that x=root3 satisfies both statements 1 and 2.
So, for statement 1, if x = root3, then y is not an integer.
So statement 1 is INSUFFICIENT
Here's the bonus of choosing numbers that satisfy both statements.
Statement 2: x^2 is an integer
x=2 means that y is an integer.
x=root3 means that y is not an integer.
So statement 2 is INSUFFICIENT
Since we used the same two x values for both statements, we know that the statements combined are
INSUFFICIENT, which means the answer is E
