VJesus12 wrote:$$\text{Is}\ y\ \text{an}\ \text{integer}\ \text{if}\ y=2x^2−3x−35?$$ 1. (2x+7)(13x-65) = 0
2. x = 11
The OA is the option D.
How can I prove that each statement alone is sufficient? Experts, can you help me? Thanks in advanced.
We have to calculate the value of y=2x^2−3x−35 and deduce whether y is an integer.
1. (2x + 7)(13x - 65) = 0
=> (2x + 7) = 0 or (13x - 65) = 0. This implies that either x = -7/2 or 65/13 = 5
Case 1: At x = 5, we can see that y = 2x^2 − 3x − 35 is an integer.
Case 2: At x = -7/2, we can see that y = 2x^2 − 3x − 35 = 2*(-7/2)^2 − 3*(-7/2) − 35 = 2*(49/4) + 21/2 - 35 = 49/2 + 21/2 -35 = 70/2 - 35 = 0; an integer. Sufficient
2. x = 11
Needless to calculate the value of y at x = 11 as it is going to render an integer value for y. Sufficient.
The correct answer:
D
Hope this helps!
-Jay
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