[spoiler]We are given the quadratic equation x^2 - kx + 16 = 0 and asked to find value of x, given that k and x are positive integers, and that k is a constant.
Statement 1 tells us that k is even. We don't know the value of k, but we can try factoring x^2 - kx + 16 in different ways to see what values of k (and x) are possible. To do this, we find pairs of factors of 16, since the constant term in the quadratic expression is 16: (1,16), (2, 8), (4, 4). This means that we can factor the expression as follows:
(x - 1)(x - 16), which gives us x^2 - 17x + 16. In this case, k is odd (17), and x = 1 or x = 16.
(x - 2)(x - 8), which gives us x^2 - 10x + 16. In this case, k is even (10), and x = 2 or x = 8.
(x - 4)(x - 4), which gives us x^2 - 8x + 16. In this case, k is even (8), and x = 4.
k is even in cases 2 and 3. In the case 2, x can be 2 or 8. In case 3, x must be 4. Since x can have three different values, Statement 1 is insufficient. The answer is choice B, C or E.
Statement 2 tells us that k > 9. We can see from the list above that this means that k is either 10 or 17. Depending on the value of k, x could be 1, 2, 8, or 16. Statement 2 is also insufficient. The answer is choice C or E.
Together, we know that k is even and greater than 9. From the list above, we can see that k = 10. However, this only gives us the value of k.
When k = 10, x = 2 or x = 8. Since we still cannot narrow down x to one possible value, the statements together are not sufficient.[/spoiler]
Answer choice
E is correct.
neoreaves wrote:bhumika ....can you please post the OA ....
