If integer $k > 0$ and $x^2 - 7x + k = 0,$ what is the value of $k?$ - The Beat The GMAT Forum

If integer $k > 0$ and $x^2 - 7x + k = 0,$ what is the value of $k?$

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Wed Oct 07, 2020 10:42 am

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If integer $k > 0$ and $x^2 - 7x + k = 0,$ what is the value of $k?$

(1) Both roots are prime numbers.
(2) $2$ is one of the roots of the equation.

Answer: D

Source: Princeton Review

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Source: Beat The GMAT — Data Sufficiency | Wed Oct 07, 2020 10:42 am

alishagmat: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Thu Oct 01, 2020 4:48 amFollowed by: 1 member

Re: If integer $k > 0$ and $x^2 - 7x + k = 0,$ what is the value of $k?$

by alishagmat » Sat Oct 10, 2020 8:03 am

let the roots be a and b
a+b=7
ab=k
all possible values of a and b are
a. b
1. 6
2. 5
3. 4
4. 3
5. 2
6. 1
-1. -6
-2. -5
-3. -4
-4. -3
-5. -2
-6. -1

Using 1 -, only (2,5) and (5,2) satisfies answer, giving k =10 Hence, sufficient
Using 2 - again only (2,5) and (5,2) satisfies answer, giving k =10 Hence, sufficient
Hence, answer = D

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