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 Author: MathRevolution [ 27 Jun 2019, 02:35 ] Post subject: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. [GMAT math practice question]Both roots of the quadratic equation $$x^2-39x+a = 0$$ are prime numbers. How many different possible values of a are there?$$A. 1$$ $$B. 2$$ $$C. 3$$ $$D. 4$$ $$E. 5$$

 Author: nick1816 [ 27 Jun 2019, 02:52 ] Post subject: Re: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. IMO Answer must be A.Sum of roots = 39Sum is odd that implies one root is even and other is odd.There is only 1 even prime number that is 2, hence other root must be 39-2=37.a= 2*37=74There is only one value possible.MathRevolution wrote:[GMAT math practice question]Both roots of the quadratic equation $$x^2-39x+a = 0$$ are prime numbers. How many different possible values of a are there?$$A. 1$$ $$B. 2$$ $$C. 3$$ $$D. 4$$ $$E. 5$$

 Author: MidhilaMohan [ 27 Jun 2019, 03:15 ] Post subject: Re: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. nick1816 wrote:IMO Answer must be A.Sum of roots = 39Sum is odd that implies one root is even and other is odd.There is only 1 even prime number that is 2, hence other root must be 39-2=37.a= 2*37=74There is only one value possible.MathRevolution wrote:[GMAT math practice question]Both roots of the quadratic equation $$x^2-39x+a = 0$$ are prime numbers. How many different possible values of a are there?$$A. 1$$ $$B. 2$$ $$C. 3$$ $$D. 4$$ $$E. 5$$I agree with your answer. Even I have arrived at the same but here the answer is showing as 4. is the answer marked correctly?

 Author: nick1816 [ 27 Jun 2019, 03:22 ] Post subject: Re: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. He should change the question to "What's the unit digit of a". LOLThis guy gonna post official solution in next 2 days. Gotta wait till then!!Midhila wrote:nick1816 wrote:IMO Answer must be A.Sum of roots = 39Sum is odd that implies one root is even and other is odd.There is only 1 even prime number that is 2, hence other root must be 39-2=37.a= 2*37=74There is only one value possible.MathRevolution wrote:[GMAT math practice question]Both roots of the quadratic equation $$x^2-39x+a = 0$$ are prime numbers. How many different possible values of a are there?$$A. 1$$ $$B. 2$$ $$C. 3$$ $$D. 4$$ $$E. 5$$I agree with your answer. Even I have arrived at the same but here the answer is showing as 4. is the answer marked correctly?

 Author: MathRevolution [ 30 Jun 2019, 18:05 ] Post subject: Re: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. =>Assume $$p$$ and $$q$$ are roots of $$x^2-39x+a = 0.$$Then $$(x-p)(x-q) = x^2 –(p+q)x + pq = x^2-39x+a = 0$$So, $$p + q = 39$$ and $$pq = a.$$Since $$p$$ and $$q$$ are prime numbers and $$p + q = 39$$ is an odd number, one of $$p$$ and $$q$$ is an even prime number. Since the only even prime number is $$2$$, one of $$p$$ and $$q$$ must be $$2$$. Let $$p = 2$$. Then $$q = 37$$, and $$a = 2*37 = 74.$$There is only one possible value of $$a$$.Therefore, the answer is A.Answer: A

 Author: bumpbot [ 22 Nov 2022, 10:57 ] Post subject: Re: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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