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| Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. https://gmatclub.com/forum/both-roots-of-the-quadratic-equation-x-2-39x-a-0-are-prime-numbers-298844.html |
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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? \(A. 1\) \(B. 2\) \(C. 3\) \(D. 4\) \(E. 5\) |
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| 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 = 39 Sum 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=74 There 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? \(A. 1\) \(B. 2\) \(C. 3\) \(D. 4\) \(E. 5\) |
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| 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 = 39 Sum 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=74 There 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? |
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| 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". LOL This 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 = 39 Sum 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=74 There 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? |
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| 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 |
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| 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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