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# Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers.

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers.  [#permalink]

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Updated on: 30 Jun 2019, 18:04
1
1
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Difficulty:

65% (hard)

Question Stats:

69% (01:54) correct 31% (01:37) wrong based on 39 sessions

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[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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 27 Jun 2019, 02:35. Last edited by MathRevolution on 30 Jun 2019, 18:04, edited 1 time in total. Director Joined: 19 Oct 2018 Posts: 705 Location: India Re: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. [#permalink] ### Show Tags 27 Jun 2019, 02:52 1 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? $$A. 1$$ $$B. 2$$ $$C. 3$$ $$D. 4$$ $$E. 5$$ Manager Joined: 03 Mar 2017 Posts: 98 Location: India Re: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. [#permalink] ### Show Tags 27 Jun 2019, 03:15 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? Director Joined: 19 Oct 2018 Posts: 705 Location: India Re: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. [#permalink] ### Show Tags 27 Jun 2019, 03:22 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? Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7612 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers. [#permalink] ### Show Tags 30 Jun 2019, 18:05 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: Both roots of the quadratic equation x^2-39x+a = 0 are prime numbers.   [#permalink] 30 Jun 2019, 18:05
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