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Question of the week  33 (A quadratic equation is in the form ......)
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25 Jan 2019, 05:22
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Re: Question of the week  33 (A quadratic equation is in the form ......)
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25 Jan 2019, 06:53
Bunuel sir, This question has been posted twice. https://gmatclub.com/forum/questionoftheweek33aquadraticequationisintheform287275.html#p2214412Can you merge the replies?
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Re: Question of the week  33 (A quadratic equation is in the form ......)
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25 Jan 2019, 07:13
EgmatQuantExpert wrote: A quadratic equation is in the form of \(x^2 – 2px + m = 0\), where m is divisible by 5 and is less than 120. One of the roots of this equation is 7. If p is a prime number and one of the roots of the equation, \(x^2 – 2px + n = 0\) is 12, then what is the value of p + n – m? IMO D prime numbers will be 2,3,5,11 Multiples of 5 which can give us a 7 => 35,70 and 105 \(x^2 – 2px + m = 0\), here p can be 11 and m will be 105 \(x^2 – 22x + m = 0\) \(x^2 – 15x 7x + 105 = 0\) \(x(x – 15) 7(x 15) = 0\) \(x^2 – 2px + n = 0\), here p can be 11 and n will be 120 \(x^2 – 22x + 120 = 0\) \(x^2 – 10x 12x +120 = 0\) \(x(x – 10) 12(x  10) = 0\) so values of p + n – m 11 + 120  105 Answer D P.S. I was down to realize that the value was 11(in 2 mins), and when i was writing this solution to ask some help on how to solve this question. I didn't realize that the factors of 105 would have given me 22. Always take all the possibilities of the factors
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Re: Question of the week  33 (A quadratic equation is in the form ......)
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25 Jan 2019, 09:55
\(x^2 – 2px + m = 0\) given one value of x=7 4914p+m=0 p=2,3,5,7,11,13... upon doing substitution for values of p only at 11 we get m as a integer which is divisible by 5 so 4914*11+m=0 m= 105 \(x^2 – 2px + n = 0\) at x=12 14424p+n p=11 n=120 so p + n – m 11+120105 26 IMO D EgmatQuantExpert wrote: A quadratic equation is in the form of \(x^2 – 2px + m = 0\), where m is divisible by 5 and is less than 120. One of the roots of this equation is 7. If p is a prime number and one of the roots of the equation, \(x^2 – 2px + n = 0\) is 12, then what is the value of p + n – m?
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Re: Question of the week  33 (A quadratic equation is in the form ......)
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25 Jan 2019, 19:24
This is doable, but a very tricky question. Considering m could take 35, 70, and 105 was important, as the value of "m" was not 35, or 70, it was 105.



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Re: Question of the week  33 (A quadratic equation is in the form ......)
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29 Jan 2019, 23:43
Solution Given:• A quadratic equation, \(x^2 – 2px + m\) = 0
o m is divisible by 5, and o m < 120 o 7 is one root of the equation o p is a prime number • 12 is one root of the equation, \(x^2 – 2px + n = 0\) To find:Approach and Working: In the quadratic equation, \(x^2 – 2px + m = 0\), let us assume that the other root is “b” • Sum of the roots = 7 + b = 2p
o Implies, 7 + b must be even, that is b must be odd • Product of the roots = 7b = m = a multiple of 5
o Implies, b is a multiple of 5 • Thus, b is an odd multiple of 5 • And, we are given that m < 120
o Implies, 7 * m = 7 * 5k < 120 o \(k < \frac{24}{7}\) o Thus, k = 1 or 3 • If k = 1, then b = 5
o In this case, 2p = 7 + 5 = 12 o p = 6, which is not prime • If k = 3, then b = 15
o In this case, 2p = 7 + 15 = 22 o p = 11, which is a prime number • So, p = 11, m = 7 * 15 = 105, and n = 12 * 10 = 120 Therefore, p + n – m = 11 + 120 – 105 = 26 Hence the correct answer is Option D. Answer: D
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Re: Question of the week  33 (A quadratic equation is in the form ......)
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31 Jan 2019, 07:27
Hello Archit3110 !
I was reading your approach and I liked it, I just have a question.
Why can we equal x to one of the roots? Would it be the same result if we equate x to the other unknown root?
I am a bit confused with that:
"given one value of x=7 4914p+m=0"
Kind regards!



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Question of the week  33 (A quadratic equation is in the form ......)
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31 Jan 2019, 07:31
EgmatQuantExpert wrote: Solution Given:• A quadratic equation, \(x^2 – 2px + m\) = 0
o m is divisible by 5, and o m < 120 o 7 is one root of the equation o p is a prime number • 12 is one root of the equation, \(x^2 – 2px + n = 0\) To find:Approach and Working: In the quadratic equation, \(x^2 – 2px + m = 0\), let us assume that the other root is “b” • Sum of the roots = 7 + b = 2p
o Implies, 7 + b must be even, that is b must be odd • Product of the roots = 7b = m = a multiple of 5
o Implies, b is a multiple of 5 • Thus, b is an odd multiple of 5 • And, we are given that m < 120
o Implies, 7 * m = 7 * 5k < 120 o \(k < \frac{24}{7}\) o Thus, k = 1 or 3 • If k = 1, then b = 5
o In this case, 2p = 7 + 5 = 12 o p = 6, which is not prime • If k = 3, then b = 15
o In this case, 2p = 7 + 15 = 22 o p = 11, which is a prime number • So, p = 11, m = 7 * 15 = 105, and n = 12 * 10 = 120 Therefore, p + n – m = 11 + 120 – 105 = 26 Hence the correct answer is Option D. Answer: DHello EgmatQuantExpert I was doing the same approach as you but I had a problem with the following: If its given that one of the roots is 7, why it doesn't mean that x = 7 because if one root is 7, that would mean that: (x 7) Isn't it? So the sum of the root 2px shouldn't be (7) + b? Could you please help me with this? Thank you in advance! Kind regards!



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Re: Question of the week  33 (A quadratic equation is in the form ......)
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31 Jan 2019, 07:58
jfranciscocuencag wrote: Hello Archit3110 !
I was reading your approach and I liked it, I just have a question.
Why can we equal x to one of the roots? Would it be the same result if we equate x to the other unknown root?
I am a bit confused with that:
"given one value of x=7 4914p+m=0"
Kind regards! jfranciscocuencagits given in the question that one of the roots of equation is 7 .. so value of x has been substituted as 7.. by roots in quadratic eqn it means that upon doing substitution of the value of x we would get value "= 0"
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Re: Question of the week  33 (A quadratic equation is in the form ......)
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01 Feb 2019, 01:39
jfranciscocuencag wrote: Hello EgmatQuantExpert
I was doing the same approach as you but I had a problem with the following:
If its given that one of the roots is 7, why it doesn't mean that x = 7 because if one root is 7, that would mean that:
(x 7) Isn't it? So the sum of the root 2px shouldn't be (7) + b?
Could you please help me with this?
Thank you in advance!
Kind regards!
Hi, If x  7 is a factor of the quadratic equation, then we can write (x  7) = 0, which implies, x = 7
Similarly, if x = 7 is a root of a quadratic equation, then (x  7) is a factor of the quadratic equation
Regards, Sandeep
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Re: Question of the week  33 (A quadratic equation is in the form ......)
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