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A quadratic equation is in the form of x^2–2px + m = 0, where m is
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31 May 2019, 09:17
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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?
Re: A quadratic equation is in the form of x^2–2px + m = 0, where m is
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02 Jun 2019, 11:06
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x^2–2px + m=0 Products of the root=m let the second roots of above equation is 'a'. 7*a=m Because m is a multiple of 5, a must be multiple of 5 too. a=5k , where k is an integer
7*5k<120 35k<120 k<3.xyz
Also 2p is the sum of both roots and p is a prime number. 1. As 7+5k is an integer, 5k must also be an integer. 2. k can only take value 3 because then sum of roots, 2p is 22 and value of p is 11, which is a prime number.
m= 7*15=105
x^2–2px + n = 0 one root is 12, and let second root is b 12+b=22 b=10 n=12*10=120
p+n-m=11+120-105=26
kiran120680 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?
Re: A quadratic equation is in the form of x^2–2px + m = 0, where m is
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08 Jun 2019, 03:24
kiran120680 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?
A. 0 B. 6 C. 16 D. 26 E. 27
Hi VeritasKarishma, Can you please provide a good and easy solution for the above question? Thanks.
Re: A quadratic equation is in the form of x^2–2px + m = 0, where m is
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08 Jun 2019, 08:17
Top Contributor
kiran120680 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?
A. 0 B. 6 C. 16 D. 26 E. 27
GIVEN: x = 7 is one of the roots of the equation x² – 2px + m = 0 This means (x - 7) must be one of the factors of the expression on the left side of the equation. That is, x² – 2px + m = 0, can be rewritten as (x - 7)(x +/- something) = 0 [notice that x = 7 is definitely a solution to the new equation] Let's assign the variable k to the missing number (aka "something") We can write: x² – 2px + m = (x - 7)(x - k)
GIVEN: m is divisible by 5 and is less than 120 We already know that: x² – 2px + m = (x - 7)(x - k) If we expand the right side we get: x² – 2px + m = x² – kx - 7x + 7k Now rewrite the right side as follows: x² – 2px + m = x² – (k + 7)x + 7k
We can see that 2p = k + 7 And we can see that m = 7k
In order for m to be divisible by 5, it must be the case that k is divisible by 5. So, k COULD equal 5, 10, 15, 20, 25, etc Let's test a few possible values of k
If k = 5, then 2p = 5 + 7 = 12 When we solve this, we get: p = 6 HOWEVER, we're told that p is PRIME So, it cannot be the case that k = 5
If k = 10, then 2p = 10 + 7 = 17 When we solve this, we get: p = 8.5 HOWEVER, we're told that p is PRIME So, it cannot be the case that k = 10
If k = 15, then 2p = 15 + 7 = 22 When we solve this, we get: p = 11 Aha! 11 is PRIME So, it COULD be the case that k = 15. Let's confirm that this satisfies the other conditions in the question.
If k = 15, then we get: x² – 2px + m = (x - 7)(x - 15) Expand and simplify the right side: x² – 2px + m = x² – 22x + 105 So, this meets the condition that says m is divisible by 5 and is less than 120
We now know that p = 11 and m = 105 All we need to do now is determine the value of n
GIVEN: x = 12 is one of the solutions of the equation x² – 2px + n = 0 Plug in x = 12 to get: 12² – 2p(12) + n = 0 Since we already know that p = 11, we can replace p with 11 to get: 12² – 2(11)(12) + n = 0 Simplify: 144 - 264 + n = 0 Simplify: -120 + n = 0 Solve: n = 120
What is the value of p + n – m? p + n – m = 11 + 120 - 105 = 26
Re: A quadratic equation is in the form of x^2–2px + m = 0, where m is
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08 Jun 2019, 12:02
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substitute x = 7 in first equation to get 49-14p+m = 0
Substitute x = 12 in second equation to get 144-24p+n = 0
n - m = 24p - 144 + 49 - 14p = 10p - 95
p + n - m = 11p - 95
p must be a prime number which when multiplied by 11 is greater than 95. prime values greater than 7 satisfy our requirement. p = 11 gets us option D.
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A quadratic equation is in the form of x^2–2px + m = 0, where m is
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08 Jun 2019, 21:04
GMATPrepNow wrote:
kiran120680 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?
A. 0 B. 6 C. 16 D. 26 E. 27
GIVEN: x = 7 is one of the roots of the equation x² – 2px + m = 0 This means (x - 7) must be one of the factors of the expression on the left side of the equation. That is, x² – 2px + m = 0, can be rewritten as (x - 7)(x +/- something) = 0 [notice that x = 7 is definitely a solution to the new equation] Let's assign the variable k to the missing number (aka "something") We can write: x² – 2px + m = (x - 7)(x - k)
GIVEN: m is divisible by 5 and is less than 120 We already know that: x² – 2px + m = (x - 7)(x - k) If we expand the right side we get: x² – 2px + m = x² – kx - 7x + 7k Now rewrite the right side as follows: x² – 2px + m = x² – (k + 7)x + 7k
We can see that 2p = k + 7 And we can see that m = 7k
In order for m to be divisible by 5, it must be the case that k is divisible by 5. So, k COULD equal 5, 10, 15, 20, 25, etc Let's test a few possible values of k
If k = 5, then 2p = 5 + 7 = 12 When we solve this, we get: p = 6 HOWEVER, we're told that p is PRIME So, it cannot be the case that k = 5
If k = 10, then 2p = 10 + 7 = 17 When we solve this, we get: p = 8.5 HOWEVER, we're told that p is PRIME So, it cannot be the case that k = 10
If k = 15, then 2p = 15 + 7 = 22 When we solve this, we get: p = 11 Aha! 11 is PRIME So, it COULD be the case that k = 15. Let's confirm that this satisfies the other conditions in the question.
If k = 15, then we get: x² – 2px + m = (x - 7)(x - 15) Expand and simplify the right side: x² – 2px + m = x² – 22x + 105 So, this meets the condition that says m is divisible by 5 and is less than 120
We now know that p = 11 and m = 105 All we need to do now is determine the value of n
GIVEN: x = 12 is one of the solutions of the equation x² – 2px + n = 0 Plug in x = 12 to get: 12² – 2p(12) + n = 0 Since we already know that p = 11, we can replace p with 11 to get: 12² – 2(11)(12) + n = 0 Simplify: 144 - 264 + n = 0 Simplify: -120 + n = 0 Solve: n = 120
What is the value of p + n – m? p + n – m = 11 + 120 - 105 = 26
Answer: D
Cheers, Brent
Hello Brent,
I got that approach.But, I was trying to find out the gap in my reasoning.
substitute x = 7 in first equation to get 49-14p+m = 0
Substitute x = 12 in second equation to get 144-24p+n = 0
You can multiple first equation with -1 and then add it to second equation .
This gives
n-m=-24p+14p +144-49= 95 - 10p
Now adding 'p' on both sides gives
p+n-m = 95 - 9p
Now p =7 gives p+n-m as 27 and not 26 which is option D.
Re: A quadratic equation is in the form of x^2–2px + m = 0, where m is
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09 Jun 2019, 01:36
If we consider equation one and two as q1 and q2, and subtract them n-m =0 (x^2-2px +m -x^2+2px -n=0) thus the value of p+n-m should be p which is a prime number and none of the options are prime number kindly explain it
Re: A quadratic equation is in the form of x^2–2px + m = 0, where m is
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09 Jun 2019, 06:34
prabsahi wrote:
GMATPrepNow wrote:
kiran120680 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?
A. 0 B. 6 C. 16 D. 26 E. 27
GIVEN: x = 7 is one of the roots of the equation x² – 2px + m = 0 This means (x - 7) must be one of the factors of the expression on the left side of the equation. That is, x² – 2px + m = 0, can be rewritten as (x - 7)(x +/- something) = 0 [notice that x = 7 is definitely a solution to the new equation] Let's assign the variable k to the missing number (aka "something") We can write: x² – 2px + m = (x - 7)(x - k)
GIVEN: m is divisible by 5 and is less than 120 We already know that: x² – 2px + m = (x - 7)(x - k) If we expand the right side we get: x² – 2px + m = x² – kx - 7x + 7k Now rewrite the right side as follows: x² – 2px + m = x² – (k + 7)x + 7k
We can see that 2p = k + 7 And we can see that m = 7k
In order for m to be divisible by 5, it must be the case that k is divisible by 5. So, k COULD equal 5, 10, 15, 20, 25, etc Let's test a few possible values of k
If k = 5, then 2p = 5 + 7 = 12 When we solve this, we get: p = 6 HOWEVER, we're told that p is PRIME So, it cannot be the case that k = 5
If k = 10, then 2p = 10 + 7 = 17 When we solve this, we get: p = 8.5 HOWEVER, we're told that p is PRIME So, it cannot be the case that k = 10
If k = 15, then 2p = 15 + 7 = 22 When we solve this, we get: p = 11 Aha! 11 is PRIME So, it COULD be the case that k = 15. Let's confirm that this satisfies the other conditions in the question.
If k = 15, then we get: x² – 2px + m = (x - 7)(x - 15) Expand and simplify the right side: x² – 2px + m = x² – 22x + 105 So, this meets the condition that says m is divisible by 5 and is less than 120
We now know that p = 11 and m = 105 All we need to do now is determine the value of n
GIVEN: x = 12 is one of the solutions of the equation x² – 2px + n = 0 Plug in x = 12 to get: 12² – 2p(12) + n = 0 Since we already know that p = 11, we can replace p with 11 to get: 12² – 2(11)(12) + n = 0 Simplify: 144 - 264 + n = 0 Simplify: -120 + n = 0 Solve: n = 120
What is the value of p + n – m? p + n – m = 11 + 120 - 105 = 26
Answer: D
Cheers, Brent
Hello Brent,
I got that approach.But, I was trying to find out the gap in my reasoning.
substitute x = 7 in first equation to get 49-14p+m = 0
Substitute x = 12 in second equation to get 144-24p+n = 0
You can multiple first equation with -1 and then add it to second equation .
This gives
n-m=-24p+14p +144-49= 95 - 10p
Now adding 'p' on both sides gives
p+n-m = 95 - 9p
Now p =7 gives p+n-m as 27 and not 26 which is option D.
Re: A quadratic equation is in the form of x^2–2px + m = 0, where m is
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10 Jun 2019, 05:55
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kiran120680 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?
A. 0 B. 6 C. 16 D. 26 E. 27
x^2 - 2px + m = 0 has root 7. Plug in 7 in this equation. 49 - 14p + m = 0 ... (I) m = 14p - 49 Now note that m is a multiple of 5. So 14p - 49 is a multiple of 5. 14p will be even so it should have 4 as the units digit to get m as a multiple of 5. Hence p should have 1 as the units digit so first such prime number will be 11. If p = 11, we get m = 105 (less than 120). Any other value of p will give m > 120.
x^2 - 2px + n = 0 has root 12. Plug in 12 in this equation. 144 - 24*11 + n = 0 ... (II) n = 120
p + n - m = 11 + 120 - 105 = 26
Answer (D)
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Re: A quadratic equation is in the form of x^2–2px + m = 0, where m is
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10 Jun 2019, 06:16
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VeritasKarishma wrote:
kiran120680 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?
A. 0 B. 6 C. 16 D. 26 E. 27
x^2 - 2px + m = 0 has root 7. Plug in 7 in this equation. 49 - 14p + m = 0 ... (I) m = 14p - 49 Now note that m is a multiple of 5. So 14p - 49 is a multiple of 5. 14p will be even so it should have 4 as the units digit to get m as a multiple of 5. Hence p should have 1 as the units digit so first such prime number will be 11. If p = 11, we get m = 105 (less than 120). Any other value of p will give m > 120.
x^2 - 2px + n = 0 has root 12. Plug in 12 in this equation. 144 - 24*11 + n = 0 ... (II) n = 120
p + n - m = 11 + 120 - 105 = 26
Answer (D)
Thanks for the great explanation.
I got that approach.But, I was trying to find out the gap in my reasoning.
substitute x = 7 in first equation to get 49-14p+m = 0
Substitute x = 12 in second equation to get 144-24p+n = 0
You can multiple first equation with -1 and then add it to second equation .
This gives
n-m=-24p+14p +144-49= 95 - 10p
Now adding 'p' on both sides gives
p+n-m = 95 - 9p
Now p =7 gives p+n-m as 27 and not 26 which is option D.
Re: A quadratic equation is in the form of x^2–2px + m = 0, where m is
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10 Jun 2019, 07:07
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prabsahi wrote:
VeritasKarishma wrote:
kiran120680 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?
A. 0 B. 6 C. 16 D. 26 E. 27
x^2 - 2px + m = 0 has root 7. Plug in 7 in this equation. 49 - 14p + m = 0 ... (I) m = 14p - 49 Now note that m is a multiple of 5. So 14p - 49 is a multiple of 5. 14p will be even so it should have 4 as the units digit to get m as a multiple of 5. Hence p should have 1 as the units digit so first such prime number will be 11. If p = 11, we get m = 105 (less than 120). Any other value of p will give m > 120.
x^2 - 2px + n = 0 has root 12. Plug in 12 in this equation. 144 - 24*11 + n = 0 ... (II) n = 120
p + n - m = 11 + 120 - 105 = 26
Answer (D)
Thanks for the great explanation.
I got that approach.But, I was trying to find out the gap in my reasoning.
substitute x = 7 in first equation to get 49-14p+m = 0
Substitute x = 12 in second equation to get 144-24p+n = 0
You can multiple first equation with -1 and then add it to second equation .
This gives
n-m=-24p+14p +144-49= 95 - 10p
Now adding 'p' on both sides gives
p+n-m = 95 - 9p
Now p =7 gives p+n-m as 27 and not 26 which is option D.
Please help.
Thanks
if 49-14p+m = 0 and 144-24p+n = 0, then how are you getting n-m=-24p+14p +144-49= 95 - 10p?
n = 24p-144 and m = 14p-49 , which makes n-m = 24p-144-14p+49 = 10p-95.
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61% (03:19) correct 
