GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Feb 2019, 09:07

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

# Question of the week - 33 (A quadratic equation is in the form ......)

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2597
Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

### Show Tags

25 Jan 2019, 05:22
00:00

Difficulty:

55% (hard)

Question Stats:

55% (02:20) correct 45% (02:49) wrong based on 49 sessions

### HideShow timer Statistics

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

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Director
Joined: 18 Jul 2018
Posts: 680
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

### Show Tags

25 Jan 2019, 06:53
Bunuel sir, This question has been posted twice.

Can you merge the replies?
_________________

Press +1 Kudo If my post helps!

VP
Joined: 09 Mar 2018
Posts: 1003
Location: India
Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

### Show Tags

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?

A. 0
B. 6
C. 16
D. 26
E. 27

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

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
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

SVP
Joined: 18 Aug 2017
Posts: 1928
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

### Show Tags

25 Jan 2019, 09:55
1
$$x^2 – 2px + m = 0$$

given one value of x=7
49-14p+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
49-14*11+m=0
m= 105

$$x^2 – 2px + n = 0$$
at x=12
144-24p+n
p=11
n=120
so
p + n – m
11+120-105

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?

A. 0
B. 6
C. 16
D. 26
E. 27

_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Intern
Joined: 14 Sep 2018
Posts: 10
Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

### Show Tags

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.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2597
Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

### Show Tags

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:
• The value of p + n – m

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.

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Joined: 12 Sep 2017
Posts: 142
Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

### Show Tags

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
49-14p+m=0"

Kind regards!
Manager
Joined: 12 Sep 2017
Posts: 142
Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

### Show Tags

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:
• The value of p + n – m

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.

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?

Kind regards!
SVP
Joined: 18 Aug 2017
Posts: 1928
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

### Show Tags

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
49-14p+m=0"

Kind regards!

jfranciscocuencag
its 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"
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2597
Re: Question of the week - 33 (A quadratic equation is in the form ......)  [#permalink]

### Show Tags

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?

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
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: Question of the week - 33 (A quadratic equation is in the form ......)   [#permalink] 01 Feb 2019, 01:39
Display posts from previous: Sort by