Author 
Message 
TAGS:

Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 542
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
Updated on: 17 Jun 2017, 13:26
Question Stats:
65% (01:04) correct 35% (01:10) wrong based on 1088 sessions
HideShow timer Statistics
If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ? A. 36 B. 42 C. 48 D. 49 E. 51
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Md. Abdur Rakib
Please Press +1 Kudos,If it helps Sentence CorrectionCollection of Ron Purewal's "elliptical construction/analogies" for SC Challenges
Originally posted by AbdurRakib on 17 Jun 2017, 08:20.
Last edited by Bunuel on 17 Jun 2017, 13:26, edited 2 times in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 49320

If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
17 Jun 2017, 13:35




BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3136
Location: India
GPA: 3.12

If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
17 Jun 2017, 10:37
AbdurRakib wrote: If m and p are positive integers and \(\sqrt{m} + \sqrt{p}\) < 100, what is the greatest possible value of mp ? A. 36 B. 42 C. 48 D. 49 E. 51 AbdurRakibKindly change the highlighted part of the question. it must be \(m^2 + p^2 < 100\)
_________________
You've got what it takes, but it will take everything you've got



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3136
Location: India
GPA: 3.12

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
17 Jun 2017, 10:49
Given m and p are postive integers and we need to find out the greatest value of mp? Since \(m^2 + p^2\) < 100, evaluating the answer options.. 36 = 6*6, 42 = 6*7, 48 = 6*8, 49 = 7*7 and 51 = 3*17 Of the available only 51(3*17) has a value of \(m^2 + p^2\) greater than 100 Since we have to find out the greatest value of mp, 49, where m=p=7 (Option D) will have value of \(m^2 + p^2\) =\(7^2 + 7^2\) = 98 which is less than 100
_________________
You've got what it takes, but it will take everything you've got



Math Expert
Joined: 02 Sep 2009
Posts: 49320

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
17 Jun 2017, 13:36



Manager
Joined: 28 Apr 2016
Posts: 97

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
13 Jul 2017, 07:21
Does this mean that in GMAT questions we can always assume x may be equal to y, unless specifically mentioned that they are 'distinct numbers'?



Manager
Joined: 24 Jun 2017
Posts: 122

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
13 Jul 2017, 08:16
My solution m^2 + p^2 = (m  p)^2+2mp<100, so if we assume that (m  p)^2 = 0 in order to maximize the value of 2mp, then 2mp < 100, mp < 50 answer 49



Math Expert
Joined: 02 Sep 2009
Posts: 49320

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
13 Jul 2017, 10:14



Director
Joined: 13 Mar 2017
Posts: 619
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
14 Jul 2017, 00:26
AbdurRakib wrote: If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36 B. 42 C. 48 D. 49 E. 51 AM >= GM \((m^2+p^2 )/ 2 >= \sqrt{m^2*p^2}\) \(mp =< (m^2+p^2 )/ 2 <100/2\) mp < 50 Greatest possible value = 49 Answer D.
_________________
CAT 99th percentiler : VA 97.27  DILR 96.84  QA 98.04  OA 98.95 UPSC Aspirants : Get my app UPSC Important News Reader from Play store.
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3515
Location: United States (CA)

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
16 Jul 2017, 17:37
AbdurRakib wrote: If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36 B. 42 C. 48 D. 49 E. 51 The product of two positive integers is greatest if they are as close as possible, that is, if they are equal. Thus, we can let p = m, and our inequality becomes m^2 + m^2 < 100. Let’s solve it: 2m^2 < 100 m^2 < 50 m < √50 Since m is a positive integer and the largest positive integer less than √50 is 7, m = 7. In that case, p is also 7. Thus the greatest possible value of mp is 7 x 7 = 49. Alternate Solution: Let’s test each answer choice, starting from the greatest, which is 51. Notice that 51 = 3 x 17, so our only choices for m and p are 3 and 17 or 1 and 51. Neither of these choices satisfy m^2 + p^2 < 100, and therefore mp cannot equal 51. Next, let’s test 49. Since the choice m = 49 and p = 1 does not satisfy m^2 + p^2 < 100, let’s take a look at m = 7 and p = 7. Since m^2 + p^2 = 49 + 49 = 98 < 100, mp can equal 49. Since we are looking for the greatest possible value of mp, it is 49. Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Senior Manager
Joined: 29 Jun 2017
Posts: 418

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
21 Jul 2017, 02:08
AbdurRakib wrote: If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36 B. 42 C. 48 D. 49 E. 51 I think gmat will not force us to remember any rules here. just pick specific numbers and see what happen if m=p, we have m=7 increase m and reduce p m=8, p=5 m=9, p=3 so, it is best if m=p



CEO
Joined: 12 Sep 2015
Posts: 2883
Location: Canada

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
22 Aug 2017, 08:19
AbdurRakib wrote: If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36 B. 42 C. 48 D. 49 E. 51 Let's test some pairs of values. Since m and p are POSITIVE INTEGERS, we won't have a ton of options Try m = 9 and p = 4 (aside: if m = 9, then 4 is the biggest possible value of p) In this case, mp = (9)(4) = 36 Try m = 8 and p = 5 (aside: if m = 8, then 5 is the biggest possible value of p) In this case, mp = (8)(5) = 40 Try m = 7 and p = 7 (aside: if m = 7, then 7 is the biggest possible value of p) In this case, mp = (7)(7) = 49 Try m = 6 and p = 7 (aside: if m = 6, then 7 is the biggest possible value of p) In this case, mp = (6)(7) = 42 Try m = 5 and p = 8 At this point, we can see that, if we continue, we'll be duplicating the work we did earlier. That is, this case (m = 5 and p = 8) is the SAME as the 2nd case we examined. If we continue, the next case we test will be m = 4 and p = 9. which is the SAME as the 1st case we examined, etc. Since we've now tested all possible (and relevant) cases, we can see that the maximum value of mp is 49 Answer: Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails



Manager
Joined: 07 Jan 2015
Posts: 67
Location: United States
GPA: 3.4
WE: Engineering (Manufacturing)

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
05 Sep 2017, 04:38
AbdurRakib wrote: If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36 B. 42 C. 48 D. 49 E. 51 I learned one of these concepts from Bunnel (\((MP)^2>= 0\) Therefore M^2 +P^2 >= 2MP . Greatest Value of 2MP = M^2+P^2 . Great Value of M^2+P^2 = 99 or 98 There MP = 99/2 = Integer (not possible  Integer X Integer = Integer) or 98/2 =49 Please give Kudos if you like this explanation



Intern
Joined: 31 Oct 2017
Posts: 1

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
05 Nov 2017, 22:54
I think the answer should be 42. The question says m and p are integers. 'Are integers' should mean two distinct integers, not a single integer. So, we cant take 7 as the value of both m and p. Rather we can take 6 and 7 where the sum of their square is 85 that is lower than 100. And 7 times 6 equals to 42. So, the answer is 42.



Math Expert
Joined: 02 Sep 2009
Posts: 49320

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
05 Nov 2017, 22:57



Intern
Joined: 13 Jan 2018
Posts: 5
Location: Canada
GPA: 3.59

If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
03 Mar 2018, 17:38
AbdurRakib wrote: If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36 B. 42 C. 48 D. 49 E. 51 Using Bunnel and Satsurfs explanations above, here is how i made sense of the solution: M^2+P^2 <100 If (mp)^2 =0 then m^2 +p^22mp=0; m^2+p^2 =2mp Inserting this into the original equation; Therefore; 2mp < 100; mp<50 The greatest possible value of mp is therefore 49



Intern
Joined: 15 Oct 2016
Posts: 31

If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
03 Mar 2018, 23:47
AbdurRakib wrote: If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36 B. 42 C. 48 D. 49 E. 51 The basic concept behind nailing this problem is the fact that for real positive numbers a and b, (a+b)/2 >= (ab)^0.5. This is known as the AMGM inequality. Therefore, (m^2+p^2)/2 >= mp => mp <50. Hence the greatest value of mp is 49 (without the restriction on m and p of being integers). Since we have got this for any real positive m and p, you just need to ensure 49 is possible as a product of integers (since m and p have to be integers). If no, then keep moving backwards from 49. Luckily, 49 does get expressed as a product of two integers. Hence, max (mp) = 49



Intern
Joined: 15 Oct 2016
Posts: 31

Re: If m and p are positive integers and m^2 + p^2 < 100, what is the
[#permalink]
Show Tags
03 Mar 2018, 23:51
meyba2ty wrote: AbdurRakib wrote: If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36 B. 42 C. 48 D. 49 E. 51 Using Bunnel and Satsurfs explanations above, here is how i made sense of the solution: M^2+P^2 <100 If (mp)^2 =0 then m^2 +p^22mp=0; m^2+p^2 =2mp Inserting this into the original equation; Therefore; 2mp < 100; mp<50 The greatest possible value of mp is therefore 49 The expression above gives you the max product of real positives m and p (not necessarily for integers). So, please make sure you do not miss the part where you need to check whether the maximum product value of 49 is valid for product of integers.




Re: If m and p are positive integers and m^2 + p^2 < 100, what is the &nbs
[#permalink]
03 Mar 2018, 23:51






