• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Discuss the toughest problem solving questions.

This topic has 1 expert reply and 8 member replies

Discuss the toughest problem solving questions.

Post
Hey guys,

I am an engineer by profession and would like to discuss the toughest questions on the GMAT.The buzz is that under the Pearson-vue the standard of quant questions has increased exponentially Shocked , so lets take no chances.Starting tommorrow i will post some of the tough questions i have come across during my preparation for the past couple of months.

_Kiran..

  • +1 Upvote Post
  • Quote
  • Flag
Junior | Next Rank: 30 Posts Default Avatar
Joined
09 Apr 2006
Posted:
27 messages
Upvotes:
28
Post
The points P, Q, R lie on a line in that order with PQ=9, QR=21. Let O be a point not on PR such that PO=RO and the distances PO and QO are integral.
Then sum of all possible perimeters of triangle PRO is

(a) 320 (b) 350 (c) 380 (d) 410

The answer will be posted tomm.

  • +1 Upvote Post
  • Quote
  • Flag
Newbie | Next Rank: 10 Posts Default Avatar
Joined
18 Apr 2006
Posted:
8 messages
Post
Whats the answer, don't you need at least one angle? or the height? Does involve Trig? Trig isn't tested, is it?

  • +1 Upvote Post
  • Quote
  • Flag
Junior | Next Rank: 30 Posts Default Avatar
Joined
09 Apr 2006
Posted:
27 messages
Upvotes:
28
Post
Let PO = x = RO, and QO = y,
then by stewart's theorem
(http://planetmath.org/encyclopedia/ProofOfStewartsTheorem.html)

21*x^2 + 9*x^2 = 30*y^2 + 30*9*21 => x^2 - y^2 = (3^3)*(7)

(x+y)(x-y) = (27*7)(1) = 63(3) = 27(7) = 21(9)

We are required to find the sum of all 2x + 30.

From, (x+y)(x-y) = (27*7)(1) = 63(3) = 27(7) = 21(9)
(x,y) can take values as (95,94) (33,30), (17,10) (15,6)
but (x,y) as (15,6) is not possible as QO + RO > QR.

Hence, the required sum is 2(95 + 33 + 17) + 3*30 = 380

Hence, choice (c) is the correct answer.

Note that remembering the result from stewart's theorem can make
you derive the length of median, angle bisector easily

  • +1 Upvote Post
  • Quote
  • Flag
Newbie | Next Rank: 10 Posts Default Avatar
Joined
18 Apr 2006
Posted:
8 messages
Post
i've been prepping for about 6 months now, i think i have a pretty good feel for the type of material that is "fair game" for the test.

That question is well beyond the scope of the GMAT...

Lets try to keep material thats posted, to material thats relevant!

The site is just getting started, and posting questions that aren't relevant doesn't add any value...

  • +1 Upvote Post
  • Quote
  • Flag
Newbie | Next Rank: 10 Posts Default Avatar
Joined
08 Aug 2006
Posted:
2 messages
Post
I disagree with the previous message. The problem is actually not that complex as it looks, and it does not require any specific knowledge, such as the Stewart's theorem. Therefore, I can easily imagine hitting at this problem during GMAT examination, and thanks dkiran01 for giving us this sample.

One can solve this problem using the banal Pythagorean theorem: the first step will be to draw down the height of the isosceles POR triangle, say, to point X on PR, and get two right-angled triangles of POX and QOX. Obviously, QX is PR/2-PQ=30/2-9=6. So:

QO^2=OX^2+36 and
PO^2=OX^2+225, therefore

PO^2=QO^2+189, therefore

PO^2-QO^2=189, therefore

(PO-QO)(PO+QO)=189.

189 is 1*3*3*3*7, and we know from the formulation of the given problem that both brackets result in integer values. It logically means that values are integrally divisible by divisors of 189.
As PO-PQ is less than PO+PQ, we can check up only those divisors of 189 that suit PO-PQ so that it is less than PO+PQ. Easily, it's 1, 3, 7 and 9. As dkiran01 showed, the last option is invalid because the sum of any two legs of any triangle is bigger than the thrid leg. So, we get suiting values of PO-QO and, therefore, PO: 98, 33 and 17. That's what we needed to calculate the sum of all possible perimeters of the triangle POR. Easy? I think, as soon as you grip the idea of how to solve this problem, it will take up to 1 minute to make a calculation. Suitable for GMAT.

  • +1 Upvote Post
  • Quote
  • Flag
Junior | Next Rank: 30 Posts Default Avatar
Joined
30 Sep 2006
Posted:
16 messages
Upvotes:
1
Post
please help

can somebody explain how this question is solved - As i understand it - the angle bisector of POR is perpendicular to PR and thereby divides PR into 2 equal halves - hence if PX = 15, OP has to be 17 (pythagorean triplets)

now, here are my questions?

a. why are we finding the distance QX?
b. how did you figure the other values of 98 and 33

  • +1 Upvote Post
  • Quote
  • Flag
Newbie | Next Rank: 10 Posts Default Avatar
Joined
08 Aug 2006
Posted:
2 messages
Post
Quote:
a. why are we finding the distance QX?
There is no problem with finding it, indeed, it's just a step of calculations. Obviously, QX is 6. Why we want to know it - because there is a crucial condition that QO is an integral, and we want to find such PRO triangles that satisfy this condition. Knowing that QX in triangle QXO is 6, we can find possible XOs that make QO integral.

Quote:
b. how did you figure the other values of 98 and 33
Please specify. Values other than 98 and 33? Or other values in triangles where PO is 98 or 33?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
27 Dec 2006
Posted:
2228 messages
Followed by:
684 members
Upvotes:
639
GMAT Score:
780
Post
Please post the sources for any problems you post. The sources help members to decide whether they want to study a problem or whether they think it might not be representative of the GMAT. Thanks!

_________________
Please note: I do not use the Private Messaging system! I will not see any PMs that you send to me!!

Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT

Contributor to Beat The GMAT!

Learn more about me

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
Junior | Next Rank: 30 Posts Default Avatar
Joined
09 Mar 2007
Posted:
14 messages
Upvotes:
1
Post
Assuming: PO = x and QO = y

x.x - 15.15 = y.y - 6.6 (equating the Perpendicular from O on PR)

=> (x+y).(x-y) = (15+6).(15-6)
= 21.9
= 21.3.3 = 7.3.3.3
Since x and y are integers hence their 'addition' and 'difference' will also be integer Therefore:

Sol1:
*Since, O is not on PR hence (x+y) = 21 and (x-y) = 9 is not possible because it gives x=15 and y=6

*Also, Any solution (x+Y) < (x-Y) is not possible (x > y > 0)

Sol2:
(x+y) = 7.3.3 = 63
(x-y) = 3

=> x = 33 => Perimeter1 = 2.33+30 = 96

Sol3:
(x+y) = 21.3.3 = 189
(x-y) = 1

=> x = 95 => Perimeter2 = 2.95+30 = 220

Sol4:
(x+y) = 3.3.3 = 27
(x-y) = 7

=> x = 17 => Perimeter3 = 2.17+30 = 64



Sum of Total perimeters: 96+ 220 + 64 = 380

Isn't this easy?

Not necessary to remember the big theorem !!!

Enjoy !!!

  • +1 Upvote Post
  • Quote
  • Flag
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Top First Responders*

1 Brent@GMATPrepNow 65 first replies
2 fskilnik@GMATH 55 first replies
3 Jay@ManhattanReview 44 first replies
4 GMATGuruNY 34 first replies
5 Rich.C@EMPOWERgma... 32 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

135 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

103 posts
3 image description Max@Math Revolution

Math Revolution

90 posts
4 image description Jay@ManhattanReview

Manhattan Review

82 posts
5 image description Rich.C@EMPOWERgma...

EMPOWERgmat

80 posts
See More Top Beat The GMAT Experts