Absolute distances

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

ov25: Master | Next Rank: 500 Posts; Posts: 201; Joined: Sat Jul 10, 2010 2:23 pm; Thanked: 7 times; Followed by:1 members

Absolute distances

by ov25 » Mon Dec 13, 2010 7:19 am

In a number line, there are points M, N, P and Q not necessarily in that order. If MN=15, NP=5, MQ=12, which of the following could be the distance between P and Q?
I) 2
II) 8
III) 22

A) I only
B) II only
C) III only
D) II and III
E) I, II and III

I tend to waste a lot of time to solve these questions. Is there a quick combination type method to encompass all the possibilities for solving such questions quickly? Appreciate your time

Quote

Source: Beat The GMAT — Data Sufficiency | Mon Dec 13, 2010 7:19 am

clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 am; Thanked: 85 times; Followed by:3 members

by clock60 » Mon Dec 13, 2010 1:44 pm

hi ov25, for me it is also time-killer problem, and i am not sure that i solved it right, need your verification and expert`s replies. my way
|m-n|=15.
|n-p|=5
|m-q|=12. and we need to find |p-q|-?
1)m>n, and m>q.
m-n=15.
m-q=12. substract and left with m-n-m+q=3.

q-n=3
n-p=5 , if n>p now add q-n+n-p=8, q-p=8 looks like 2 answer is valid

2) n-m=15, if m<n, n-p=5 if n>p again substract both
n-m-n+p=10, p-m=10, and m-q=12 if m>q, now i want to add, p-m+m-q=22, p-q=22 third answer also looks valid

3)p-n=5 if n<p and m-q=12 if m>q, add both p-n+m-q=17, and m-n=15. if m>n here i substract
p-n+m-q-m+n=2, p-q=2
my answer is E

Quote

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pm; Thanked: 215 times; Followed by:7 members

by kvcpk » Mon Dec 13, 2010 11:32 pm

ov25 wrote:In a number line, there are points M, N, P and Q not necessarily in that order. If MN=15, NP=5, MQ=12, which of the following could be the distance between P and Q?
I) 2
II) 8
III) 22

A) I only
B) II only
C) III only
D) II and III
E) I, II and III

I tend to waste a lot of time to solve these questions. Is there a quick combination type method to encompass all the possibilities for solving such questions quickly? Appreciate your time

I dont think there is a shortcut to it except to think logically quick by drawing the picture.
its given the that the points are on number line.

Q......12......M.........15........N.....5....P
Dist between P and Q is 32

Q......12......M.....10.......P.....5...N
Dist between P and Q is 22

M.........12..Q....3..N.....5....P
Dist between P and Q is 8

M.....10....P..2..Q....3..N
Dist between P and Q is 2

Hence I, II and III are possible

pick E.

"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)

Quote

Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 am; Thanked: 378 times; Followed by:123 members; GMAT Score:760

by Geva@EconomistGMAT » Mon Dec 13, 2010 11:56 pm

ov25 wrote:In a number line, there are points M, N, P and Q not necessarily in that order. If MN=15, NP=5, MQ=12, which of the following could be the distance between P and Q?
I) 2
II) 8
III) 22

A) I only
B) II only
C) III only
D) II and III
E) I, II and III

I tend to waste a lot of time to solve these questions. Is there a quick combination type method to encompass all the possibilities for solving such questions quickly? Appreciate your time

a potential speed-up is process of Elimination = eliminate answer choices as you come up with possible results.

Begin with the most banal, linear setting: Start with M, move 15 to the right to find N, add another 5 to get P. P is now 20 from M. With the last bit of MQ=12, we get that PQ=8, So II is a possible.
Before you move on, ask: Which answer choices can we eliminate? any answer choice that does not include II is gone, so we eliminate A and C, and are down to B, D and E.

Now shift one element of your chosen configuration: Start with M, move 15 to the right to find N, but now move 5 to the left to find P. P is now 15-5=10 away from M. With the last bit of MQ=12, we get that PQ=2, So I is a possible.

Again, now ask: Between B, D, E, what can we eliminate now? Everything that doesn't contain I is gone, so B and D are out, and we can choose E and move on - no need to search for a distance of 22.

In "statements" questions, it is better to eliminate answer choices as you go - you just might find that one (or more) of the statements does not need to be addressed because of POE.

Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

Quote

Woozler: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Sat Nov 06, 2010 12:04 pm

by Woozler » Tue Dec 14, 2010 12:25 pm

M---12----Q
|
15
|
N--5---P

Just imagine the MQ and NP arms swinging in both directions, and then do quick mental math. It took me less than a minute to go through all three options.