In the rectangular coordinate system, are the points (a, b)

Oldest

Best Reply

Author

Message

TAGS:

Intern

Joined: 12 Aug 2011

Posts: 4

Followers: 0

Kudos [?]: 1 [0], given: 1

In the rectangular coordinate system, are the points (a, b) [#permalink]

17 Aug 2011, 11:42

00:00

Question Stats:

75% (03:08) correct

25% (01:13) wrong

based on 1 sessions

In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) sqrt(a^2)+sqrt(b^2) =sqrt(c^2) +sqrt(d^2)

OA follows..

OA is C.

I have seen a couple of nice approaches on number plugging, but just checking if there are any other innovative ideas to think conceptually on this. I myself tried algebra...then tried to switch mid-way to plugging and messed it on time...

So pointers on CONCEPT, GUESSING, TAKEAWAYS on how to recognize what approach to adopt,,... all welcome.

Thank you

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-rectangular-coordinate-system-are-the-points-a-b-92533.html

TOPIC IS LOCKED.

[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Apr 2012, 08:28, edited 1 time in total.

Topic is locked

Kaplan Promo Code

Knewton GMAT Discount Codes

Manhattan GMAT Discount Codes

Manager

Status: Quant 50+?

Joined: 02 Feb 2011

Posts: 109

Concentration: Strategy, Finance

Followers: 1

Kudos [?]: 21 [0], given: 22

Re: Guaranteed Toughie 700+ - looking for creative ideas ways.. [#permalink]

18 Aug 2011, 07:23

mokap25 wrote:

Not too difficult I think.

(1) A/B = C/D tells us that a/b & c/d are proportionally the same. Take an example of a/b = 1/2 and c/d = -4/-8 to understand it is not sufficient.

Now (2) is basically saying the absolute value of the sum is the same for both points. Of course this could be true with (2,2) and (4,0) which are not the same distance from the origin.

(1)+(2) Now if you just think about it, two points that have the same ratio, and the same absolute sum must be the same distance from the origin.

Director

Joined: 03 May 2007

Posts: 903

Schools: University of Chicago, Wharton School

Followers: 4

Kudos [?]: 30 [0], given: 6

Re: Guaranteed Toughie 700+ - looking for creative ideas ways.. [#permalink]

18 Aug 2011, 17:33

mokap25 wrote:

Toughie from MGMAT - looking for creative and different approaches to approach this problem.

In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2)sqrt(a^2)+sqrt(b^2) =sqrt(c^2) +sqrt(d^2)

OA follows..

OA is C.

I have seen a couple of nice approaches on number plugging, but just checking if there are any other innovative ideas to think conceptually on this. I myself tried algebra...then tried to switch mid-way to plugging and messed it on time...

So pointers on CONCEPT, GUESSING, TAKEAWAYS on how to recognize what approach to adopt,,... all welcome.

Thank you

The question is asking about the distance from the origin.

Statement 1 says only about the ratio (a/b = c/d) of the coordinates of the points (a, b) and (c, d).
If a = 3 and b = 1, a/b = 3.
c/d could be three in many ways...That's clearly not sufficient..

Statement 2:
sqrt(a^2)+sqrt(b^2) =sqrt(c^2) +sqrt(d^2)
i.e. a+b = c+d.

This is possible in many ways. This is also not sufficient..

Statements 1 and 2: I wonder how to solve algebraically!

a/b = c/d ........................(i)
a + b = c + d ....................(ii)

suppose a/b = c/d = 3
a = 3b
c = 3d

3b + b = 3d + d ....................(iii)
4b = 4d
b = d

If b = d, a has to be equal to c. If so, coordinates points (a, b) and (c, d) are in equi-distance from the origin...

C.

Manager

Joined: 28 Apr 2011

Posts: 188

Followers: 0

Kudos [?]: 3 [0], given: 6

Re: Toughie from MGMAT - looking for creative and different [#permalink]

07 Apr 2012, 08:19

IMO B......

bunnel request your explanation why b alone can't be sufficient......

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11506

Followers: 1791

Kudos [?]: 9526 [0], given: 826

Re: Toughie from MGMAT - looking for creative and different [#permalink]

07 Apr 2012, 08:26

vdbhamare wrote:

IMO B......

bunnel request your explanation why b alone can't be sufficient......

In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

Distance between the point A (x,y) and the origin can be found by the formula: D=\sqrt{x^2+y^2}.

So we are asked whether \sqrt{a^2+b^2}=\sqrt{c^2+d^2}? Or whether a^2+b^2=c^2+d^2?

(1) \frac{a}{b}=\frac{c}{d} --> a=cx and b=dx, for some non-zero x. Not sufficient.

(2) \sqrt{a^2}+\sqrt{b^2}=\sqrt{c^2} +\sqrt{d^2} --> |a|+|b|=|c|+|d|. Not sufficient.

(1)+(2) From (1) a=cx and b=dx, substitute this in (2): |cx|+|dx|=|c|+|d| --> |x|(|c|+|d|)=|c|+|d| --> |x|=1 (another solution |c|+|d|=0 is not possible as d in (1) given in denominator and can not be zero, so d\neq{0} --> |c|+|d|>0) --> now, as |x|=1 and a=cx and b=dx, then |a|=|c| and |b|=|d| --> square this equations: a^2=c^2 and b^2=d^2 --> add them: a^2+b^2=c^2+d^2. Sufficient.

Answer: C.

IN CASE OF ANY QUESTION PLEASE POST IT HERE: in-the-rectangular-coordinate-system-are-the-points-a-b-92533.html
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Re: Toughie from MGMAT - looking for creative and different [#permalink] 07 Apr 2012, 08:26

		Similar topics	Author	Replies	Last post
Similar Topics:		In the rectangular coordinate system, are the points (a, b)	Piter	3	23 Aug 2007, 13:51
	1	In the rectangular coordinate system, are the points (a, b)	eyunni	4	10 Dec 2007, 16:44
		In the rectangular coordinate system, are the points (a, b)	jimjohn	2	17 Dec 2007, 14:57
		In the rectangular coordinate system, are the points (a, b)	jimmyjamesdonkey	5	15 Jul 2008, 18:51
		In a rectangular coordinate system, are the points (a,b) and	tarek99	8	15 Nov 2008, 15:56

In the rectangular coordinate system, are the points (a, b)

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

In the rectangular coordinate system, are the points (a, b)

In the rectangular coordinate system, are the points (a, b)

Main navigation

GMAT Resources

Partners

MBA Resources