In the rectangular coordinate system, are the points (a, b) : DS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 07:53

### 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 June
Open Detailed Calendar

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

Author Message
Manager
Joined: 09 Dec 2006
Posts: 96
Followers: 1

Kudos [?]: 32 [0], given: 0

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

### Show Tags

23 Aug 2007, 12:51
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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)
VP
Joined: 09 Jul 2007
Posts: 1104
Location: London
Followers: 6

Kudos [?]: 103 [0], given: 0

### Show Tags

23 Aug 2007, 13:57
Piter wrote:
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)

I think it is E.
as take any points

1;2 and then 2;1 those points are quidistant from the origin 0
or take -1;2 and -2;1 and those as well. so 1 is not suff.

2. the same thing only sum of the coordinates. a+b=c+d which is not sufficient to say yes or no

so E
Manager
Joined: 09 Dec 2006
Posts: 96
Followers: 1

Kudos [?]: 32 [0], given: 0

### Show Tags

23 Aug 2007, 14:29
OA NOT E
OA and explanations later...
It's horrible problem...
Manager
Joined: 09 Dec 2006
Posts: 96
Followers: 1

Kudos [?]: 32 [0], given: 0

### Show Tags

24 Aug 2007, 06:43
OA C
Quote:
To find the distance from the origin, we simply take the square root of the sum of the squared x- and y-coordinates, i.e. SQRT(x^+y^2).

(1) INSUFFICIENT: This simply tells us that the proportions between the x- and y-coordinates of both points are the same. E.g. take a = 5, b = 10, c = 6 and d = 12. The proportions are the same but the coordinate points are not the same distance from the origin. Conversely, if a = 5, b = 10, c = -5 and d = -10, then the proportions are equal and the coordinate points are the same distance from the origin.

(2) INSUFFICIENT: By simplifying the expression, we get |a| + |b| = |c| + |d|. This is not enough to tell if the points are equidistant. E.g. take a = 11, b = 1, c = 6 and d = 6. The expression |a| + |b| = |c| + |d| is true but the coordinate points are not the same distance from the origin. Conversely, if a = -6, b = 6, c = 6 and d = 6, then the given expression is true and the coordinate points are the same distance from the origin.

(1) AND (2) SUFFICIENT: Together the statements are sufficient. Why? If we know the proportion of a to b is the same as c to d and that |a| + |b| = |c| + |d|, then it must be the case that |a| = |c| and |b| = |d|. Plugging this into our distance formula, we get:

SQRT(a^+b^2) = SQRT(c^+d^2) ; Plug in |a| = |c| and |b| = |d| to get:
SQRT(a^+b^2) = SQRT(a^+b^2)

This is enough to show that the two points are equidistant.

24 Aug 2007, 06:43
Display posts from previous: Sort by