Data Sufficiency

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

(1) a/b = c/d

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

oa c, but shldnt it be e

st two can be written as |a|+|b| = |c|+|d|

sqare root of (x^2) means |x|

now square both sides and use st 1 ull see a^2 + b^2 = c^2 + d^2

sumithshah wrote: now square both sides and use st 1 ull see a^2 + b^2 = c^2 + d^2

a^2+2*|a|*|b|+b^2=c^2+2*|c|*|d|+d^2
first statement a/b=c/d or a*d=b*c
I don't see how you get a^2 + b^2 = c^2 + d^2

Please explain.

I am getting E, as per previous post of youngwolf..

Any thoughts?

youngwolf wrote:

sumithshah wrote: now square both sides and use st 1 ull see a^2 + b^2 = c^2 + d^2

a^2+2*|a|*|b|+b^2=c^2+2*|c|*|d|+d^2
first statement a/b=c/d or a*d=b*c
I don't see how you get a^2 + b^2 = c^2 + d^2

Please explain.

My bad, I was thinking AD = BC was given. But he answer is STILL C.

Picked from Mgmat forum

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(1) a/b = c/d

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

Ok,

1 is clearly not sufficient. Let's write 2 as

|a|+|b| = |c|+|d| , this is not sufficient since it can have many solutions. Now multiply both sides with |d|

|a||d|+|b||d| = |c||d|+|d||d|..................call it 3

Fom 1, ad=bc, so |a||d| = |b||c|

Replacing in our equation 3

|b||c|+|b||d| = |c||d|+|d||d|

|b| (|c|+|d|) = |d| (|c|+|d|)

Hence, |b| = |d|, and using 1 with this, |a| = |c|

So a,b and c,d have same values of co-ordinates if signs are ignored.

Since ditance from origin is square root of sum of squares of x and y co-ordinates, these 2 are equidistant from origin.

So, C is the answer.

cool explanation man. My GMAT is approaching quickly but I dont think that I would be able to tackle tquant questions like these in about 2 mins.

well, we know the ratios of (a/b) is equal to (c/d) so it means that they might have different signs (-/-) = (+/+) or same signs such as (+/+) = (+/+) ---> HINT 1 ( equal ratios) + HINT 2 ( they might or not have same signs )

and we know that the sum of their absolute values are the same!

since absolute values are always + numbers

Hence, |b| = |d| & |a| = |c|

Hope this approach helps to simply this question for you.

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

(1) a/b = c/d

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

i did it this way....

(1) a/b = c/d

adding 1 to both sides, we get
(a/b)+1 = (c/d)+1
(a+b)/b=(c+d)/d ----(A)


from (2)
root (a^2)+root (b^2) = root (c^2) + root (d^2)
it can be simplied as
a+b=c+d ---(B)
(irrespective of if they are +ve or -ve numbers)


from (A) and (B), if numerators are same, then numerators must be same
ie b=d ---(C)

from (C) and (B) we get
a=c

So the points (a, b) and (c, d) equidistant from the origin.


Did I missed out on something by not considering the sign of the numbers here?