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

(1) a/b = c/d
(2) + = +

hi Agganitk..
st:1 looks insufficient, lets assume a=5, b=3, c=5, d =3 or a=5, b=3, c=10, d =6 the condition is fulfilled with different values so Yes and No.

not too sure about st. 2

Thanks, Preet

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

(1) a/b = c/d
(2) + = +

_
after rephrasing the stem asks us Is a^2+b^2 = c^2 +d^2

St 1:

a/b = c/d
Not much of idea...Insufficient

St 2:

Squaring both sides :

a^2 +b ^2+2 ab= c^2 +d^2+2cd

This scenario is possible only if |a^2| =|c^2|; |b^2|= |d^2|; |ab| = |cd|

St 2 is sufficient

example (a,b) : (1,0)
c,d : (-1,0)

Is a^2+b^2 = c^2 +d^2
YES
Pick B

answer is C
https://www.manhattangmat.com/forums/in- ... -t915.html

outreach wrote:answer is C
https://www.manhattangmat.com/forums/in- ... -t915.html

@Outreach,

can u plz tel me why ST 2 alone is not SUFFICIENT?

in order for the points to be equidistant

a^2 + b^2 = c^2+ d^2 -----> eq X

St 1 a/b=c/d -(1)
ad=bc
insuff


St 2 sqrt(a)^2+sqrt(b)^2=sqrt(c)^2+sqrt(d)^2 -(2)
i.e. a+b=c+d - (3)
multiple sol possible

INSUFF


combining 1 and 2

eq 1 a/b=c/d
can be written as (a+b)/b = (c+d)/d
sub value of eq 3
b=d - (4)


similarly eq 1 can be written as b/a = d/c
a+b/a = d+c/c
sub eq 1 we get a = c -(5)

on sub values of eq 4 and 5, eq X is satisfied

In st 2, u have squared the individual components rather than the whole expression..

Is that so?

sq root(a^2)=a
sq root(b^2)=b

sq root(c^2)=c
sq root(d^2)=d

gmatmachoman wrote:In st 2, u have squared the individual components rather than the whole expression..

Is that so?

gmatmachoman wrote:In st 2, u have squared the individual components rather than the whole expression..

Is that so?

Hey machoman,

outreach didn't actually square both sides - he (she?) just simplified the terms.