Is point (r,s) on the line y=2x+3? (I) (2r-s+3)(4r+2s-6)=0

Question

Is point (r,s) on the line y=2x+3?

(I) (2r-s+3)(4r+2s-6)=0
(II) (3r+2s-5)(2r-s+3)=0

MA · Answer

HONGHU, you have good collection of GMAT questions.

D. each statement is sufficient to answer the answer. 

From i, r = 0 and s = 3
from ii, r = -1/7, s = 19/7


both values of r and s satisfy the above equation.

prep_gmat · Answer

E.
St1: 2r-s+3 may or may not equal zero, so insufficient.
St2: 2r-s+3 may or may not equal zero, so insufficient.
St1 + St2: r=1 and s can be anything, so (r,s) may or may not be on the line. Insufficent.

MA · Answer

from statement (I), 
2r-s=-3 ............................. eq (1)
4r+2s=6 ........................... eq (2)
solving these equations yields r = 0 and s = 3 
y=2x+3 => s=2r+3 => s=2(0)+3=3
satisfies the eq.



from statement (II), 
3r+2s=5............................. eq (3)
2r-s=-3 ........................... eq (4)
solving these equations yields r = -1/7, s = 19/7 
y=2x+3 => s=2r+3 => s=2(-1/7)+19/7=19/7
also satisfies the eq.......

OA is D....

banerjeea_98 · Answer

MA, u can't assume that both of the eqn in state 1 is 0 at the same time i.e. either one of them can be 0 to make the eqn valid, so no solution is possible. Same goes for eqn 2. U have to combine them to get an ans.

MA · Answer

baner,

Could you pls be more specific with some examples..........?

toddmartin · Answer

If you have 2 things multiplied together you don't know for sure they are both 0. For example, you could have the equation (x)*(0)=0

 Now you know that one term or both terms are 0, but you don't know that x=0. x could = 50 or anything and the equation would still be true.

tareks · Answer

So one cant multiply both equations together and then solve and check? I do understand that we dont know which one equals zero, so is that a good enough reason to answer E? Or are more calculations needed?

HongHu · Answer

OA is E, prep_gmat's explanation is correct.

MA · Answer

Honghu,

explanation pls..........

HongHu · Answer

Meaning, is 2r-s+3=0?

(I) (2r-s+3)(4r+2s-6)=0
=>
2r-s+3=0 or 
4r+2s-6=0 =>2r+s-3=0
insufficient
eg: (1,-1) is on the line while (1,1) isn't, both satisfy (I)

(II) (3r+2s-5)(2r-s+3)=0
3r+2s-5=0 
or
2r-s+3=0
insufficient
eg: (1,-1) is on the line while (1, 1) isn't, both satisfy (II)

Combine (I) and (II), the same examples can still be used to satisfy both combined, while (1,-1) is on the line while (1,1) is not.

Vijo · Answer

I know I am late.... the answer will be E.

vprabhala · Answer

thanks HongHu.. thats a good explanation..

Is point (r,s) on the line y=2x+3? (I) (2r-s+3)(4r+2s-6)=0

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards