If r − s = 240, does r = 320?

Question

(1) r = 4s
(2) s = 80

Kritesh · Answer

Consider statement A :

r = 4s

Substituting it into the equation r -s = 240 we get ,

4s -s = 240

3s = 240

s = 80 . Therefore r = 4*80 = 320 .  Statement A is sufficient.

Consider statement B :

s = 80

Substituting it into the equation r -s = 240 we get ,

r - 80 = 240

r =320 .  Statement B is sufficient.

Answer is option D.

BrentGMATPrepNow · Answer

Given :  r − s = 240

Target question :    Does r = 320?

Statement 1 : r = 4s

When we add this information to our given information we have two equations: 
 r − s = 240 
r = 4s

There are several different approaches we can take from here.

One approach this to recognize that, since we have a system of 2 linear equations with 2 variables, we COULD solve the system for r and for s, which means we COULD answer the  target question  with certainty.
So, statement 1 is SUFFICIENT
---------
Another approach is to actually solve the system. How to do that also (for "fun")
Take:  r − s = 240 
Replace r with 4s to get: 4s - s = 240
Simplify to get: 3s = 240
Divide both sides by 3 to get: s =  80 
Now take r = 4s, and replace s with  80  to get: r = 4( 80 ) = 320
So,  r = 320 
So, statement 1 is SUFFICIENT

Statement 2 : s = 80 
Take the given equation,  r − s = 240 , and replace s with 80 to get:  r − 80 = 240 
Solve the equation to get  r = 320 
So, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Kinshook · Answer

Asked: If r − s = 240, does r = 320?

(1) r = 4s
4s - s = 240 ; 3s = 240 ; s = 80
r = 4s = 320 
SUFFICIENT

(2) s = 80
r = s + 240 = 80 + 240 = 320
SUFFICIENT

IMO D

hiranmay · Answer

If r − s = 240, does r = 320?
 Question is asking, r − s = 240 => r=s+240, does r =320? => s+240=320?=> s=80?

(1) r = 4s -->  suff: 4s-s=240 => s = 80 
(2) s = 80 -->  suff: s =80

Answer: D

If r − s = 240, does r = 320?

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