Rachel drove the 120 miles from A to B at a constant speed. What was

Question

Rachel drove the 120 miles from A to B at a constant speed. What was this speed?

(1) If she had driven 50% faster, her new time would have by 2/3 of her original time.
(2) If she drove 20 mph faster, she would have arrived an hour sooner.

smashbiker84 · Accepted Answer

Ans : B Stmnt 1: insufficient..its a trap 8-)

, doesnt give any new info..it is a known fact based on percent change and product constancy since time and speed are inversely related for a fixed distance. Stmnt 2: sufficient eqn : 120/x - 120 /(x+20) =1..solving yields x=40 ( & thus original time = 3 hrs to travel 120 kms. can be verified with new conditions as per stmnt 2 i.e if speed increased to x+20 or 60 kms, then time reqd is 2 hrs which is 1 hr less than the original )

Psiva00734 · Answer

from statement 1 
if rachel drove 50% faster then speed S is 3/2S then time is
2/3Tof original time.
So insufficient.

Statement 2
 if rachel drove 40mph ,then she reaches destinations in 3hrs .
if she increase speed 20mph , that is 60mphs than she reaches destination in 2hrs. 
So it is suffiecient 
answer is B.

chetan2u · Answer

hi,
1) statement one does not give any specific value to work on..... any increase in speed by 50% will save 1/3rd time so insufficient..
2) here statement two gives us a value to work on ... if we take initial spped as x.. then an equation with x can be formed and value of x can be found sufficient
ans B

ynaikavde · Answer

s= speed 
t= time taken
d= 120 miles
we have two variables and we need two equations to solve it
statement 1)  \frac{120}{1.5s} = \frac{2}{3} *t>> 120=s*t >>two variables one equation insufficient.

if we look here 
120=s*t

120=20*6
120= 40*3

120= 30*4
120=30(1.5)*4(2/3)= 45*8/3
we can have several combinations they need not be integer.

statement 2)  \frac{120}{(s+20)}=t-1 >> insufficient

120 = (s+20)*(t-1)
s=28,t=3.5>>(28+20)*(3.5-1)=48*2.5=120
s=40,t=3 >>(40+20)*(3-1)=60*(2)=120

we can use both the statements to get a solution 
Hence correct answer C.

chetan2u · Answer

'hi B is sufficient....
let the speed be X.... then time taken =120/x..
increased speed =20+x, time taken= 120/(x+20)..
with increased speed , he saves one hour..
so 120/x=1 + 120/(x+20)....
 x comes as 40 or -60..
as speed cannot be -ive. x=40 thus sufficient...

ynaikavde · Answer

Yes , you are right, I missed that t=120/s

adityadon · Answer

only B is sufficient

EMPOWERgmatRichC · Answer

Hi All,

It looks like everyone's correctly answered the prompt, so I won't rehash any of that work here. Instead, I'm going to offer a bit more explanation as to why Fact 1 is insufficient. It's actually based on a "math truism", which in real simple terms is a "math fact that most people don't realize."

The Distance Formula is...

Distance = (Rate)(Time)

....and it's a formula that you'll likely use a couple of times on the Official GMAT (so it's worth knowing).

Fact 1 tells us that increasing the rate by 50% would lead to a time that is 2/3 of the original. Using the Distance Formula, we can prove that this occurs for ANY speed...

D = (R)(T)

Raising the Rate by 50% and decreasing the Time to 2/3 of the original time gives us...

(3/2)(R)(2/3)(T).

Since we're multiplying 'elements', we can put them in any order:

(3/2)(2/3)(R)(T)

(3/2)(2/3) = 6/6 = 1

So we have (1)(R)(T)

D = (R)(T)

In the end, the information in Fact 1 is NOT new information - it's a math fact when dealing with ANY speed and nothing more. Fact 1 is insufficient.

GMAT assassins aren't born, they're made,
Rich

mehrdadtaheri92 · Answer

Answer is B....

Data 1 ) 50% faster , she would travel 2/3 time that she spent : we have r*t =120 miles,

so data gives us that : 1.5 r * (2/3) t =120 or : 15/10 *r * 2/3 t =120 if we cancel out these two fractions we reach to : r*t =120 ( the same relation that we already have ,so this this info does not help us ) so insufficient

Data 2 ) : if she had drive 20 miles faster , she would have reached to the B , ONE hour earlier,

So, plug in : (r+20 ) ( t-1) =120 Or: rt- r +20*t -20 =120 , we are given from the problem that : rt=120 , so replace this in the equation,

120-r + 20*t -20 =120 and cancel 120 from each side, so we have : 20t -r -20 =0 so we can obtain r and t in term of each other, for example: t=(20+ r)/20

so , we can replace it in the relation rt =20 and we can count the r ( speed )

so this data is sufficient ..... ans :B

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

Rachel drove the 120 miles from A to B at a constant speed. What was this speed?
Let’s say the original variables are D = 120, R, and T, and the original case is 120 = RT.

Statement #1: If she had driven 50% faster, her new time would have by 2/3 of her original time.

To increase by 50%, we will multiply by the  multiplier  1.5. This means that the new speed, R2, is R2 = 1.50*R = (3/2)*R. The new time is T2 = (2/3)*T. Well, we know, that 120 = (R2)*(T2) — the new speed and time must have the small product as the original speed and time. 120 = (R2)*(T2) =  *  = (3/2)*(2/3)*RT = RT. This information leads in a big logical circle right back to the original equation 120 = RT. It gives us no new information at all. Therefore, this statement, by itself, does not provide any insight into the answer to the prompt question. This statement is insufficient.

Statement #2: If she drove 20 mph faster, she would have arrived an hour sooner.
Now, we know R2 = R + 20 and T2 = T – 1. Again, we know that 120 = (R2)*(T2), so
120 = (R + 20)*(T – 1) = RT – R + 20T – 20
120 – RT = 0 = 20T – R – 20

That is one equation with two unknowns, and 120 = RT is a second equation with two unknowns. We have  two clearly different equations for the two unknowns , so even without solving, this is sufficient to determine a unique value for the variables R & T.

Answer = B.

Businessconquerer · Answer

STATEMENT 1
 YOU'LL ULTIMATELY GET
120/(1.5X)= 2/3(120/(X))
X's get cancelled. you get nothing

STATEMENT 2
YOU'LL ULTIMATELY GET
120/(X+20)= (120-X)/X
SOLVING(TIDIOUS)
YOU'LL GET X=-60,40
SINCE SPEED CANNOT BE NEGATIVE(IN PHYSICS IT CAN BE BUT NOT HERE)
WE GET X =40

HENCE B

exc4libur · Answer

rate(time)=distance;rt=120

(1) If she had driven 50% faster, her new time would have by 2/3 of her original time.   insufic.

(3/2)r•(2/3)t=120…rt=120…(3/2)r•(2/3)t=rt…1=1

(2) If she drove 20 mph faster, she would have arrived an hour sooner.   sufic.

(r+20)(t-1)=120…rt=120…(r+20)(t-1)=rt…rt-r+20t-20=rt…r=20(t-1) 
 rt=120…20(t-1)t=120…t^2-t-6=0…(t-3)(t+2)=0…t=3 
 rt=120…r3=120…r=40

Answer (B)

Basshead · Answer

Rachel drove the 120 miles from A to B at a constant speed. What was this speed?

(1) If she had driven 50% faster, her new time would have by 2/3 of her original time.

Insufficient. If we solve (1.5r) = (d / 2/3t ) we will end up with the original equation 120 = rate * time. This statement does not give us any new information.

(2) If she drove 20 mph faster, she would have arrived an hour sooner.

( r + 20 )( t - 1) = 120
rt - r + 20t - 20 = 120
-r + 20t - 20 = 0

We know rt = 120. We have two different equations with two unknowns; thus, this statement is sufficient to determine the rate.

Answer is B.

ShankSouljaBoi · Answer

Dear Moderators,

Please fix statement one, the new time by 2/3 of original time .  Increased or decreased or became  ... what ???

Basshead · Answer

2/3 of the original time.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Rachel drove the 120 miles from A to B at a constant speed. What was

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

GMAT Data Sufficiency (DS) Questions

Rachel drove the 120 miles from A to B at a constant speed. What was

Prep Toolkit

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