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

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

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.

'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...

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

only B is sufficient

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

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

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)*R]*[(2/3)*T] = (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.

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

\(rate(time)=distance;rt=120\)

(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)

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.

Dear Moderators,

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

2/3 of the original time.

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