Greg and Brian are both at Point A (above). Starting at the

Question

Greg and Brian.jpg Greg and Brian are both at Point A (above). Starting at the same time, Greg drives to point B while Brian drives to point C. Who arrives at his destination first? (1) Greg's average speed is 2/3 that of Brian's. (2) Brian's average speed is 20 miles per hour greater than Greg's.

walker · Accepted Answer

A

~20 sec method:

ratio AB:AC is fixed, so only ratio speed_G:speed_B matters. 
1) we know ration speed_B:speed_G. sufficient
2) it can be 20.0001:0.0001 (Brian is first) or 10020:10000 (Greg is first). Insufficient

fluke · Answer

Greg's speed:  s_g 
Distance covered by Greg:  D 
Time taken by Greg:  t_g=\frac{D}{s_g}

Brian's speed  s_b 
Distance covered by Greg  D\sqrt{2}  (Hypotenuse of right isosceles triangle = root(2) times base)
Time taken by Brian  t_b=\frac{D\sqrt{2}}{s_b}

1.
 s_g=\frac{2}{3}s_b 
 t_g=\frac{D}{s_g}=\frac{D}{\frac{2}{3}s_b}=\frac{3D}{2s_b} -------------1
 t_b=\frac{\sqrt{2}D}{s_b} ----------------2

Comparing 1 and 2:
 \frac{3}{2} > \sqrt{2} . Thus, Greg took relatively more time to reach his destination.
Sufficient.

2.
 s_b=s_g+20 
 t_b=\frac{\sqrt{2}D}{s_b}=\frac{\sqrt{2}D}{s_g+20} 
 t_g=\frac{D}{s_g}

Let's prove opposite of st1:
 t_b>t_g 
 \frac{\sqrt{2}D}{s_g+20}>\frac{D}{s_g} 
 \frac{\sqrt{2}}{s_g+20}>\frac{1}{s_g} 
 s_g\sqrt{2}>s_g+20 
 0.4s_g>20 
 s_g>50

Thus, if greg's speed is approx more than 50, brian would take more time, otherwise greg would take more time.

Not Sufficient.

Ans: "A"

vivesomnium · Answer

Answer is A.
We know distances for both as x and xroot2
A gives us ratio of speeds, if we know ratio of speeds and ratio of distance, we can find ratio of time, as variables for distance and speed will get eliminated/cancelled, and only the ratio will remain
B gives us comparison between teo speeds, but not as a ratio- in this case, the variables will not get eliminated- more specifically, the varibale for speed.
In other words, this would make the answer yes or no dependent upon the value of speed. Hence it is not sufficient.
A alone is sufficient

walker · Answer

Vivesomnium,

The fact, that statement 2 doesn't fix speed ratio is not enough to say that it's not sufficient.
For example, if statement 2 were following:

"Greg's average speed is 20 miles per hour greater than Brian's."

statement 2 would be sufficient.

subhashghosh · Answer

Let AB = D

then AC = D * root(2)

(1)

B's speed = v

G's Speed = 2v/3

D/v - Brian

D * root(2)/2v/3 - Greg

Now, D/v * 3root(2)/2 > D/v because 3root(2)/2 > 1

Sufficient

(2)

D/v - Brian

D * root(2)/(v-20) - Greg

D * root(2)/(v-20) may be < or > D/v depending on value of v

If v = 21, then D * root(2)/(v-20) is > D/v

If v = 40, then D * root(2)/(v-20) is < D/v

Insufficient.

Answer - A

amit2k9 · Answer

a. the distances are 2^(1/2) and 1 units each.

B = 1 unit/interval then G = 2/3 unit/interval

thus 2^(1/2)/ 1 < 1/ (2/3). Hence sufficient.

b 2^(1/2)/ (g+20) < 1/g

for g = 1

LHS < RHS meaning B travels faster.

for g=100
LHS>RHS meaning G travels faster. not sufficient.

Hence A.

praveenmittal95605 · Answer

let AB = x

hence AC= sqrt2*x (using pythagorus)

assuming speed,distance and time taken by Brian = v1, d1, t1

and v2, d2, t2 be the time taken by Greg

1) V2 = 2V1/3

hence t1/t2 = 2*sqrt2/3

This is sufficent

2) V1 = V2 + 20

==sqrt2*x/t1 = x/t2 + 20

==sqrt2/t1 = 1/t2 + 20/x

since we dont know the value of x that is distance this is not sufficient

Hence, Answer is A

kajaldaryani46 · Answer

—-
Hi could u pls explain the concept here?

Posted from my mobile device

RohitSaluja · Answer

In the question stem we are not told what path they did take to reach their destinations, so why is it that we assume each one of them must have taken the shortest path to travel, an expert can you help here
 VeritasKarishma   GMATNinja

ManyataM · Answer

Is it not the same? 
you just chAnged the names . Rest is same ?

AnirudhaS · Answer

statement 2 is not sufficient.

let speed of brain is b 
let distance AB=x, then distance AC=x \sqrt{2} 
tme taken by greg =  \frac{x}{b-20} 
time taken by brian =  \frac{x\sqrt{2}}{b} 
so it cannot be definitively said which time is greater.

AnirudhaS · Answer

greg is travelling smaller distance (x as opposed to x \sqrt{2} )
so if greg's speed is greater, then there is no doubt that greg will reach B faster than brian will reach C.
Hope this helps.

KarishmaB · Answer

We have an isosceles right triangle since AB = BC. So ratio of sides is 1:1:1.414 (i.e. sqrt2).

Distance to be travelled by Greg : Brian = 1 : 1.414
For them to reach together at their destinations (in same time), their ratio of speeds must be 1 : 1.414.

Statement 1:
But actually ratio of their speeds is 2:3 (which is same as 1 : 1.5 ).
Since Brian's speed is higher than what is required, he will reach before Greg.
Sufficient

Statement 2: 
We are given the actual difference between their speeds. We don't know their relative speeds/ratio of their speeds. 
If speed of Greg & Brian are 10 & 30 mph, Brian will reach first (ratio 1 : 3)
If speed of Greg and Brian are 80 and 100 mph, Greg will reach first (ratio 1 : 1.25)
Not sufficient

Answer (A)

Sonia2023 · Answer

KarishmaB Bunuel chetan2u can you please explain why the below method is not right for Statement 2? We need to find out who reaches first so TIME is constant; given time is constant, ratio of \frac{speed of B}{speed of G } = \frac{distance of B}{ distance of G} Assuming speed of G to be x, speed of B is x+20 Setting up the equation: \frac{x+20}{x } = \frac{1.44}{1} Solving for x, we get 45.4 m/hr. Therefore speed of G is 45.4 m/hr and speed of B is 65.4 miles per hour (close to the ratio of 2/3) Given we have the ratio of the distances, we can find the time. Can anyone kindly explain what is wrong with this method? Thank you

chetan2u · Answer

Why would be time be constant? We are actually looking at time itself, so you cannot equate the ratio of speed to ratio of distance. 
We actually have no relation between x+20/x and 1.414/1, reason for statement II not being sufficient.

KarishmaB · Answer

When we talk about time, we mean to say 'time taken to complete this distance.'

Since they are both travelling different distances at different speeds, we cannot assume that 'time taken by them for their respective journeys' will be the same. Hence time is not constant. When one person reaches first, the other one is still covering his distance and his time taken will be more than the first person's. Hence time taken by both will not be the same and hence we cannot say that 'time is constant.'

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