Data Sufficiency

On his trip from Alba to Benton, Julio drove the first x miles at an avg rate of 50 m/hr and the remaining distance at an avg rate of 60m/hr. How log did it take Julio to drive the first X miles?
(1) On this trip, Julio drove for a total of 10 hours and a total of 530 miles
(2) On this trip, Julio took 4 more hours to drive the first x miles than to drive the remaining distance

ans (d)

I think that the answer to this problem would be A.

First of all, we need to keep in mind our trusty formula d = rt (distance = rate * time).

We have a rate (which we can express as a function of x) in the question stem, and we get a distance and a time in (I). We have one equation and one unknown, so that's enough info to solve the question.

If you wanted to solve, which you don't need to do here, you would have the formula.

530 = r * 10

Rate is calculated as a weighted average:

r = (x/530)(50) + ((530 - x)/530)(60)

(see, you really don't want to do the math here if you don't have to...)

Anyway, one eq. one unknown - (I) is sufficient.

I approach (II) by thinking about the two distinct legs of the journey - the journey to mile x, and the journey after that.

To set up my d = rt, I have:

x = 50 * t1
total dist - x = 60 * (t1 - 4)

We add them together and get total dist = (50 * t1) + (60 * (t1 - 4)). We can't solve for t1 because we don't have total distance. So, (II) is not sufficient.

Since (I) is sufficient, and (II) is not sufficient, the answer is A.

I agree..the answer should be A

Distance = Rate * Time

According to the question,

x=50*T1------>(a)

(d-x)=60*T2------->(b)

We need to find T1

(1) says x+(d-x)=530 or d=530 substitute this value in (a) to get T1

(2) says T1=T2+4 but we are not given any additional information..So its INSUFFICIENT

Hence ans A

Ans A here.

For statement 2, i tried for a whole half hour but to end up with no answer !!

moneyman wrote:I agree..the answer should be A

Distance = Rate * Time

According to the question,

x=50*T1------>(a)

(d-x)=60*T2------->(b)

We need to find T1

(1) says x+(d-x)=530 or d=530 substitute this value in (a) to get T1

(2) says T1=T2+4 but we are not given any additional information..So its INSUFFICIENT

Hence ans A

I'm trying to follow your steps but can't substitute d with equation a because d didn't mentioned their.. ?? could you go further..

Whats the OA?

moneyman wrote:I agree..the answer should be A

Distance = Rate * Time

According to the question,

x=50*T1------>(a)

(d-x)=60*T2------->(b)

We need to find T1

(1) says x+(d-x)=530 or d=530 substitute this value in (a) to get T1

(2) says T1=T2+4 but we are not given any additional information..So its INSUFFICIENT





Hence ans A

moneyman,

with your approach:
x+(d-x) = 530
and x=50*T1

We have 3 unknowns. This cannot be solved, I belive.

On his trip from Alba to Benton, Julio drove the first x miles at an avg rate of 50 m/hr and the remaining distance at an avg rate of 60m/hr. How log did it take Julio to drive the first X miles?
(1) On this trip, Julio drove for a total of 10 hours and a total of 530 miles
(2) On this trip, Julio took 4 more hours to drive the first x miles than to drive the remaining distance


speed = distance / time

time = x / 50 + 530-x/60

10 = x / 50 + 530-x/60

Suff


2) T1 - T2 = X/60 + Y/50

it can't be D

can someone explain this one more in detail? i dont get it

@alexdallas

Lets the total distance be y
Given: x miles at 50 m/hr
Given: remaining miles = y-x at 60 m/hr

Choice A: 10 hrs and total of 530 miles. The way to split for 10 is 60 m * 3 + 50m * 7 = 530 miles.

SUFF

Choice B: took 4 more hours to drive the first x miles than to drive the remaining distance

So whats the total distance driven? and whats the total hours?

INSUFF

Hence Answer is A

Knocking myself on the head for not seeing through this question during a practice test

Basically Rate (R) x Time (T) = Distance (D)

Therefore from the question stem we know that
1st half R(50) x T(x/50) = D(X)
2nd half R(60) x T(Y) = D (60Y)

Statement 1: Total Time = 10 hours, Total Distance = 530miles

x + y = 10
50x + 60y = 530

so we have simultaneous eqns and can solve for x and y hence SUFFICIENT

[spoiler]Statement 2: 60y = x/50 + 4 - INSUFFICIENT[/spoiler]

I wished they'd just add on 5 more minutes to this exam.

Please don't post a certain answer unless you're sure about it (unless its the OA). Even if its the OA, use the spoiler feature! I spent like half an hour trying to figure out why Statement 2 would be sufficient!

shanrizvi - I stand corrected and have used the spoiler feature