Camping Trip & Town Distance

[Rospino]

A. On a camping trip, X campers each paid Y dollars per food. What percent of the total food expenses did each camper pay?
(1) If there were one fewer camper, each camper would owe 1 dollar more.
(2) If there were half as many campers, each camper would owe 7 dollars more.

B. What is the distance from Town A to Town B, in miles?
(1) If Steve had traveled from Town A to Town B at an average speed that was 10 miles per hour faster, he would have traveled 5 fewer hours.
(2) If Steve had traveled from Town A to Town B at an average speed that was 50 percent greater, the amount of time he traveled would have been the time it actually took reduced by 1/3.

[Mike@Magoosh]

A. On a camping trip, X campers each paid Y dollars per food. What percent of the total food expenses did each camper pay?
(1) If there were one fewer camper, each camper would owe 1 dollar more.
(2) If there were half as many campers, each camper would owe 7 dollars more.

Notice, we have two unknowns, and essentially, we want to solve for the values. If we know the numerical value of X we can figure out the percentage: for example, if there are 4 people, each pays 25%; are 10 people, each pays 10%, etc. Notice, also, XY is the total amount of money amassed for food.

Statement #1
We can set up the equation XY = (X - 1)(Y + 1). Two unknowns, one equation, can't solve. This statement is insufficient.

Statement #1
We can set up the equation XY = (X/2)(Y + 7). ===> 2XY = X*(Y + 7) ==> 2Y = Y + 7 ===> Y = 7
We can solve for Y, but not for X, which we need to answer the question. This statement is insufficient.

Combined statements:
From statement #2, we know the value of Y. We can plug this into the equation from statement #1 and find the value of X, which would allow us to answer the question. Sufficient.

Answer = C

B. What is the distance from Town A to Town B, in miles?
(1) If Steve had traveled from Town A to Town B at an average speed that was 10 miles per hour faster, he would have traveled 5 fewer hours.
(2) If Steve had traveled from Town A to Town B at an average speed that was 50 percent greater, the amount of time he traveled would have been the time it actually took reduced by 1/3.

Notice, from the prompt, we don't know D or R or T, just that D = RT. We have three variables, and only one equation. The prompt is asking for the value of D.

Statement #1
We can set up the equation D = (R + 10)(T - 5). Now we have three unknowns and two equations, so we can't solve. Insufficient.

Statement #2
We can set up the equation D = [(3/2)*R]*[(2/3)*T] = RT
This statement is tautological, and reduces to the original D = RT equation. It contains no new or useful information. Insufficient.

Combined statements:
Because Statement #2 is tautological and, essentially, says nothing, with the combined statements we are no better off than when we had Statement #1 by itself. That information is still insufficient.

Answer = E

Do these make sense?

Here's a video lesson you might find helpful.
https://gmat.magoosh.com/lessons/361-int ... ufficiency

Let me know if you have questions on anything I have said.

Mike

[dhonu121]

A. On a camping trip, X campers each paid Y dollars per food. What percent of the total food expenses did each camper pay?
(1) If there were one fewer camper, each camper would owe 1 dollar more.
(2) If there were half as many campers, each camper would owe 7 dollars more.

Total money paid = XY.
Rephrasing the question = Y/XY*100 = 100/X. So we need to find X.

1.So Y+1 = XY/(X+1).Insuff.
2.So Y+7 = XY/(X/2). Insuff.
Together 1 and 2. Suff. Hence C.

B. What is the distance from Town A to Town B, in miles?
(1) If Steve had traveled from Town A to Town B at an average speed that was 10 miles per hour faster, he would have traveled 5 fewer hours.
(2) If Steve had traveled from Town A to Town B at an average speed that was 50 percent greater, the amount of time he traveled would have been the time it actually took reduced by 1/3.

1. Distnace = d, speed = s.
Hence t=d/s. Now
t-5 = d/(10). insuff.

2.t-1/3 = d/(1.5s). We know that d/s=t. hence
t-1/3 = t/1.5. Solve this for t.Insuff.

Using 1 and 2, put value of t from 2 in 1, we get d.
hence C.

[dhonu121]

Statement #2
We can set up the equation D = [(3/2)*R]*[(2/3)*T] = RT
This statement is tautological, and reduces to the original D = RT equation. It contains no new or useful information. Insufficient.

Mike,
How did you set up this equation. The question says that time he traveled would have reduced by 1/3. Shouldn't this mean new time T' = T-1/3 ?
I see that you made new time T' = T-T/3.

Can you please clarify this here ?

[Mike@Magoosh]

B. What is the distance from Town A to Town B, in miles?
(1) If Steve had traveled from Town A to Town B at an average speed that was 10 miles per hour faster, he would have traveled 5 fewer hours.
(2) If Steve had traveled from Town A to Town B at an average speed that was 50 percent greater, the amount of time he traveled would have been the time it actually took reduced by 1/3.

1. Distnace = d, speed = s.
Hence t=d/s. Now
t-5 = d/(10). insuff.

2.t-1/3 = d/(1.5s). We know that d/s=t. hence
t-1/3 = t/1.5. Solve this for t.Insuff.

Using 1 and 2, put value of t from 2 in 1, we get d.
hence C.

Dear dhonu121

First of all,I want to point out a mistake in your work:

In Statement #1, the problem says "an average speed that was 10 miles per hour faster", not simply "an average speed that was 10 miles per hour". We don't know the numerical value of the rate in the Statement #1 scenario --- all we know is that it's 10 mph less than the original, so (R - 10) is that rate.

Mike, How did you set up this equation. The question says that time he traveled would have reduced by 1/3. Shouldn't this mean new time T' = T-1/3 ?
I see that you made new time T' = T-T/3.
Can you please clarify this here ?

"time he traveled would have been the time it actually took reduced by 1/3"

The phrase "reduced by 1/3" means NOT to subtract the number 1/3 but rather that 1/3 of the whole was subtracted. You see, if you they wanted us to add or subtract the number, they would have given us units of time. For example, if they said "time was decreased by 1/3 of an hour" --- that would mean: subtract the number 1/3 from the numerical value of the time. Whenever a problem just says "reduced by 1/3", "decreased by 1/3", and no units are given, then implicitly it always means --- don't subtract the number 1/3, but rather subtract 1/3 of the whole. When something decreases by 1/3, that means 1/3 of it is removed or goes away, and what's left is 2/3 of the original.

Notice, if the rate increases by 50%, it goes up to (3/2)*R, and if the time decreases by 1/3 it goes down to (2/3)*T, and when we multiply these, we get D = RT, the original equation all over again. Statement #2 is actually a vacuous tautological statement --- whenever distance is fixed and average rates increases by 50%, but a factor of 3/2, then time is reduced by a 1/3. Statement #2 contains zero information about this particular problem. That's why E, not C, is the answer.

BTW, a little BTG etiquette --- when you give a solution to the problem, hide your answer with the "spoiler" (as I did in the preceding paragraph) so that folks who glance at the post have the opportunity to do the problem for themselves with seeing the answer right away.

Does all this make sense? Let me know if you have any further questions.

Mike

[dhonu121]

Got it!
Thanks.