GMAT Math

I am having a problem understanding the following:

A group of 10 people decide to share equally in an apartment that costs r dollars to rent each month. If x people drop out of the group, how much more, in dollars, must each remaining person pay?

I used r= 100 and x= 5 below is the explanation I got from a review text. I dont understand why you have to take $20-$10 to get target of 10

Plug in: r = 100; x = 5. At first, each one of the 10 people pays $10. When 5 people drop out, the 5 remaining people must each pay $20. $20 - $10 = $10. The target is 10


Thanks

10 ppl, rent = r.
rent per person = r/10.
Now only (10-x) ppl remain.
Thus rent per eprson = r/(10-x)
thus extra rent paid by each person = r/(10-x) - r/10.
(That's why we subtract coz we have been asked how much more does each person pays)

=

BKNY718 wrote:A group of 10 people decide to share equally
in an apartment that costs r dollars to rent
each month. If x people drop out of the group,
how much more, in dollars, must each remaining
person pay?

(A) rx / 10(10-x)
(B) 10r / r
(C) r / 10(10-x)
(D) r / 10-x
(E) rx / 10-x

Let r = 20.
For 10 people, monthly rent per person = r/10 = 20/10 = 2.
Let x=5.
New number of people sharing the monthly rent = 10-x = 10-5 = 5.
For 5 people, monthly rent per person = r/5 = 20/5 = 4.

The TARGET is the answer to the question being asked: How much more per month must each remaining person pay?

(Rent per person for 5 people) - (rent per person for 10 people) = 4-2 = 2.
Thus, the target = 2.

Now we plug r=20 and x=5 into the answers to see which yields our target of 2.

Only answer choice A works:
rx / 10(10-x) = (20*5) / 10*(10-5) = 100/50 = 2.

The correct answer is A.

Mitch If we plug in r = 100 then both A & B are right. So what is the best way to pick nos ?

pm wrote:Mitch If we plug in r = 100 then both A & B are right. So what is the best way to pick nos ?

Don't worry about the first plug in - choose numbers that are comfortable to begin with. If you have more than one answer choice that matches your goal, repeat the process with a different set (for example, change r=100 into something else and leave everything else the same), find the new goal, and plug the new set into the remaining answer choices - only A and B). In this particular case, it is easy to see that B will equal 10 for any r that you choose - it's just a coincidence that for r=100 B matches the goal, but for any other choice of r B will be eliminated. Thus, it's not even necessary to repeat the process - it is clear that B can be eliminated, so A remains the only possible answer choice.

pm wrote:Mitch If we plug in r = 100 then both A & B are right. So what is the best way to pick nos ?

As Geva noted, if more than one answer choice is equal to the target:

1. Plug in new numbers.
2. Get a new target.
3. Try the remaining answer choices again.

To minimize the chance that more than one answer choice will yield the target, don't plug in values that remind you of numbers in the problem or of numbers in the answer choices.
In the problem above, r=100 will yield a staring rent per person of 100/10 = 10, a number that is included in all the answer choices.
Thus, we should plug in a different number for r.