Vacation House

[jmitchell.rhc]

Dear Test Makers,

I recently received the "Vacation House" question in my line up when taking a CAT exam. I believe the question to be ambiguous based on the answer given as being correct. I believe the language of the question infers that the percentage increase is an increase based on a 20% dollar value (thus an increase of 25%, or 5/20), rather than an increase on total purchase price of the home (5%, or an increase from 20% to 25%--currently 5% is the "correct" answer).

Thanks,

Jeremy M.

[mikers5]

it may also mean that About 5% of homes sold in 2009 were vacation homes or there has been increase of 5% then previous year

[esledge]

Please always post the text of the question, not just the name, even if it is a concern about wording. The comments above mention "purchase price" and "dollar value" and "% of homes" that are vacation houses, but the question in our database does not. Either that means the question has already been edited, or you have some concern I am not fully understanding.

Here is the question/explanation:

Five friends agree to contribute equal amounts to rent a vacation house. If one of the friends drops out of the agreement, by what percent will the individual contributions of the remaining four friends need to increase in order to cover the cost of the house?
A 5%
B 10%
C 20%
D 25%
E 33 1/3%

Because the problem talks about a price for the vacation house but never provides an actual value, either in the problem or in the answer choices, we can pick our own number. Let's say the cost of the house is $100. Originally, the five friends would each have paid 100/5 = $20. When one friend drops out, the remaining four friends would have to pay, 100/4 = $25 each.

To find the percent increase, we take the difference divided by the original amount:
(25 - 20)/20 = 5/20 = 1/4 = 25%

The correct answer is D.

[SheriS67]

Hello, could you please assist me in understanding why the answer is not 5%?
100%/5 friends = each person pays 20%. 100%/4 friends = each person pays 25%. If there are 4 people versus five, each individual will have to pay 5% more than had it been split with 5 friends.

[Sage Pearce-Higgins]

Percentages are a tricky part of word problems. Imagine I ask my friend how much he paid for his new phone and he replies '4 percent'. His answer doesn't make any sense, because we need to understand percent of what?. So, keep in mind that whenever we use percentages, we need to have percentage of something. We can call this "something" the base value. Now, imagine crime increases from 10 incidents in 2017 to 15 incidents in 2018. Hopefully you can say that crime has increased 'by 50%'. But if I say crime increased from 10% in 2017 to 15% in 2018, we might get confused.

However, we need to remember that the base value in this case is 'crime in 2017'. Our language implies that when we say 'Crime increased from 10% in 2017... '. So, it's true that "Crime increased by 50%", but we could also say "Crime increased by 5 percentage points". This confusion is often found in newspapers.

Back to the problem above, it might make things easier to think of the smart numbers that Emily suggested above. If my share of the holiday payment increased from $20 to $25, the base value is $20, so that's not a 5 percent increase, that's a 25 percent increase.