Population - CAT 1, Question 3

[Alexander]

Hi -

I don't understand the picking numbers explanation given for this problem.

An effective approach to this problem is to pick some representative numbers. Suppose that we use p = 0.5 = 50% for the percent changes. Let there be 10 women and 9 men in 2009. Because the number of men increased by 50%, there must have been 6 men in 2008, and because the number of women decreased by 50%, there must have been 20 women in 2008. This example shows clearly that the total population of Pleasantville decreased from 2008 to 2009.

How is the highlighted part possible? Why is such a high % being used? In my example:

2008: 100 Men, 200 Women --> 50% is the percent change --> 2009: 150 men, 100 Women. When I try it with a 10% change it works, you can see the population decreases and therefore B is correct.

Can you please advise?

Thanks,
Alexander

[tommywallach]

Hey Alexander,

I am so sorry not to have responded sooner. A glitch in the forum made it so I didn't see this post. The mistake with your numbers is that you misread the final sentence of the prompt:

"...such that women still outnumbered men in 2009."

With your 50% example, men outnumber women, so this set of numbers doesn't fit the constraint.

I would also recommend you just think of this logically. If we lose 50% of a bigger number and gain 50% of a smaller number, our total will decrease.

-t

[anuraag.advani]

I have one more question with this problem.. I feel 'a' should be the ans as percent change should be +ve,

[tommywallach]

Agreed. I've never seen a question discuss percent change as a positive or negative. You just always call it positive. We'll get that switched up.

-t

[Alexander]

No worries Tommy. Your verbal reasoning makes sense, and I understand where my constraint error was.

Thanks

[tommywallach]

Glad to help!

-t