Annual rent

Amrabdelnaby wrote:Guys could you please help with this?

The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. was the annual rent collected in 1999 more than in 1997?

1) x>y
2) xy/100 < x-y

See here for a discussion of this problem: https://www.beatthegmat.com/easier-approach-t285138.html

My approach:

Rent in 1997 = r

Rent in 1998 = r * (1 + (x/100))

Rent in 1999 = r * (1 + (x/100)) * (1 - (y/100))

We want to know if 1999 > 1997, so the question becomes

Is (1 + (x/100))(1 - (y/100)) * r > r?

Dividing by r and foiling, we have

Is 1 + x/100 - y/100 - xy/10,000 > 1?

or

Is x/100 - y/100 - xy/10,000 > 0?

or

Is (x - y)/100 > xy/10,000 ?

or

Is (x - y) > xy/100 ?

S2 says exactly this, so it's sufficient.

Thanks Matt,

Your solution was very helpful.

I already knew the answer to the first statement but I couldn't figure out statement 2. so again thank you

Matt@VeritasPrep wrote:My approach:

Rent in 1997 = r

Rent in 1998 = r * (1 + (x/100))

Rent in 1999 = r * (1 + (x/100)) * (1 - (y/100))

We want to know if 1999 > 1997, so the question becomes

Is (1 + (x/100))(1 - (y/100)) * r > r?

Dividing by r and foiling, we have

Is 1 + x/100 - y/100 - xy/10,000 > 1?

or

Is x/100 - y/100 - xy/10,000 > 0?

or

Is (x - y)/100 > xy/10,000 ?

or

Is (x - y) > xy/100 ?

S2 says exactly this, so it's sufficient.