Annual rent

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Amrabdelnaby: Master | Next Rank: 500 Posts; Posts: 137; Joined: Fri Nov 13, 2015 11:01 amFollowed by: 2 members; Thanked: 1 times

by Amrabdelnaby » Tue Dec 08, 2015 10:48 am

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

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Source: Beat The GMAT — Problem Solving | Tue Dec 08, 2015 10:48 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Tue Dec 08, 2015 5:15 pm

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

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Dec 11, 2015 2:53 pm

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.

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Amrabdelnaby: Master | Next Rank: 500 Posts; Posts: 137; Joined: Fri Nov 13, 2015 11:01 amFollowed by: 2 members; Thanked: 1 times

by Amrabdelnaby » Sun Dec 13, 2015 5:33 am

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.

Like this post

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