Percentage Help!!

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anuu: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed Feb 23, 2011 9:41 am; Thanked: 1 times

by anuu » Sat May 14, 2011 8:52 am

Hi All,

Can anyone pls suggest an easier appraoch for the following problem?

A man spends 70% of his salary on food expenses, 40% of the rest on traveling expenses, 90% of the rest on house rent and was finally left with $3600. How much did he spend on traveling expenses?

I did start of with x as the salary and found the remaining amount at each stage and then applied successive percentage for that stage..this method took me nearly 8 min+

Is there an easier appraoch?

The answer choices are : 24000,18000, 25000,22000, 20000

Regards,
Anu

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Source: Beat The GMAT — Problem Solving | Sat May 14, 2011 8:52 am

pankajks2010: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 12:51 amFollowed by: 1 member; Location: New Delhi, India; Thanked: 12 times

by pankajks2010 » Sat May 14, 2011 9:41 am

Let the salary be x. The complete salary is 100%.

Food expense = 70% of x, Therefore the remaining amount is 30% of x (this can be done mentally to save time)

Out of this 30% of x, 40% is spent on travelling, which is (40/100) (30/100) x = 12% of x (this again can be solved mentally)

Thus, the remaining amount is (100-70-12)% or 18% of x. Of this 18%, 90% is spent on house rent. That means the final amount which gets saved is only 10% of (18% of x) which is 1.8% of x.

Now, I'll do some calculations to find out x: x=3600*100/1.8=200,000

Travelling expense is 12% of x: (12/100)*200000=24,000

So, the time saving approach is to calculate the remaining amount by substracting the used percentage directly from 100, this helps to avoid lengthy calculations.
Ex: 1) The amount remaining after food expense was directly calculated as (100-70)% of x
2) The amount left after house rent was calculated as (90-10)% of (18% of x)

Hope it helps!!

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smackmartine: Legendary Member; Posts: 516; Joined: Fri Jul 31, 2009 3:22 pmFollowed by: 13 members; Thanked: 112 times

by smackmartine » Sat May 14, 2011 10:40 am

Back solving is a great method for solving these types of problems

(money left after Paying Travel expense = 90% of "money left after Paying Travel expense" on Rent + $3600 )

Left amount $ 3600 = 10% of money left after Paying Travel expenses

So, money left after Paying Travel expenses = $36000 = 60% of money left after Paying Food expenses

money left after Paying Food expenses = 36000 /0.6 = $ 60,000

Now given that : Travel Expenses = 40% of money left after Paying Food expenses = 0.4 * 60,000 = $ 24000

So A

Hope this helps!

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sat Sep 03, 2011 10:50 am

Is this a valid GMAT problem?
Source please!

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smackmartine: Legendary Member; Posts: 516; Joined: Fri Jul 31, 2009 3:22 pmFollowed by: 13 members; Thanked: 112 times

by smackmartine » Sat Sep 03, 2011 11:09 am

GmatKiss wrote:Is this a valid GMAT problem?
Source please!

I would say this is a valid problem, because you can clearly see that there are various methods by which you can solve this problem. Someone took 8min +, while using back solving method,you can solve the problem in 2 min. Back solving is, for sure, tested on GMAT.
I do not know the source though. The original poster should post the source.

Smack is Back ...
It takes time and effort to explain, so if my comment helped you please press Thanks button

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thestartupguy: Master | Next Rank: 500 Posts; Posts: 150; Joined: Thu May 05, 2011 10:04 amFollowed by: 4 members; Thanked: 5 times

by thestartupguy » Sat Sep 03, 2011 12:36 pm

I took the salary to be 100 units and solved it. It took me less than a minute to solve.

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