Raincoats and umbrellas

Expert replies

hemant_rajput: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 22, 2012 7:13 amFollowed by: 13 members; Thanked: 46 times; GMAT Score:700

by hemant_rajput » Mon Feb 04, 2013 10:01 am

Q15 . On 26th July Mumbai was flooded , Rain shield enterprise is in the business of manufacturing umbrellas and raincoats. An umbrella can shield 2 people while a raincoat can shield 1 person. People under an umbrella can walk 1/3rd the speed of a person wearing a raincoat. The cost of an umbrella and cost of raincoat are in the ration 2:5. Points A and B are 100 m apart and it takes 20 min for a person wearing a raincoat to travel the distance . At the max how many people will be transported today from A to B, if only 1000/- is available for transporting 20 people? Cost of traveling time is 2/- per min per head(assume cost of Raincoat to be 100/-)
a. 6
b. 7
c. 4
d. 11
e. 16
[spoiler]oa:b[/spoiler]

I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

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Source: Beat The GMAT — Problem Solving | Mon Feb 04, 2013 10:01 am

vkb001: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Wed Feb 23, 2011 7:32 amFollowed by: 2 members; Thanked: 8 times; GMAT Score:740

by vkb001 » Tue Feb 05, 2013 5:50 pm

Let no. of umbrella's bought be u, and no. of raincoats bought be r.

No. of people who can travel using umbrella = 2u
No. of people who can travel using raincoat = r

Speed of people using raincoat = 100/20 = 5 m/min
Speed of people using umbrella = 1/3 * 5 = 5/3 m/min

Cost of raincoat = Rs.100
Cost of umbrella = Rs. 40 (calculated from the cost ratio of 2:5)

Total cost of getting umbrellas and moving people = u*(2 people/umbrella)*(Rs.2/min)*(60 min travel time) + u*(Rs.40 purchase cost) = 240u + 40u = 280u
Total cost of getting raincoats and moving people = r*(1 people/raincoat)*(Rs.2/min)*(20 min travel time) + r*(Rs.100 purchase cost) = 140r

Grand total = 280u + 140r should be equal to Rs.1000 to maximize the no. of people benefiting from the purchase.

280u + 140r = 1000 (at maximum)
=> 2u + r = 7.14 (at maximum) ---- Equation 1

But, (2u+r) is also the number of people who'd be able to travel. From Eq. 1, we know that at maximum, that can be 7.14 or 7 people.

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GMAT/MBA Expert

Tommy Wallach: GMAT Instructor; Posts: 451; Joined: Thu Jan 21, 2010 11:58 amFollowed by: 120 members; Location: New York City; Thanked: 188 times; GMAT Score:770

by Tommy Wallach » Tue Feb 05, 2013 7:21 pm

Whoa! Is this supposed to be a GMAT question, or to somehow help with GMAT skills? Just to be super-clear, it is not, and does not! The problem with unrealistic GMAT question is that they might send your studies off in weird directions. Worse than that, you might actively develop bad habits. For example, most GMAT questions are predicated on trickery/theory, as opposed to calculation. If you get into the habit of doing calculation to solve, you will often end up on the wrong path when it comes to a real GMAT question.

There are maximization questions on the GMAT, by the way, but I've never seen one like that. Also, the punctuation has me confused here. What comes after 1000? Is that money?

Hope I don't sound critical; I just want everyone to be studying useful material!

-t

Tommy Wallach, Company Expert
ManhattanGMAT

If you found this posting mega-helpful, feel free to thank and/or follow me!

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shenoydevika: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Wed Jan 09, 2013 5:03 amFollowed by: 4 members; Thanked: 9 times; GMAT Score:700

by shenoydevika » Wed Feb 06, 2013 1:10 am

Hemant,

Is this a CAT/XAT question? It seems like one of those overly complicated CAT questions.

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