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# How to solve these types of question efficiently?

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Manager
Joined: 10 Aug 2009
Posts: 123
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Kudos [?]: 14 [0], given: 13

How to solve these types of question efficiently? [#permalink]

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22 Feb 2010, 08:36
Hi,

I've noticed that the following type of question appears very often:

"Someone bought x amount of product 1 for some price, and y amount of product 2 for some other price. The total amount of the purchase was Z. How much of each did he buy?"

For the easiest ones you can just run through all the multiples of the prices and find the answer, but this is extremely inefficient. You can find the value of y in terms of x and you may get lucky (i.e. x has to be divisible by 5). Is there a fast way to solve these problems?
Manhattan GMAT Instructor
Joined: 28 Aug 2009
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Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)
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Re: How to solve these types of question efficiently? [#permalink]

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22 Feb 2010, 14:52
1
KUDOS
In a DS context, these problems are sometimes about spotting a certain combination of variables.

For example
At a certain store, all t-shirts have the same price and all hats have the same price. What is the total price of 2 t-shirts and 5 hats?
Translation: What is (2T + 5H)?

(1) The total price of 4 t-shirts and 10 hats is $50. Translation: 4T + 10H =$50
2(2T + 5H) = $50 Therefore, (2T + 5H) =$50/2 = $25 Plugging in test numbers would potentially cost a lot of time unnecessarily; we don't care about T and H individually, so it doesn't pay to plug in for them individually. Take-away: Translate to algebra, and if the question concerns a combination of variables, look for that combo in the statements. In other DS questions, these scenarios can be about an implied integer constraint. For example The post office sells only 3 cent stamps and 16 cent stamps. If a total of 25 stamps were sold on Wednesday, how many 3 cent stamps were sold on Wednesday? (1) The total price of the stamps sold on Wednesday was more than$2.72 and less than \$2.95.
Translation:
3x + 16y = total, which is in the range 272 to 295.
x + y = 25

For such a small range for total price (23 cents is not much more than a single 16 cent stamp!), it is worth it to plug in some possible x and y pairs to see how many give a total in the range (it's gonna be one or two pairs that work).

To keep the time manageable, just be organized about it.

15*(16 cents) = 240 and 10*(3 cents) = 30. Total = 270...too low.
16*(16 cents) = 256 and 9*(3 cents) = 27. Total = 283...OK.
17*(16 cents) = 272 and 8*(3 cents) = 24. Total = 296...too high.

The number of 3 cent stamps must be 9, SUFFICIENT.
Take-away: Don't be lazy about plugging on DS; you might see the trick with just a little work.

If you see this on PS, some plugging is probably necessary too.

For example
At a certain store, all t-shirts have the same integer price and all hats have the same integer price. Which of the following could be the total price of 2 t-shirts and 6 hats?

Tips:
(1) Factor as much as you can. What could be 2T + 6H? ---> What could be 2(T+3H)? The answer will be even.
(2) If you must plug, do so in a chart. Be organized. Look for patterns. Cross off answers as you go.
Take-away: Be neat, and trust the process. The problems are designed to be done in 2 minutes, so how bad can plugging be?
_________________

Emily Sledge | Manhattan GMAT Instructor | St. Louis

Manhattan GMAT Discount | Manhattan GMAT Course Reviews | Manhattan GMAT Reviews

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Re: How to solve these types of question efficiently? [#permalink]

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23 Feb 2010, 05:36
Thanks esledge. I guess plugging is inevitable, I'll do my best to be organised about it. The thing is that I get nervous when I have to do a lot of plugging (I start to think that maybe there is a shortcut that I'm missing, which I why I asked this question actually).
Re: How to solve these types of question efficiently?   [#permalink] 23 Feb 2010, 05:36
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