In a DS context, these problems are sometimes about spotting a certain combination of variables.

For exampleAt 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 exampleThe 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 exampleAt 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?
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Emily Sledge | Manhattan GMAT Instructor | St. Louis

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