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but i suppose we could do it by trying out different combinations of pencils that add up to 6 pencils, and see which one gives exactly 130, and get the answer.. but that is not mathematically defined right?

Tells us total 6 pencils are purchased but does not provide how many of these are 21 cent pencils and how many are 23 cents pencil.

So cannot answer the question

Statement 2:

Tells us total of 130 cents are spent but in what proportion is not mentioned.

So cannot answer the question.

Now combine Both Statement 1 & 2

Assume total 21 cent pencils are X, so total 23 cents pencils will be (6-X), as total pencils are 6 (from statement 1).

Now Total cost = 21*X + 23*(6-X) = 130 => X = 4

So total 23 cents pencils are 2.

Answer is C.

I agree with this response and calculation.

I'm confused when answering these problems as well.

When reading this problem if we assume that X is the number of 21 cent pencils and Y is the number of 23 cent pencils then we get this from the the statements.

1. X+Y=6 2. 21X+23Y=130

This is a common problem on the gmat and 99% of the time you clearly need two equations to solve becasue there are two variables. So a quick glance will give you the answer C. The problem is that in some cases (this being one of them) there is only one possible combination and it can therefore be deduced from stmt 2 alone. I cant figure out a quick systematic way of determening which is which. Becasue most of the prep courses tell you to stop DS problems as soon as you figure out you have enough information without solving.

Gixxer you are making a assumption that 2nd alone is giving you both the equations, however truth is 2nd statement alone is giving you only 21X+23Y=130.

It is from 1st statement that you are getting X+Y=6, which you canno include as part of statement 2, when considering it on it own.

As you require both the equations, to get the answer, so answer is C.

Bill Gates bough several pencils. If each pencil was either a 23 cent pencil or a 21 cent pencil, how many 23 cent pencil did Bill Gates Buy

1 – Bill Gates bought a total of 6 pencils. 2 – The total value of pencils Bill Gates bought was 130 cents

GiantSwan, To tackle such question, start with the question stem. You know there are 3 variables you need to know and the variable that you are looking for is no. of 23 cent pencils?

Let x be the no. of 23 cent pencil Let y be the no. of 21 cent pencil

23x + 21y = ?

Statement 1: x + y = 6 -----> this gives you a clue that Bill bought 6 pencils but not sure the combination. Thus, this statement alone can't answer the question.

Statement 2: Total value of pencil = 130 cents ie 23x + 21y = 130. Still, this statement alone does not answer the question.

If we combine the hints from statement 1 and 2, we can solve