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Bill Gates bough several pencils. If each pencil was either

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Bill Gates bough several pencils. If each pencil was either [#permalink] New post 28 Feb 2008, 16:32
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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
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Re: DS - Bill Gates [#permalink] New post 28 Feb 2008, 17:08
E). Not enough data i suppose..

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?
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Re: DS - Bill Gates [#permalink] New post 28 Feb 2008, 17:15
23*x+21*(6-x) = 130
2x +126 = 130
x= 2

Answer is C
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Re: DS - Bill Gates [#permalink] New post 28 Feb 2008, 17:16
it is B

a total of 130 cents

meaning that there are 6 pencils together, 2 23cents pencils and 4 21cents pencils.

This is a gmatprep question, someone substituted the name "bill gates" in place of "marta"

Last edited by gmatnub on 28 Feb 2008, 19:11, edited 1 time in total.
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Re: DS - Bill Gates [#permalink] New post 28 Feb 2008, 17:58
gmatnub wrote:
it is B

a total of 130 cents

meaning that there are 6 pencils together, 2 23cents pencils and 4 21cents pencils.

This is a gmatprep question, someone substituted the name "bill gates" in place of "maria"


What was your logic going from 130, to knowing there were 6 pencils.
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Re: DS - Bill Gates [#permalink] New post 29 Feb 2008, 08:12
B

21 cent pencils

21 - 1 pencil
42 - 2 pencil
63- 3 pencil
84- 4 pencil
105- 5 pencil

23 cent pencils

23- 1 pencil
46- 2 pencil
69- 3 pencil
92- 4 pencil
115- 5 pencil


The only combination of these pencils that add up to 130 is

4 21 cent pencils and 2 23 cent pencils = 84+46cents = 130 cents

quickly look at the last digits to see what adds up and gives you a value of 0 between them instead of adding each combination up.
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Re: DS - Bill Gates [#permalink] New post 29 Feb 2008, 08:19
Statement 1:

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.
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Re: DS - Bill Gates [#permalink] New post 29 Feb 2008, 08:26
abhijit_sen wrote:
Statement 1:

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.
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Re: DS - Bill Gates [#permalink] New post 29 Feb 2008, 11:36
RyanDe680 wrote:
abhijit_sen wrote:
Statement 1:

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.
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Re: DS - Bill Gates [#permalink] New post 12 Mar 2008, 22:20
anyone help with a solid approach to these?
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Re: DS - Bill Gates [#permalink] New post 13 Mar 2008, 01:11
terp26 wrote:
B

21 cent pencils

21 - 1 pencil
42 - 2 pencil
63- 3 pencil
84- 4 pencil
105- 5 pencil

23 cent pencils

23- 1 pencil
46- 2 pencil
69- 3 pencil
92- 4 pencil
115- 5 pencil


The only combination of these pencils that add up to 130 is

4 21 cent pencils and 2 23 cent pencils = 84+46cents = 130 cents

quickly look at the last digits to see what adds up and gives you a value of 0 between them instead of adding each combination up.


This one is a good explanation. I agree..
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Re: DS - Bill Gates [#permalink] New post 13 Mar 2008, 06:09
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.
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Re: DS - Bill Gates [#permalink] New post 13 Mar 2008, 08:00
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kizito2001 wrote:
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

y = (6 - x)
=> 23x + 21(6 - x) = 130
=> 23x + 126 - 21x = 130
=> 2x = 130 - 126
=> 2x = 4
Thus, x = 2

Ans: C - both statements together are sufficient but neither statement alone is sufficient.

The trick is convert all statements into algrebric (?) statement.
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Re: DS - Bill Gates [#permalink] New post 17 Mar 2008, 18:11
Anyone has other answers? I rechecked and sticking to "C". Perhaps the answer sheet is wrong. :lol:
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Re: DS - Bill Gates [#permalink] New post 17 Mar 2008, 20:44
kizito2001 wrote:
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


B too.

xa + yb = 130
23a + 21b = 130

plug-in:
23x2 + 21x4 = 130
46 + 84 = 130

bingo: a = 2 and b = 4. so altogather 6 pencils.
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Re: DS - Bill Gates   [#permalink] 17 Mar 2008, 20:44
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