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# How must a grocer mix 4 types of peanuts worth 54 c, 72 c.

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Director
Joined: 01 Feb 2003
Posts: 756
How must a grocer mix 4 types of peanuts worth 54 c, 72 c.  [#permalink]

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07 Jul 2004, 13:02
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0% (00:00) correct 100% (00:01) wrong based on 3 sessions

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How must a grocer mix 4 types of peanuts worth 54 c, 72 c. \$1.2 and \$1.44 per pound so as to obtain a misture at 96 cents per pound?
(A)8:4:4:7
(B)24:12:12:50
(C)4:8:7:4
(D)16:42:28:10
(E)Cannot be uniquely determined

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Director
Joined: 01 Feb 2003
Posts: 756

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07 Jul 2004, 13:42
Intern
Joined: 29 Jun 2004
Posts: 25

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07 Jul 2004, 22:56
The rule of alligation or mixture is
Qty. of cheaper/Qty. of dearer = Cost price(dearer) - Mean price/ Mean price - Cost price (cheaper)

1.44 - 0.96/ 0.96-054 = 0.48/0.42 = 8/7 (8:7)

1.20-0.96/0.96-0.72 = 4:4 (when divided by 6)

Therefore 8:4:4:7 is the answer (A)
Senior Manager
Joined: 07 Oct 2003
Posts: 332
Location: Manhattan

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10 Jul 2004, 11:25
Vithal wrote:
How must a grocer mix 4 types of peanuts worth 54 c, 72 c. \$1.2 and \$1.44 per pound so as to obtain a misture at 96 cents per pound?
(A)8:4:4:7
(B)24:12:12:50
(C)4:8:7:4
(D)16:42:28:10
(E)Cannot be uniquely determined

I tried choices A & D, didn't get the answer, took me 4 minutes, at this point I would just guess on of the remaining ones.

for A, I did 8(54)+4(72)+4(120)+7(144)/(8+4+4+7), the answer is around 2368/23, which is a little over a dollar a pound

similar method can be applied to the rest of the problem

The problem with this method is time consumption -- it's huge.
Does anyone know another method that tried n' tested?
CIO
Joined: 09 Mar 2003
Posts: 454

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10 Jul 2004, 19:32
The answer is A, and the best way to figure it out is a little tricky, but wonderful to understand for the GMAT.

First of all, the problem is too hard for the test, in my opinion, even at the highest level. It takes far too long, and plugging in the answers is laborious.

But an easier version could definately be there, and I'll put one down here so we can learn the trick and then apply it. Imagine this question:

60% of the boys and 30% of the girls in a class play basketball. If 40% of all the kids play basketball, what is the ratio of boys to girls in the class?

The answer here is 1:2. You can do it two ways. The first is with algebra, but the best way is to draw a scale that looks like this:

|---10---|-----20-----|
30------40-----------60
G.........all...............B

This might seem random, but for those of you who know the algebra behind a problem like this, it'll make sense. Now, cross connect the 10 to the B and the 20 to the G, and you'll get something that looks like this:

B:G = 10:20 = 1:2

We can do the same thing with this problem (I used W, X, Y, and Z for the different nuts):

|------- 42------|------- 48---------|
............|--24---|---24--|
54------72------96------120------144
W.........X........all.........Y...........Z

(all the periods here are just as space holders in this html system)

Now, for some reason, this works here as well. Cross everything, and connect the 48 to w, 24 to x, 24 to y, and 42 to z, and we get

W:X:Y:Z = 48:24:24:42 = 8:4:4:7

Of course, by the time you do all that, and trust that you're right, the test is over, which is why this, in my opinion, wouldn't be there. But if it were, plugging in the answers is probably better.
Director
Joined: 01 Feb 2003
Posts: 756

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11 Jul 2004, 01:36
OA is E

In this problem, both A and C are correct

Instead of the huge calculation given by Ian, just remember as a rule that in the cases where four different things are mixed, the ratio cannot be uniquely determined - there are infinite solutions possible!
CIO
Joined: 09 Mar 2003
Posts: 454

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11 Jul 2004, 23:13
You're right, Vithal. I'm going to have to be much sharper to get along with this crowd!

But don't discount the method. It's great for the other example, it beats algebra, and anyone, regardless of their abilities, can get a question like it right, while the algebra can be bewildering.
Director
Joined: 01 Feb 2003
Posts: 756

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12 Jul 2004, 11:30
Ian,

your method will be useful if the question were to be framed as "Which of the following options provides one of the ratios in which peanuts can be mixed?"

well...to get 800, one definitely needs know your method (esp. when the numbers are close!)
CIO
Joined: 09 Mar 2003
Posts: 454

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12 Jul 2004, 15:49
Vithal, with the amount of work you're doing, you should be able to jump up to the 700's! I'm sure you're going to get the score you want...
Manager
Joined: 21 Jun 2004
Posts: 52

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17 Jul 2004, 00:02
ian7777 wrote:
The answer is A, and the best way to figure it out is a little tricky, but wonderful to understand for the GMAT.

First of all, the problem is too hard for the test, in my opinion, even at the highest level. It takes far too long, and plugging in the answers is laborious.

But an easier version could definately be there, and I'll put one down here so we can learn the trick and then apply it. Imagine this question:

60% of the boys and 30% of the girls in a class play basketball. If 40% of all the kids play basketball, what is the ratio of boys to girls in the class?

The answer here is 1:2. You can do it two ways. The first is with algebra, but the best way is to draw a scale that looks like this:

|---10---|-----20-----|
30------40-----------60
G.........all...............B

This might seem random, but for those of you who know the algebra behind a problem like this, it'll make sense. Now, cross connect the 10 to the B and the 20 to the G, and you'll get something that looks like this:

B:G = 10:20 = 1:2

We can do the same thing with this problem (I used W, X, Y, and Z for the different nuts):

|------- 42------|------- 48---------|
............|--24---|---24--|
54------72------96------120------144
W.........X........all.........Y...........Z

(all the periods here are just as space holders in this html system)

Now, for some reason, this works here as well. Cross everything, and connect the 48 to w, 24 to x, 24 to y, and 42 to z, and we get

W:X:Y:Z = 48:24:24:42 = 8:4:4:7

Of course, by the time you do all that, and trust that you're right, the test is over, which is why this, in my opinion, wouldn't be there. But if it were, plugging in the answers is probably better.

really good method, but need a short cut to save time

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Non-Human User
Joined: 09 Sep 2013
Posts: 10949
Re: How must a grocer mix 4 types of peanuts worth 54 c, 72 c.  [#permalink]

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18 Mar 2019, 14:37
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Re: How must a grocer mix 4 types of peanuts worth 54 c, 72 c.   [#permalink] 18 Mar 2019, 14:37
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