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

Question

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

Vithal · Answer

Pl. explain your answer for the benefit of others!

sid_477 · Answer

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)

lastochka · Answer

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?

ian7777 · Answer

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.

Vithal · Answer

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!

ian7777 · Answer

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.

Vithal · Answer

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!)

ian7777 · Answer

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...

K_s_r · Answer

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

bumpbot · Answer

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

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