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Problem solving

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by Newaz111 » Mon May 04, 2015 4:24 am
Chris mixed 3 pounds of raisins with 4 pounds of nuts. If a pound of nuts costs 3 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?

A.3/7
B.1/3
C.1/4
D.1/5
E.1/7
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by Brent@GMATPrepNow » Mon May 04, 2015 7:19 am
Newaz111 wrote:Chris mixed 3 pounds of raisins with 4 pounds of nuts. If a pound of nuts costs 3 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?

A.3/7
B.1/3
C.1/4
D.1/5
E.1/7
A fast approach is to choose some nice values for the per-pound costs.

Let the raisins cost $1 PER POUND
This mean the nuts cost $3 PER POUND [since a pound of nuts costs 3 times as much as a pound of raisins]

3 pounds of raisins costs (3 pounds)($1/pound) = $3
4 pounds of nuts costs (4 pounds)($3/pound) = $12
TOTAL COST = $3 + $12 = $15

The total cost of the raisins was what fraction of the total cost of the mixture?
$3/$15 = [spoiler]1/5 = D[/spoiler]

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Brent
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by [email protected] » Mon May 04, 2015 11:41 am
Hi Newaz111,

TESTing VALUES (the approach that Brent used) is a great approach for these types of questions. You can also solve this question with Algebra...

We have 3 pounds of raisins and 4 pounds of nuts. We're told that a pound of nuts costs 3 TIMES as much as a pound of raisins, so we can call the prices:

X = price per pound of raisins
3X = price per pound of nuts

The total price of this mixture would then be:

3(X) + 4(3X) = 3X + 12X = 15X

We're asked for the total cost of the raisins divided by the total cost of the mixture:

Total cost of raisins: 3X
Total cost of he mix: 15X

3X/15X = 1/5

Final Answer: D

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