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Problem Solving mixture question. Fruit Salad mixture

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by 90thonebetter » Tue Mar 15, 2011 10:19 am
A fruit-salad mixture consists of apples, peaches, and grapes, in the ration 6:5:2, respectively, by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

A) 15
B) 12
C) 9
D) 6
E) 4

I'm looking for a good quick method through this problem. Thanks for your help!
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by force5 » Tue Mar 15, 2011 11:11 am
easiest--

apple is 6/13
grape is 2/13
total weight 39 pounds
hence apple 6/13*39 = 18
grape = 2/13*39=6

difference = 12 henceB
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by Stuart@KaplanGMAT » Tue Mar 15, 2011 2:18 pm
90thonebetter wrote:A fruit-salad mixture consists of apples, peaches, and grapes, in the ration 6:5:2, respectively, by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

A) 15
B) 12
C) 9
D) 6
E) 4

I'm looking for a good quick method through this problem. Thanks for your help!
A slightly different way to think about this (and similar) ratio problem.

The total number of parts in the ratio is 13 (6+5+2). Since our mixture weighs 39 pounds, our multiplier is 3 (39/13 = 3).

So, we have 3*6 = 18 lbs of apples and 3*2 = 6 lbs of grapes. 18-6=12, choose (B).

The math is the exact same as in Force5's approach, we've just broken it down a little differently.
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by Abhishek009 » Sat Mar 15, 2014 10:09 am
90thonebetter wrote:A fruit-salad mixture consists of apples, peaches, and grapes, in the ration 6:5:2, respectively, by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?
A : P : G = 6x : 5x : 2x

So , A + P + G = 13x ( 6x + 5x + 2x) => 39

13x = 39

So X = 3


Now we are required to find - how many more pounds of apples than grapes.

According to the ratio A = 6x and G = 2x

So A > G by 4x

Or A - g = 4 * 3 = 12

Hence IMO (B)
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by Bill@VeritasPrep » Mon Mar 17, 2014 9:29 am
^Nailed it. The math isn't tricky here, but it'd be very easy to answer a question that wasn't actually being asked. This is common with ratio questions, so be careful!
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by smkhan » Mon Jul 07, 2014 7:21 am
The way I did it is below. Do comment if it's the right approach.

A:P:G=6:5:2, so 4 pounds more of apple in the total of 13 pounds. In 39 pounds of mixture, it would be (39/13)*4=12.

Ans: B.
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by mcdesty » Wed Jul 09, 2014 2:18 pm
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by [email protected] » Wed Jul 09, 2014 4:31 pm
Hi smkhan,

There are several different ways to "do the math" in this question; your way is just as valid as any.

Ratio questions on the GMAT are ultimately about "multiples." Here, since the ratio is 6:5:2, the total weight would be a multiple of 13 points (composed of equivalent multiples of 6, 5 and 2). From there, the math approach you take is up to you.

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by Scott@TargetTestPrep » Fri Jul 10, 2015 4:16 am
90thonebetter wrote:A fruit-salad mixture consists of apples, peaches, and grapes, in the ration 6:5:2, respectively, by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

A) 15
B) 12
C) 9
D) 6
E) 4

I'm looking for a good quick method through this problem. Thanks for your help!
Solution:

We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:2, respectively, by weight. Thus, we can say:

apples : peaches : grapes = 6x : 5x : 2x

We are given that 39 pounds of the mixture is prepared so we can set up the following equation and determine a value for x:

6x + 5x + 2x = 39

13x = 39

x = 3

Now we can determine the number of pounds of apples and of grapes.

pounds of apples = (6)(3) = 18

pounds of grapes = (2)(3) = 6

Thus, we know that there are 18 - 6 = 12 more pounds of apples than grapes.

Answer: B

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by Jim@StratusPrep » Fri Jul 10, 2015 4:43 am
Start looking at the differences in the ratios. As everyone said, the ratio multiplier is 3, but then just do (6 - 2) x 3 = 12. While maybe not important for this problem, getting used to these techniques will help with more challenging computation and DS problems.
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