A fruit-salad mixture consists of apples, peaches, and grape

Hi All,

Ratio/percent questions occur frequently on the GMAT; one of the great things about these questions is that they can be solved in a variety of ways:

Here, we have a ratio of Apples:Peaches:Grapes in the ratio of 6:5:2. We're told that 39 pounds of this mixture is prepared and we're asked how many MORE pounds of Apples are there than pounds of Grapes.

Since the answer choices are numbers, we can use them to our advantage and avoid some of the math. From the original ratio, we know that....

The pounds of....
Apples will be a multiple of 6
Peaches will be a multiple of 5
Grapes will be a multiple of 2
Total will be a multiple of 13

So, the difference in the pounds of Apples and Grapes will be 6 - 2 = some multiple of 4 pounds.

If we had 13 pounds total, then the difference would be 4 pounds. Since the total is MORE than 13 pounds, the difference will be MORE than 4 pounds (but still a multiple of 4). Only one answer fits that pattern:

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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 question 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 grapes = (2)(3) = 6

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

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

Answer is B.

6w + 5w + 2w = 39

Or, 13w = 39

Or, w = 3

According to the ratio Apples : Grapes = 6 : 2 , so Apple is 12 { 3 ( 6 - 2 ) } more than Grapes...

Answer will be (B)

Note that A:P:G = 6:5:2
We need to find A - G by actual weight.
As A - G = 4
the answer would be multiple of 4
Hence A, C and D is out.

Out of B and E, E is out because total weight is not multiple of '1' of '13'.

Answer B.

A:P:G

6:5:2

6x + 5x +2x = 39

13x = 39

x = 3

A - G => 6(3) - 2(3) = 18 - 6 = 12

The answer is B.

EMPOWERgmatRichC
Thanks for the nice explanation.

What if question talks about ''the mixture includes how many more pounds of apples than peaches?
The difference=6-5-->1. The multiple of 1 could be any digit. Then how can we take decision about the answer option? I think it makes sense.
Thank you Rich...

Hi Asad,

The approach(es) that you might take to solving any given Quant question will depend a great deal on the type of information that you're given, the specific question that is asked and how the answer choices are written. In the situation that you're asking about, we'd still be able to deduce that for every 13 pounds to fruit-salad, the difference between the pounds of apples and the pounds of peaches would be 6 - 5 = 1. This essentially gives us a new ratio to work with.

With 39 pounds of fruit-salad, we have 3 thirteen-pound "groups".... and each group would have 1 more pound of apples than peaches, so there would be 3(1) = 3 more pounds of apples than peaches in total.

If the answer choices were 'close together' (for example: 1, 2, 3, 4 and 5), then doing some variation of that math would be necessary. If the answers were more 'spread out' though (for example: 3, 6, 9, 12, 15), then you might recognize that 39/13 is a relatively small number - and only the number 3 would make sense.

GMAT assassins aren't born, they're made,
Rich

the ratio of apples: peaches: grapes
6: 5 :2
=6/13: 5/13: 2:13
39 pounds in total

apples:
6/13 * 39 = 18

grapes:
2/13* 39 = 6

apples-grapes:
18-6 = 12//

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