Official Guide Explanation:
Problem Solving #162




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Solution and Metadata

Question: 162
Page: 175
Difficulty: 5 (Moderate)
Category 1: Word Problems > Rate Problems > other
Category 2: Arithmetic > Ratio and Proportion >

Explanation: Whenever you're given a part - to - part ratio (like the applies : peaches : grapes ratio in this question) it implies a part - to - whole ratio. For instance, for every six pounds of apples, there's 6 + 5 + 2 = 13 pounds total. Thus, if there are 39 total pounds, you can set up a ratio to find out the total number of apples: (6/13) = ((x)/39) , or x = 18. Do the same for grapes: (2/13) = ((x)/39), or x = 6. So, there are 18 - 6 = 12 more pounds of apples than grapes, choice (B). Note that you don't have to set up the ratio: if you realize that the parts add up to 13 and the total weight is 39, you may realize that you can simply triple the numbers in the ratio for the actual weight of each type of fruit.

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