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Integers a and b are consecutive multiples of 6. Integers x
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17 Nov 2016, 16:32
17 Nov 2016, 16:32
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Integers a and b are consecutive multiples of 6. Integers x and y are consecutive multiples of 8. In terms of a, b, x, and y, what is the ratio of the average of a and b and the average of x and y?
A. \(\frac{(x+y)}{(a+b)}\)
B. \(\frac{(a+b)}{(x+y)}\)
C. \((a+\frac{b}{4})/(y-\frac{x}{4})\)
D. \((a+\frac{b}{4})/(y-\frac{x}{2})\)
E. \(\frac{1}{2}\frac{(a+b)}{(x+y)}\)
A. \(\frac{(x+y)}{(a+b)}\)
B. \(\frac{(a+b)}{(x+y)}\)
C. \((a+\frac{b}{4})/(y-\frac{x}{4})\)
D. \((a+\frac{b}{4})/(y-\frac{x}{2})\)
E. \(\frac{1}{2}\frac{(a+b)}{(x+y)}\)
Drill 4
Question: 8
Page: 294
Question: 8
Page: 294
Re: Integers a and b are consecutive multiples of 6. Integers x
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17 Nov 2016, 16:37
17 Nov 2016, 16:37
Expert Reply
Explanation
You should Plug In on this question. Variables a and b can be consecutive numbers such as 6 and 12. Plug in consecutive multiples of 8 for x and y, such as 8 and 16. Finding the ratio of the averages is easy now; the averages of each pair of numbers will be the halfway point between the two numbers. For 6 and 12, the average is 9. For 8 and 16, the average is 12.
The ratio of these averages is \(\frac{3}{4}\). Now, plug your original numbers into the answer choices and
look for the one that equals \(\frac{3}{4}\). Choice (A) gives you \(\frac{4}{3}\), which is the reciprocal of what you want. Cross it off. Choice (B) gives you \(\frac{3}{4}\)which is what you’re looking for. But don’t stop yet—keep checking all of the answers. Choice (D) also works with these numbers. No harm done, just try a different set of numbers and check the two remaining choices.
Plug in some really unusual numbers, like 24 and 30 for a and b, and 80 and 88 for x and y. Now you are looking for an answer to give you \(\frac{9}{28}\) Choice (B) no longer works, so choice (D) is your answer.
Hence option D is the only correct option.
You should Plug In on this question. Variables a and b can be consecutive numbers such as 6 and 12. Plug in consecutive multiples of 8 for x and y, such as 8 and 16. Finding the ratio of the averages is easy now; the averages of each pair of numbers will be the halfway point between the two numbers. For 6 and 12, the average is 9. For 8 and 16, the average is 12.
The ratio of these averages is \(\frac{3}{4}\). Now, plug your original numbers into the answer choices and
look for the one that equals \(\frac{3}{4}\). Choice (A) gives you \(\frac{4}{3}\), which is the reciprocal of what you want. Cross it off. Choice (B) gives you \(\frac{3}{4}\)which is what you’re looking for. But don’t stop yet—keep checking all of the answers. Choice (D) also works with these numbers. No harm done, just try a different set of numbers and check the two remaining choices.
Plug in some really unusual numbers, like 24 and 30 for a and b, and 80 and 88 for x and y. Now you are looking for an answer to give you \(\frac{9}{28}\) Choice (B) no longer works, so choice (D) is your answer.
Hence option D is the only correct option.
Re: Integers a and b are consecutive multiples of 6. Integers x
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12 Jan 2017, 08:50
12 Jan 2017, 08:50
sandy could you define this approach? how can we be sure that substitution method is to be applied for this question and not solving it through algebraic method?
