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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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Question Stats:
51% (01:32) correct
48% (01:16) wrong based on 47 sessions
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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. (x+y)(a+b)
B. (a+b)(x+y)
C. (a+b4)/(y−x4)
D. (a+b4)/(y−x2)
E. 12(a+b)(x+y)
A. (x+y)(a+b)
B. (a+b)(x+y)
C. (a+b4)/(y−x4)
D. (a+b4)/(y−x2)
E. 12(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 34. Now, plug your original numbers into the answer choices and
look for the one that equals 34. Choice (A) gives you 43, which is the reciprocal of what you want. Cross it off. Choice (B) gives you 34which 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 928 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 34. Now, plug your original numbers into the answer choices and
look for the one that equals 34. Choice (A) gives you 43, which is the reciprocal of what you want. Cross it off. Choice (B) gives you 34which 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 928 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?
