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# Integers a and b are consecutive multiples of 6. Integers x and y are

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Integers a and b are consecutive multiples of 6. Integers x and y are  [#permalink]

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11 Oct 2018, 03:06
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Difficulty:

45% (medium)

Question Stats:

65% (01:51) correct 35% (02:31) wrong based on 123 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. $$\frac{(x+y)}{(a+b)}$$

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. $$\frac{1}{2}\frac{(a+b)}{(x+y)}$$

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Re: Integers a and b are consecutive multiples of 6. Integers x and y are  [#permalink]

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11 Oct 2018, 03:12
Bunuel wrote:
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 = 6*1 = 6
b= 6 *2 = 12

Total = 12 + 6 = 18

Average : 18 / 2 = 9

x = 8*1 = 8

y = 8*2 = 16

total = 18 + 6 = 24

Average = 24 / 2 = 12

Ratio: a + b/2 : x + y/2 = 9 : 12 = 3 : 4.

Option A) a + b / x + y = 18 / 24 = 3: 4.

Thus A is the best answer.

Intern
Joined: 14 Dec 2017
Posts: 3
Re: Integers a and b are consecutive multiples of 6. Integers x and y are  [#permalink]

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13 Oct 2018, 09:40
Step 1: Identify multiples of 6 and 8

Multiples of 6: 6, 12, 18, 24, 30, 36,42,...
Multiples of 8: 8, 16, 24, 32, 40, 48, 54,...

Step 2: Pick any consecutive multiples in each set for a, b and add, theN for x and y and then add.

Step 3: Divide your respective results

Example: 6+12/8+16 = a+b/x+y

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Re: Integers a and b are consecutive multiples of 6. Integers x and y are  [#permalink]

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13 Oct 2018, 09:45
2
avg of a and b = (a+b)/2
avg of x and y =(x+y)/2
ratio= a+b/x+y
Re: Integers a and b are consecutive multiples of 6. Integers x and y are   [#permalink] 13 Oct 2018, 09:45
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