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

Question

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)}

KSBGC · Answer

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.

Abdifatah · Answer

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

Answer = B

HAPPYatHARVARD · Answer

avg of a and b = (a+b)/2
avg of x and y =(x+y)/2
ratio= a+b/x+y

Carlijn · Answer

What is wrong with answer D? 
If a= 6 and b= 12 
a+4/b=6+4/12=6+3=9

x=8 and y=16
y−x/2=16−8/2=16−4=12

So 9/12 = 3/4

dhairya18 · Answer

Your logic for Option D fails if we use different consecutive multiples.
​Let’s try a = 12 and b = 18 (multiples of 6), and x = 16 and y = 24 (multiples of 8):
​The actual ratio of averages: (12+18)/2 divided by (16+24)/2 is 15/20, which equals 0.75.
​Testing Option D: a + (b/4) is 12 + 4.5 = 16.5. Then y - (x/2) is 24 - 8 = 16. The ratio 16.5 / 16 is 1.03.
​Because the numbers don't match here, Option D cannot be the general formula. Option B is correct because the '2' in the denominator of both averages cancels out: (a+b)/2 / (x+y)/2 always simplifies to (a+b) / (x+y).

necessitatibussit · Answer

a=6
b=12
x=8
y=16
average a+b/2=9
average x+y/2=12
B. 18/24=9/12=>correct

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

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

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