### Brain Teasers

# A + B + C + D

Math
Math brain teasers require computations to solve.

A, B, C, and D are all positive whole numbers. If A is to 2 as B is to 3; B is to 6 as C is to 8; and C is to 9 as D is to 12, what is the SMALLEST possible value for the sum: A + B + C + D ?

### Hint

A/2 = B/3 or 3A = 2BB/6 = C/8 or 8B = 6C ;

C/9 = D/12 or 12C = 9D .

What's the smallest positive whole numbers that satisfies all three of the above equations?

### Answer

43A = 6 , B = 9 , C = 12 , and D = 16 .

So, A + B+ C + D = 43.

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## Comments

I didn't quite get that one...........

Why cann't A=2 B=3 C=4 D=5? Then 2+3+4+5=14. I didn't get it either.

Nice one! Taking D to be 1... C is 3/4. B is 3/4 of C = 9/16 and A is 2/3 of B = 3/8. Since they must all be whole numbers, multiply everything by 16 (the LCM of the denominators). I like it!

ok.. now some just explain it in english please

use ratio. A:B=2:3 A:B:C=4:6:8 C=9:12=3:4 A:B:C=12:18:24:32=6:9:12:16

Thank you - very nice.

Serious issue with the wording. You didn't specify that all the relationships had to be ratios.

My answer was 0 + 1 + 3+ 4 = 7

A+2 = 2

B+2 = 3

B+5 = 6

C+5 = 8

C = 3/9

D = 3/12

My answer was 0 + 1 + 3+ 4 = 7

A+2 = 2

B+2 = 3

B+5 = 6

C+5 = 8

C = 3/9

D = 3/12

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