Brain Teasers
A + B + C + D
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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