Two math students, Al and Cal, each picked a number and then performed five arit
ID: 2986102 • Letter: T
Question
Two math students, Al and Cal, each picked a number and then performed five arithmetic operations.
Al took his number and performed the following operations:
(i) subtracted 3
(ii) then multiplied by 4
(iii) then added 5
(iv) then took the square root
(v) then divided by 3
Cal did just the opposite of his math buddy. He took his number and did the following:
(i) added 3
(ii) then divided by 4
(iii) then subtracted 5
(iv) then squared the result
(v) then multiplied by 3
After performing their arithmetic, BOTH Al and Cal ended up with the same answer of 3 . Also, there were no negative results at any step along the way.
Who picked the larger number, Al or Cal ?
Explanation / Answer
Al's number : 22
Cal's number: 21
Working backwards from the final result of 3, we have:
Al : 3 x 3 = 9 ; 9 ^2 = 81 ; 81 - 5 = 76 ; 76/4 = 19 ; 19 + 3 = 22.
Cal: 3/3 = 1 ; sqrt(1) = 1 ; 1 + 5= 6;
6 x 4 = 24 ; 24 - 3 = 21.
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