### Brain Teasers

# Al and Cal

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 ?

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 ?

### Hint

Work backwards from the final result.### Answer

Al's number : 22Cal'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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