"Samosa King" food delivery sells samsoas in orders of six, nine, and twenty. What is the largest

M4maths Previous Puzzles

27 May 2020 Order

"Samosa King" food delivery sells samsoas in orders of six, nine, and twenty.
What is the largest number of samosa's you cannot order from "Samosa King"?

OPtion

1) 3
2) 5
3) 7
4) 11
5) 31
6) 89
7) 43
8) 91
9) 113
10) None of these

Solution

Since you can buy 6 and 9, you can buy any number divisible by 3 except for 3 itself.

Let's look at numbers over 40. If a number is over 40 is not divisible by 3, you can get a number divisible by 3 by subtracting either 20 or 40.

For 43, you may subtract 40 to get the number 3. But you cannot buy packs if 3, you can only get greater multiples of 3.

For all numbers greater than 43, the number will be divisible by 3 and greater than three, or you can subtract 20 or 40 and get a number that is divisible by 3 and greater than 3.

So you can create any number greater than 43 with 0, 1 or 2 packs of 20, 0 or 1 packs of 9, and n number of packs of 6, where n can be any integer.

Correct Option: 7 Best Solution (0)