Question bank AMO 2018

Find the value of

$66+55+44+33+22+11$.

Jimmy scored five more points on a quiz than his sister Tammy. The sum of Jimmy’s scored and Tammy’s scored was 17. What was Jimmy’s scored?

Marci looked at a clock and realized that the number of hours that had passed since midnight was the same as the number of hours remaining until noon. How many hours had passed since midnight?

How many different paths that go from $A$ to $B$ to $C$ to $D$ are there in the picture below? A path can only touch each of the points $A$, $B$, $C$ and $D$ exactly once.

Adam has \$30 on Tuesday and spends \$2 every Saturday on snacks. Brandon has \$10 on the same Tuesday and gets \$2 every Saturday for allowance. After how many weeks will they have the same amount of money on a Tuesday?

I am thinking of a number. If you subtract 6 from my number and then multiply by 4, the result is 32. What number am I thinking of?

There are three numbers each represented by one of the symbols square, triangle, and diamond. It is given that



What number does the sum diamond + square represent?

What is the largest number of L-tiles (as shown) that can fit into the figure below without any overlap?

[Note: The L-tiles can be rotated in order to fit better but not cut.]

Lois is making rows of dots. The first five rows of dots are shown.



Each additional row has one more dot than the row above it. How many total dots are there in the first 10 rows combined?

Joseph has a collection of stickers. When the stickers are arranged in piles of 3, there are 2 stickers left over. When the stickers are arranged in piles of 4, there are 2 stickers left over. When the stickers are arranged in piles of 12, how many stickers are left over?

In the following, each different letter represents a different digit.



Find the first three digits of the largest possible sum.

(Example, if your answer is 1234, then write 123.)

The first 50 whole numbers are written. How many times does ‘3’ appear as a digit?

Jessie has 74 pieces of candy. Her friend Frank said: “If you give me 19 of your candies, we will both have the same number of candies”. How many pieces of candy does Frank have?

Each number from 1 through 6 is written on 6 cards, one number per card. Three cards are given to each of the two players. The sum of Player One’s cards is 13. What is the highest single card could Player Two possibly have?

A sequence of numbers was obtained by adding the same number to each term. The 1st term is 5 and the 5th term is 29. What is the 21st term of this sequence?

$5,\_\_,\_\_,\_\_,29,\_\_,\ldots$ (and so on)

What is the value of the following?

$72 + 60 + 48 + 36 + 24 + 12$

Terry and Gerald were in an essay writing competition. Gerald wrote 57 more words than Terry. They wrote 777 words altogether. How many words did Gerald write?

Heinz has 87 chocolates and receives 4 chocolates every week. Jed has 137 chocolates and gives away 6 chocolates per week. After how many weeks will they have the same number of chocolates?

There are three numbers each represented by one of the symbols □, △, and ◇. Given that the following statements are true, what number does the sum ◇ + □ represent?

Lois is making rows of dots. The first five rows of dots are shown. Each additional row has one more dot than the row above it. How many total dots are there in the first 16 rows combined?