AMO 2016 Grade 4

What is the least 3-digit even whole number that is divisible by 35?

What is the value of N that makes the following statement true?

$4 × 6 × 8 × 10 = 40 × N$

How many square units (units²) bigger is a 5 × 5 square than a 4 × 4 square?

On Wednesday, the store sign said that the new video game would be available in 45 days. On what day of the week should the sign say that it will be available in only 2 days?

Each letter in the ordered list A, B, C, D, E, F, G represents a number. The numbers are not necessarily different, which means that two letters can represent the same number. The sum of the values of any three adjacent letters (three letters in a row) is 20. When B = 6 and D = 9, what is the value of G?

In the addition shown, different letters represent different digits. What is A + B + C + D?

Three students are in an election. Twenty votes are cast. Samantha has more votes than anyone else. What is the least number of votes she could have?

The clock at Bernoulli Towers is slow. Every day, at noon, Karan corrects it from 11:15 am to 12:00 pm. When Karan went on vacation for 6 consecutive days (6 days in a row), he accidentally took the key with him. With no one to reset the clock, it fell far behind. When Karan returned after vacation to correct the clock to noon, what time did the clock show?

The number in the center of each box is the result of operations that use the four numbers in the corners of the same box. Each of the four corner numbers in a box must be used exactly once. The same set of operations is used for each box. What number should replace the N?

The Funny Book has its pages numbered in the following way: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, ... . That is, there is one 1, two 2s, three 3s, four 4s, five 5s, and so on. How many actual pages (including front and back) will the Funny Book have if it contains all possible pages that are numbered “1” through “22”, but not any that are numbered “23”?

A bicyclist takes 2 minutes and 30 seconds to travel a distance of 1 mile. At this rate, how many miles will the bicyclist travel in 2 hours? (1 mile is approximately 1609.34 metres)

In a parking lot, there are 65 cars, all of which are black or blue and all of which are Fords or Dodges. There are 25 black Dodges. There are 23 blue cars. There are 28 Fords. How many blue Fords are there?

A Super-Brick is formed by arranging nine 1cm × 1cm × 1cm cubes into a 3cm × 3cm layer, 1cm thick. Two Super-Bricks are glued together into the L-shape shown. All faces of the L-shape are completely painted. What is the area of the painted surface in square centimeters (cm²)?

Find the least whole number which when divided by 5 gives a remainder of 4 and when divided by 12 gives a remainder of 11.

Tom’s number has four digits in increasing order. The tens digit is the sum of the hundreds digit and the thousands digit. The ones digit is the sum of the other three. The sum of all four digits is 16. Find the tens digit in Tom’s number.

How many whole numbers less than 361 are divisible by 6 but not divisible by 9?

Joseph put candles on a cake. He lit $\frac14$ of those candles. Then he lit 5 more of the candles on the cake. As a result, exactly $\frac13$ of the candles on the cake were lit. What was the total number of candles on the cake?

Consider the three-by-three grid shown (middle square removed). The counting numbers from 1 to 8 are placed in the squares (one number per square) so that the top row adds to 9, the bottom row adds to 21, the left column adds to 13, and the right column adds to 15. What is the sum: A + B + C + D?

Two rectangles, each 6 cm × 10 cm, overlap to form the 8-sided shape in the diagram. The overlap is a rectangle with counting (Natural) numbers for its length and width. What is the least perimeter, in centimeters, that the 8-sided shape can have? [Diagram not drawn to scale.]

In the figure shown, the numbers 1, 2, 3, 5, 6, and 7 are to be placed one in each empty square. The following 4 sums are the same: the numbers in the left column, the numbers in the right column, and the numbers in each diagonal. What is the greatest possible product of the 3 numbers across the grey row?