IMAS 2018 — Middle Primary Grades 3–4 — Round 1

What is the value of $ 19 \times 1 + 19 \times 3 + 19 \times 5 + 19 \times 7 + \cdots + 19 \times 19 $?

If $ (\Delta \times 2 - 1) \times 2 = 2018 $, then what is the value of $ \Delta $?

Five students sit along a circle and start to call out some numbers one-by-one. Student A calls out “1”, B calls out “2”, C calls out “3”, D calls out “4”, E calls out “5” and then it returns back to Student A who calls out “6” and so on, where each student increases the previously called number by one and calls it out. Which student calls out the number “99”?

In the figure shown below, four rectangles of the same size, denoted by I, II, III and IV, are placed together, where ABCD and EFGH are both squares. If rectangle I has a perimeter of 20 cm, then what is the perimeter, in cm, of ABCD?



D

How many triangles in total are there in the figure below?

The six faces of a cube are colored using six different colors namely red, blue, yellow, green, black and white in some order. Turn the cube arbitrarily and it shows the two possible scenarios below. What is the color opposite to the face of green?

Consider every positive integers whose digits do not include 2 and that sum of its digits is equal to 3 and arrange all such integers in increasing order. What is the sum of the three smallest integers that satisfy the conditions?

In the $ 4 \times 4 $ square table shown below, a $ \triangle $ is placed on the second row and second column. What is the total number of squares with sides falling on the grid lines and containing $ \triangle $?

In the figure below, a frog jumps between the three circles. In each jump, it goes from one circle into another circle. It is known that the frog starts from A and ends at A after 4 jumps. How many different paths can the frog have?

In 1202 A.D., Italian mathematician Fibonacci (1170~1250) wrote in his book 《Liber Abaci》 the following interesting problem: Exactly two months after their birth, a pair of rabbits will give birth to a new pair (one male and one female) and then give birth to a pair each month after that. There is only one pair of new born rabbits at the beginning. If the rabbits never die, how many pair of rabbits are there after exactly 12 months?

Define “*” as an operation such that $ 4*2=82 $, $ 6*3=183 $, $ 8*4=324 $, $ 9*3=276 $ and $ 9*5=454 $. What is the value of $ 10*2 $?

Bob got a score of 94 on foreign language test, and his average score on the native language and math tests is 97. What is his average score on these three tests?

Color the surfaces of a $ 5\times5\times5 $ wooden cube red, then cut it into smaller $ 1\times1\times1 $ cube pieces. How many of these smaller cubes have exactly two red faces?

A palindrome number is a positive integer that is the same when read forwards or backwards. The numbers 909 and 1221 are examples of palindromes. How many palindrome numbers are there between 10 and 1000?

In the month of February of some year, there are more Saturdays than any other days in a week. What day is the last day of this month?

Four students namely Annie, Benny, Charlie and Deany all paid the same amount of money to buy some number of notebooks together. After distributing the notebooks, Annie, Benny and Charlie got 6, 7 and 11 notebooks more than Deany, respectively. As such, to be fair, Annie, Benny and Charlie gave back a total of 48 dollars to Deany. What is the price of each notebook?

A train left town A at 8:30 AM some day and arrived at town B at 1:50 AM of the next day. There is no time difference between the two places. How long did the train travelled for the trip?

Mike placed 4 identical squares, each with side length 5 cm and are non-overlapping, to form a new figure as shown below. Find the perimeter, in cm, of this new figure.

Adam owns an old watch, which is slower than a normal watch by the same amount of time for each hour. At 8 o'clock in the morning, the old watch reads 8 o'clock. At 9 o'clock in the morning, it reads 8:58. What time does it read when the real time is 4 o'clock in the afternoon?

Identical equilateral triangles are placed together into two figures as shown below. One can cover Figure B using 5 pieces of Figure A. How many different ways can we do the covering?



Figure A



Figure B