IMAS 2012 — Upper Primary Grades 5–6 — Round 2

Andrew converted 15,700 Yuan to US Dollars for his foreign travel. He spent 1,612 US dollars on this trip, and converted the remaining US Dollars back to Yuan. The currency exchange rate (shown below) for that day was the same as on the day when he converted his Yuan to US Dollars. How much Yuan would he get?



Exchange table (Yuan per US dollar): Buying 6.25; Selling 6.28.

Which of the statements below is always true?

The diagram shows two identical graduated cylinders of capacity 900 ml, each containing some water. In order for both cylinders to contain the same amount of water, how much water should be poured from the cylinder on the left into the cylinder on the right?

One of the following two-digit numbers is attached at the end of 2013 to make a six-digit number. Which number is attached if the six-digit number is divisible by 3, 4 and 7?

Each of the following five six-sided die has 1, 2, 3, 4, 5 and 6 spots on its faces. Which one has a different arrangement of spots from the other four?

In the 8 × 10 grid below, how many percents of the figure is shaded?

Andy and Ben started at 7:00AM from town A and jogged along the same road in the same direction. Andy jogged at a constant speed of 6 km/h while Ben jogged at a constant speed of 4 km/h. At 9:00AM, Ben borrowed a bike along the road and rode at a constant speed of 10 km/h. He caught up with Andy at town B. What was the distance between town A and town B?

In a promotional sale, anyone who buys a cup of juice at the regular price of 7 dollars can get a second cup of juice by paying 1 more dollar. What is the minimum number of dollars a party of 9 people must pay if each of them wants a cup of juice?

How many men are there in a party with 35 people if each person shakes hands with four women and six men?

A rectangular strip, 30 cm in length and 3 cm wide, is folded in a pattern shown in diagram (2), producing a right angle∠A . After the strip is completely folded as shown in diagrams (3) and (4), the lengths of AM and GM are equal. What is the length of AC in diagram (1)?

In the figure, △ABC is a right triangle while BDEC, BFGA and ACMN are squares. If the area of the shaded portion is 48 cm² , what is the area of △ABC?

The diagram shows that if a rope is folded once and be cut in halves, it will separate into 3 pieces; and if it is folded twice instead, it will separate into 5 pieces. If it is folded 6 times instead, into how many pieces will it separate?

A 50 cm × 30 cm rectangle is to be covered with a combination of 10 cm × 10 cm and 20 cm × 20 cm tiles. How many different arrangements are possible?

How many positive integers n are there such that among the integers n, n + 1, … n + 100, there are exactly six which are squares of integers?

A 9 × 9 chessboard may be covered without overlap with a combination of the following three shapes. What is the minimum number of copies of the piece consisting of three squares must be used?