IMSO 2004 Mathematics – Taiwan Selection – Short Answer

Every 7 days, a newspaper man drops a weekly magazine at Amir's house. A milkman goes there every 6 days. Last October 1st, the two men went to Amir's house. When (date and month) will they go there again on the same day?

A bus can carry 30 passengers, a minibus 8 passengers, and a train car 52 passengers. At least how many train cars are needed to carry passengers from 6 full buses and 13 full minibuses?

What is the value of $A$ to get the final result 279 as shown below?

Machine $A$ cost 500 dollars and machine $B$ cost 1000 dollars. We need 10 dollars per day to run machine $A$, and 5 dollars per day to run machine $B$. After running how many days will the total cost for both machines be equal?

Find a number greater than $\frac15$, but less than $\frac14$.

Find the number of positive integers smaller than 1000 such that the sum of the first digit and the last digit is 10.

How many integers between 999 and 2001 are divisible by 5?

What is the units digit of $3^{200}$?

A watermelon of 1 kg contains 93% water. After being left under the sun for a while, its water content went down to 90%. What is the weight of the watermelon now?

A fruit seller arranges her oranges to form a pyramid. At each level, the oranges form an equilateral triangle, except at the top level where there is only one orange. The orange pyramid has 10 levels. How many oranges are there altogether?

Find the smallest positive integer such that the product of 420 and this integer is equal to a square integer.

There are two numbers, namely 2003 and 3002. Fevi chose one of these and multiplied it by 4321. Adi chose the other number and multiplied it by 1234. The sum of the two products is even. Which number did Fevi choose?

Find the $7777777$th digit after the decimal point of the decimal equivalent of $\frac17$.

Essa and Wira bought a pen each. After paying, Essa's money is $\frac56$ of his original amount, while Wira's money is $\frac35$ of his original amount. What was the ratio of their money before they bought the pens?

Put each of the numbers 2, 3, 6, 8, and 9 in the boxes so that the product is the largest.

Use all digits 2, 3, 4, 5, 7, and 8 exactly once to get two numbers $P$ and $Q$. Both $P$ and $Q$ contain three digits and $P-Q$ is positive. Find the smallest value of $P-Q$.

In the figure, the diameter of the smaller circles equals the radius of the larger circle. The area of the larger circle is $\pi$ square units. What is the length of $ABCDEFA$?

We have 40 unit cubes with side length 1 cm. Using all cubes we build a complete rectangular solid box. If the perimeter of its base is 14 cm long, what is the height of the box?

What is $x^\circ+y^\circ$?

The length of a rectangle is increased by 10%, while its width is increased by 20%. By how many percent is the area of the rectangle enlarged?