SASMO 2014 Primary 5 (Grade 5) Contest

If $n$ is a whole number, for what values of $n$ is $\frac{24}{n}$ also a whole number?

A textbook is opened at random. To what pages is it opened if the product of the facing pages is 600?

The diagram shows a quadrant $OAB$ of a circle with centre $O$. $OPQR$ is a rectangle. Given that $PR=7$ cm, find the length of $OA$.

Find an even number between 300 and 400 that is divisible by 5 and by 7.

A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Navin has enough money to buy only 29 sweets. What is the biggest number of sweets that he can get from the shop?

Find the next term of the following sequence: $2,3,4,10,38,\ldots$

The percentage passes in an exam for two classes are 80% and 60%. The numbers of students in the two classes are 20 and 30 respectively. Find the overall percentage pass for the two classes.

A clock takes 9 seconds to make 4 chimes. Assuming that the rate of chiming is constant and the duration of each chime is negligible, how long does the clock take to make 3 chimes?

Find the value of $(1-\frac12)(1-\frac13)(1-\frac14)\cdots(1-\frac1{2014})$.

A frog fell into a drain that was 50 cm deep. After one hour, it gathered enough energy to make a jump of 6 cm but it then slid down 4 cm. If it continued in this manner after every hour, how many hours would it take to get out of the drain?

A farmer's chickens produced 4028 eggs one day. Was he able to pack all the eggs in full cartons of one dozen eggs each?

A farmer counted 40 heads and 124 legs among his sheep and ducks. How many sheep and how many ducks does he have?

Jaime puts some blue and red cubes in a box. The ratio of blue cubes to red cubes is $2:1$. She adds 12 more red cubes and the ratio becomes $4:5$. How many blue cubes are there?

The diagram shows a rectangle with its two diagonals. What percentage of the rectangle is shaded?

Given that $a\times b=2014$, where $a$ and $b$ are whole numbers and $a<b$, how many possible pairs $(a,b)$ are there?

Amy had 3 times as much money as Betty. After they had spent 60 dollars each, Amy had 4 times as much money as Betty. How much money did Amy have at first?

Billy uses identical square tiles to make the figures shown. If he continues the same pattern, in which figure will there be 6044 tiles?

What is the least number of cuts required to cut 12 identical sausages so that they can be shared equally among 20 people?

In the alphametic shown, different letters stand for different digits. Find the two-digit sum $PI$ when $IS+IS+IS+IS=PI$.

A teacher has a bag of sweets for her class. If she gave 6 sweets to each student, she would have 5 sweets left. If she gave 7 sweets to each student, she would be 30 sweets short. How many students and how many sweets are there?