SASMO 2014 Primary 3 (Grade 3) Contest

Jane is 9 years old and John is 5 years old. How old will John be when Jane is 15 years old?

A textbook is opened at random. To what pages is it opened if the product of the facing pages is 110?

Find the number $B$ such that the following statement is true:

$$8\times B=3\times9+5\times9.$$

It is given that $a\otimes b=a\times b+a-b$. For example, $2\otimes3=2\times3+2-3=5$. Find the value of $4\otimes3-3\otimes4$.

Jane has a rope of length 23 cm. She wants to cut the rope so that she can form the biggest possible square, where the length of each side, in cm, is a whole number. What is the length of the rope that she must cut to form the square?

Find the missing term in the following sequence:

$$1,\ 2,\ 6,\ 24,\ \underline{\hspace{1cm}},\ 720.$$

On National Day, 39 soldiers lined up in a straight row on opposite sides of Stadium Street to welcome Prime Minister Lee. A soldier stands on each end of Stadium Street. The distance between two adjacent soldiers on either side was 20 m. The soldiers on one side were arranged such that each soldier filled the gap between two other soldiers on the opposite side. How long was Stadium Street?

A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Sharon has enough money to buy only 11 sweets. What is the biggest number of sweets that she can get from the shop?

At a workshop, there are 10 participants. Each of them shakes hands once with every other participant. How many handshakes are there?

Ali uses identical square tiles to make the following figures. If he continues using the same pattern, how many tiles will there be in the 15th figure?

What is the least number of cuts required to cut 16 identical sausages so that they can be shared equally among 24 people?

A vending machine accepts 10¢ coins, 20¢ coins, 50¢ coins and \$1 coins only. Ivy wants to buy a can of drinks that costs \$1.60. She has eight 10¢ coins, three 20¢ coins, two 50¢ coins and one \$1 coin. If she wants to get rid of as many coins as possible, what is the combination of coins that she should put inside the vending machine?

The total cost of a pen and a pencil is \$2.90. The pen costs 60¢ more than the pencil. How much does the pen cost?

If the three-digit number $3N3$ is divided by 9, the remainder is 1. Find $N$.

Charles has 16 marbles. He divides them into 4 piles so that each pile has a different number of marbles. Find the smallest possible number of marbles in the biggest pile.

In the following alphametic, all the different letters stand for different digits. Find the three-digit sum $SEE$.

$$\begin{array}{rr}&AS\\+&A\\\hline&SEE\end{array}$$

Find the total number of triangles in the diagram.

A teacher has a bag of sweets to treat her class. If she gave 5 sweets to each student, then she would have 40 sweets left. If she gave 7 sweets to each student, then she would have 6 sweets left. How many students and how many sweets are there?

What are the last 2 digits of the sum

$$1+11+111+\cdots+\underbrace{111\ldots111}_{50\text{ digits}}?$$

Alvin tells the truth on Monday, Tuesday, Wednesday and Thursday. He lies on all other days. Doris tells the truth on Monday, Friday, Saturday and Sunday. She lies on all other days. One day they both said, “Yesterday I lied.” When was that “one day”?