ITMC 2018 Grade 4 National Preliminary set01

Let $a$ be 2,561 more than 2,018, and let $b$ be 2,018 less than 2,561. Find $a+b$.

The printed year 2018 controls catalogue identity; the supplied filename contains a different year.

Printed positive marks are preserved per question. The source uses different blank-answer and incorrect-answer rules by section, including an optional bonus penalty; the import does not reproduce that complete official scoring scheme.

Given $1+22+333+4444+55555=\square+5$, find $\square\div71$.

Given $\frac1{17}+\frac3{17}+\frac5{17}+\frac ab=1$, where $a,b$ are positive integers and $a/b$ is in simplest form, find $a+b$.

$A$ and $B$ are two different points on a piece of paper. How many straight lines can be drawn through both points?

How many of the seven shapes shown have at least one acute interior angle?

The square shown has side length 4 cm. Divide it into squares of side length 1 cm and shade four small squares. What is the ratio of the shaded area to the whole square?

In a certain year, 5 August is Sunday. What day of the week is 5 July in that year?

A train leaves a station at 11:40 and reaches its destination 75 minutes later. At what time does it arrive?

Tom has 670 dollars in his wallet: one 500-dollar note, one 100-dollar note, one 50-dollar note and one 20-dollar note. He uses one banknote to buy two bottles of water costing 7 dollars each. What is the greatest possible change he can receive?

The table gives the number of pupils in each grade of a primary school. Grades 1, 2, 3, 4, 5 and 6 have respectively 245, 253, 248, ?, 251 and 249 pupils; the total is 1,498. How many pupils are in Grade 4?

A bag contains 23 white, 19 green, 29 blue, 17 yellow and 28 red buttons. A girl picks one button at random. Which colour has the greatest chance of being selected?

In a survey of 337 pupils, each pupil chooses one favourite sport or no sport. The counts are: football 109, basketball 78, volleyball 51, swimming 35, tennis 14, table tennis 39. How many pupils choose no sport?

Given $(1+\frac13)(1+\frac14)(1+\frac15)(1+\frac16)=\frac ab$, where $a,b$ are positive integers and $a/b$ is in simplest form, find $a+b$.

How many digits are in the quotient when 111222333444555666777888999 is divided by 111?

Let $N=9+99+999+9999+99999$. What is the sum of the digits of $N$?

How many quadrilaterals are in the figure?

A large square consists of sixteen small squares. Remove four small squares so that the remaining polygon has as many sides as possible. What is that greatest number of sides?

Square sheets $A$ and $B$ have side lengths 6 inches and 9 inches respectively. Each is divided into nine equal small squares. Four small squares from sheet $B$ are placed on a table. How many small squares from sheet $A$ can cover the same area exactly?

A waiter counts pairs of chopsticks. Grouping them in threes leaves one pair; grouping in fours leaves two pairs; grouping in fives leaves four pairs. There are at most 40 pairs. How many individual chopsticks are there?

A girl folds paper stars and puts 2 stars in bag 1, 4 in bag 2, 6 in bag 3, 8 in bag 4, and so on. If she folds 90 stars, what is the smallest number of bags she needs?