IMSO 2016 — Mathematics — Short Answer

Alex and Benito can make 880 pies in 8 hours working together. If Alex can make 10 more pies in one hour than Benito, how many pies can Alex make in one hour?

Divide 108 students into four groups such that two times the number of students in Group One is
(i) half of the number of students in Group Two.
(ii) 2 less than the number of students in Group Three.
(iii) 2 more than the number of students in Group Four.
Find the number of students in Group One.

In the diagram below, $C$, $D$ and $E$ are points on line $AB$. Given that $AB=9.2$ cm and $CE=4.7$ cm, find the sum of the lengths of all ten line segments determined by these five points.

Four cubes with edge length of 1 m are to be cut into smaller cubes, each with edge length of 4 cm. If all of these smaller cubes are placed right next to each other to form a line, find the length, in m, of the line.

Michael wants to tie 20 ropes together, each measuring 50 cm. Given that 5 cm of each rope’s end is tied to 5 cm of another rope’s end resulting to a 5 cm knot. What is the length, in cm, of the new rope?

Class A and Class B have the same number of students.
- The number of students in Class A who took part in a mathematics competition is one third of the students in Class B who did not take part.
- The number of students in Class B who took part in a mathematics competition is one fifth of the students in Class A who did not take part.
Find the ratio of the number of students who did not take part in the competition in Class A to those who also did not take part in Class B.

What number can be added to both 170 and 30 so that the sums are in the ratio $3:1$?

Two different shirts were sold at the same price at a shop. While one shirt made a profit of 30%, the shop had incurred a 30% loss for the other one. Did the shop record a profit or loss from these two transactions, and by how many %?

A television show has 483 episodes. If the show starts on a Saturday and broadcasts everyday with three episodes each day, on what day will the last episode be broadcasted?

Find the area, in cm², of the isosceles trapezoid $ABCD$, such that $AD=16$ cm, $BC=8$ cm, $AB=CD$ and $\angle A=\angle D=45^\circ$.

On her 40th birthday, Mrs. Sharma makes gifts to her two sons whose ages are both prime numbers. She gives to one son some number of dollars that is equal to the square of his age and to the other son some number of dollars that is equal to his age. If she gives 300 dollars in total, what is the sum of the ages of Mrs. Sharma’s two sons?

The numbers 5, 6, 7, 8, 9, 10 are to be filled in the squares so that the sum of the numbers in the row is equal to the sum of the numbers in the column. How many different possible values of $A$ are there?

A farmer harvested 2016 apples. He wishes to pack them in as many boxes as possible, not necessarily packing all of the apples, with each box containing a whole number of apples. The second box must be 10 more than the first, the third box must be 10 more than the second and so on. What is the smallest number of apples that are left unpacked?

Three containers A, B, and C contain a total of 48 apples. First, 6 apples are taken from A and are put into B. Second, 9 apples are taken from B and are put into C. Now, each container has the same number of apples. What is the original number of apples in container A?

The square $PQRS$ has an area of 400 cm². The points $X$ and $Y$ divide $PQ$ into 3 parts.

If the perimeter of triangle $XYZ$ is $\frac14$ of the perimeter of triangle $SRZ$, find the area, in cm², of triangle $XYZ$.

In the diagram below, lines $AB$ and $DE$ meet at point $O$ and $\angle COF=88^\circ$. Given that $OE$ and $OB$ are angle bisectors of $\angle AOF$ and $\angle COF$, respectively. Find the angle measure, in degrees, of $\angle COD$.

If $\overline{243a688}\div\overline{31b2}=764$, find the value for $a\times b$.

In the diagram below, find the area, in cm², of the cross formed by using five identical squares, given that the length of $AC$ is 12 cm.

Three positive two-digit integers and 63 are arranged in a $2\times2$ table, where the product of the two numbers in each row or column is calculated. When all four products are added together, the result is 2016. What is the largest possible value of $A$?

Ali has 5 consecutive numbers while Ben has 7 consecutive numbers. If the Ali’s second number is 5, and the sum of Ali’s and Ben’s numbers is 128, what is the largest of Ben’s number?