Week-3 Selective Maths

The length of each side of square A is increased by 100 percent to make square B.

The length of each side of square B is increased by 50 percent to make square C.

By what percent is the area of square C greater than the sum of the areas of squares A and B?

A 75 percent
B 80 percent
C 100 percent
D 150 percent
E 180 percent

Pumping alone at a constant rate, an inlet pipe of type S can completely fill a water tank in 36 hours.

Pumping alone at a constant rate, an inlet pipe of type L can fill the same water tank in 18 hours.

If the same number of each type of inlet pipes are used to fill the tank in 2 hours, how many type S inlet pipes were used?

A 3
B 4
C 6
D 9
E 12

The red light bulb blinks regularly 5 times a minute.

The yellow light bulb blinks regularly 4 times a minute.

If both light bulbs blink simultaneously, after how many seconds will they blink together again?

A 20 seconds
B 24 seconds
C 30 seconds
D 60 seconds
E 300 seconds

A certain fruit vendor can purchase each basket of fruits for (x + 15) dollars.

The vendor can sell each basket of fruit for x(9 – x) dollars.

For what values of x can the fruit vendor make a profit?

A 6 < x < 9
B 6 < x < 7
C 5 < x < 7
D 5 < x < 6
E 3 < x < 5

Each diagonal of rectangle R has a length of 13 metres.

If the perimeter of rectangle R is 34 metres, what is the area of rectangle R?

A 69 square metres
B 60 square metres
C 46 square metres
D 34 square metres
E 30 square metres

The average (arithmetic mean) height of all the trees in park reservation M is 2 120 metres.

The average height of all the trees in park reservation N is 1 940 metres.

If park reservation M has twice as many trees as park reservation N, what is the average height of all the trees in park reservation M and park reservation N combine?

A 2 480 metres
B 2 120 metres
C 2 060 metres
D 1 940 metres
E 1 860 metres

-5 < u < 8 and -7 < v < 4

Which of the following gives all the possible values of uv?

A -56 < uv < 24
B -56 < uv < 35
C -40 < uv < 28
D -35 < uv < 32
E -20 < uv < 56

To meet the order deadline, Shelly needs to mine 90 crates of minerals each day.

However, Shelly was only able to mine 75 crates per day at first, leaving 690 crates of minerals to be mine during the last 6 days before the deadline.

How many days in all does Shelly have to complete the order deadline on time?

A 15
B 16
C 25
D 40
E 46

Five pipes are operating at the same constant rate.

Four of these pipes, operating simultaneously, take 30 minutes to fill a swimming pool.

How many fewer minutes does it take all five pipes, operating simultaneously, to fill the same swimming pool?

A 3
B 8
C 6
D 16
E 24

Each of the three boxes contains black and white marbles only.

There are 10 more black marbles than white marbles in the first box.

There are 4 more black marbles than white marbles in the second box.

If the average (arithmetic mean) number of white marbles in the three boxes is 3 more than the average number of black marbles in the three boxes, then the number of white marbles in the third box is how many more than the number of black marbles in the third box?

A 9
B 14
C 17
D 23
E 25

Jack, working alone, can paint a room in 3 hours.

Sonny, working alone, can paint an identical room in 6 hours.

Denver, working alone, can paint such room in x hours.

Working together, Jack, Sonny, and Denver can paint 4 such rooms in 3 hours.

How many hours can Denver paint such room working alone?

A 1.2 hours
B 2 hours
C 3.1 hours
D 4 hours
E 4.5 hours

All of the 540 managers in a certain company have either Master’s degree or a Doctorate degree.

There are twice as many female managers as male managers in the company, and three times as many managers with Master’s degrees as managers with Doctorate degrees.

If a third of the managers with a Doctorate degree are males, how many managers with a Master’s degree are female?

A 90
B 135
C 180
D 270
E 405

The average (arithmetic mean) of x and y is 10.

The average of y and z is 4.

The average of x and z is 10.

What is the average of x, y, and z?

A 3
B 5
C 6
D 7
E 8

Cylinder A contains exactly 150 litres of water.

William pours n litres of water from cylinder A into a previously empty cylinder B, filling cylinder B to 25 percent of its capacity.

He then pours the remainder of the water in cylinder A into a previously empty cylinder C, such that cylinder C is now 75 percent full.

Cylinder B is twice as tall as cylinder C, and the diameter of the base of cylinder B is 50 percent greater than the diameter of the base of cylinder C.

How many more litres were poured into cylinder B than were poured into cylinder C?

A 15 litres
B 30 litres
C 45 litres
D 60 litres
E 90 litres

Every marble in a box is either coloured red, blue, or green.

The ratio of the number of red marbles to the number of blue marbles to the number of green marbles in the box is 4 to 8 to 49.

The number of green marbles in the box is equal to y more than the total number of red marbles and blue marbles in the box, where y is a positive integer.

Which of the following could be the value of y?

A 84
B 106
C 148
D 164
E 305

Michael is 8 years older than Donald today.

The sum of the ages of Michael and Donald today is 16.

What will be Donald’s age 16 years from now?

A 4 years old
B 8 years old
C 12 years old
D 20 years old
E 24 years old