Linear Equations in One and Two Variable Quiz

In a set of five consecutive integers, the sum of the first three numbers is equal to twice the sum of the last two numbers plus 8. Find the sum of all five numbers.

1. 85
2. -80
3. -85
4. 80

Answer: (c) -85

Five-sixths of a number is more than two-thirds of the number by 6. Find the number.

1. 36
2. 24
3. -24
4. -36

Answer: (a) 36

There are some rose flowers in a garden and some bees hovering around. If two bees land on each flower, one flower is left. If one bee lands on each flower, then three bees are left. Find the number of bees in the garden.

1. 5
2. 4
3. 8
4. 2

Answer: (c) 8

Sofia plays a quiz game in which a right answer scores 10 points, but a wrong answer scores −5 points. Therefore, if r = number of right answers and w = number of wrong answers, her score is S. If Sofia answered 20 questions and her score was −10, how many questions did she answer correctly?

1. 10
2. 5
3. 8
4. 6

Answer: (d) 6

The tens place digit of a two-digit number is three times the ones place digit. The number obtained by reversing the order of the digits is 54 more than the original number. Find the original number. (Taking positive digits)

1. 93
2. 39
3. 45
4. 54

Answer: (a) 93

A line is divided into three parts. The first part is seven - thirdths the length of the second part, the third part is 2 cm shorter than the first part, and 2 cm shorter than the square of the second part. Find the length of the line.

1. 104/9 cm
2. 56/4 cm
3. 202/9 cm
4. 101/9 cm

Answer: (d) 101/9 cm

John has a certain number of puzzles with him. He solves a fixed number of puzzles every hour. After solving puzzles for 4 hours, he is left with 720 puzzles. If he had solved for 7 hours, he would have 570 puzzles left. After solving for 12 hours, he has 270 puzzles remaining. How many puzzles does he solve per hour?

1. 70
2. 50
3. 20
4. 100

Answer: (b) 50

The sum of 5/6 of A's salary and 3/4 of B's salary is $1800. Additionally, the difference between 2.5 times A's salary and 1.5 times B's salary is $600. If A’s salary is less than that of B, what is the salary of B?

1. $1,820
2. $1,080
3. $1,008
4. $1,280

Answer: (b) $1,080

A square carpet, when placed in a rectangular room, leaves a strip 1.5 metres wide uncarpeted along one pair of opposite walls and a strip 2.5 metres wide along the other two walls. If the area uncarpeted is 72 square metre, what is the length of the carpet?

1. 8.14 metres
2. 1.94 metres
3. 7.12 metres
4. 7.9 metres

Answer: (c) 7.12 metres

Two trains running at 45 km per hour and 54 km per hour cross each other in 12 seconds when they run in opposite directions. When they run in the same direction, a person in the faster train observes that he crosses the other train in 32 seconds. Find the length of the faster trains.

1. 250 m
2. 330 m
3. 80 m
4. 120 m

Answer: (a) 250 m