Free Printable Algebra and Word ProblemGAT25to 60s Worksheet Extraction

1.

If $\tfrac{2}{x}+\tfrac{7}{y}=\tfrac{3}{10}$ , and $xy=30$ , then find $6y+21x$ .

a)

12

b)

30

c)

27

d)

9

2.

Find $x$ if $(x-4)^{88}=1$ .

a)

8

b)

5

c)

4

d)

-4

3.

A man who travels between two cities at a speed of 80 km/h, he stopped after three hours and the remaining distance was 60 km, then how far are the two cities?

a)

2400

b)

210

c)

300

d)

270

4.

A car dealership had a group of cars at the beginning of the month in his car agency. He sold 15 cars and then bought 5 cars, finally the number of cars in his shop was 38 cars, how many cars were at the beginning of the month?

a)

48 cars

b)

18 cars

c)

38 cars

d)

58 cars

5.

If there are 4 water taps, the first fills the basin in an hour, the second in two hours, the third in three hours and the fourth in four hours. If the four taps were open at the same time, approximately how many hours will the basin be filled?

a)

1 hour

b)

15 minutes

c)

Half an hour

d)

45 minutes

6.

Find $y$ if $x^5\times x^4\times x^3\times x^2=(x^7)^y$ .

a)

2

b)

4

c)

6

d)

5

7.

If $x=-1$ find $x^5+x^4-x^3+x^2+9x+9$ .

a)

2

b)

0

c)

18

d)

1

8.

Ali has SAR 300, and saves 10 SAR per day; Khalid has 100 SAR, and saves 30 SAR per day. When will they have the same amount of money?

a)

After 10 days

b)

After 30 days

c)

After 20 days

d)

never

9.

$64^{(x-3)}=8^{(2y+6)}$ . Find $x$ in terms of $y$ .

a)

$x=y-6$

b)

$x=y+6$

c)

$x=\tfrac{y}{2}$

d)

$x=6-y$

10.

If $10^{(x-5)}=1000$ , then find $x$ .

a)

5

b)

10

c)

8

d)

1

11.

If $x+y=8$ and $xy=20$ , then find $x^2+y^2$ .

a)

44

b)

24

c)

104

d)

84

12.

If $x^2=y^2+36$ and $x-y=9$ , then find $x+y$ .

a)

12

b)

4

c)

2

d)

3

13.

If $y=4^x$ then find $4^{(x+1)}$ .

a)

$4y+1$

b)

$4y$

c)

$y+1$

d)

$y^2$

14.

If Ahmed's salary is twice of Salman's salary, and Salman's salary is more than Khalid's salary by 800 riyals, If Ahmed's salary is 6000 riyals, what is Khalid's salary?

a)

2200

b)

3000

c)

5200

d)

3800

15.

Find $x+5$ if $\dfrac{x+2}{3x^2+9}=0$ .

a)

-2

b)

7

c)

-7

d)

3

16.

The monthly production of a factory is 50 tons and it increases in Ramadan. If its annual production is 670 tons, how much did the factory produce in Ramadan?

a)

360

b)

120

c)

230

d)

80

17.

Find $y$ if $x$ is an integer number and $y=7x+4$ .

a)

48

b)

52

c)

42

d)

46

18.

In the morning, Hind gave her sister half of her money, and she took 8 riyals from her mother, at the end of the day she had 50 riyals. How much was with her?

a)

42

b)

50

c)

48

d)

84

19.

The first number is thrice the second number, and their sum is 36. What is the greatest number?

a)

9

b)

8

c)

27

d)

24

20.

Khaled wants to buy a car that costs 170,000 riyals. If he paid 50,000 riyals and wanted to pay the rest as a monthly instalment, then he would pay 1500 riyals monthly, so how many months does he need to pay the whole cost of the car?

a)

20

b)

70

c)

76

d)

80

21.

Find $x$ given $|2x+4|=16$ .

a)

$\pm 6$

b)

6

c)

6, -10

d)

6, 10

22.

If the sum of the square of two numbers is 400, and one of these numbers is 12 then what is the other number?

a)

12

b)

15

c)

14

d)

16

23.

One third a number is $\tfrac{8}{12}$ ; what is the number?

a)

2

b)

4

c)

6

d)

8

24.

A man has 2000 riyals, if he spent $\tfrac{1}{8}$ his money on his car fuel, and he gave 3 times the amount of the fuel to his wife, then how much money remains with him?

a)

250

b)

750

c)

1000

d)

1250

25.

5 times a number plus 4 equals 24, so what is this number?

a)

4

b)

6

c)

12

d)

7

26.

If $x+y=\tfrac{z}{2}$ , $x-y=0$ , then which statement is true?

a)

$z=2xy$

b)

$2z=2y$

c)

$z=4y$

d)

$z=4y-2x$

27.

Suleiman's salary is 700 riyals less than Khaled's, and Khaled's salary is more than Hamad's by 500 riyals, if Hamad's salary is 2800 riyals, then how much is Suleiman's salary?

a)

3300

b)

3000

c)

2600

d)

2400

28.

Lamia gets 3200 riyals for every 8 working hours a week, and for every additional working hour she will be paid an amount of money equivalent to $1\tfrac{1}{2}$ working hour. If she wants to increase her income this week to be 4400 riyals, so how many hours should she work?

a)

10

b)

50

c)

12

d)

14

29.

Lamia gets 3200 riyals for every 8 working hours in 5 days a week, and for every additional working hour she will be paid an amount of money equivalent to $1\tfrac{1}{2}$ working hour. If she wants to increase her income this week to be 4400 riyals, so how many hours should she work?

a)

120

b)

50

c)

40

d)

10

30.

Find the value of $x$ if $x^3+x^2-5x=0$ .

a)

1

b)

0

c)

-1

d)

3

31.

Salma bought 12 pens for 36 riyals and she sold every three for 10 riyals, so what will be her profit when she sells 66 pens?

a)

20

b)

23

c)

22

d)

25

32.

Find x given $25 = 5^x$ .

a)

5

b)

4

c)

2

d)

1

33.

Given $\frac{3}{4}x = \frac{4}{3}y$ , find the value of $\frac{1}{x} + \frac{1}{y}$ .

a)

$\frac{9}{16}$

b)

1

c)

$\frac{16}{9}$

d)

$\frac{1}{2}$

34.

Find a possible value for x such that $x^2 + 10 = -x + 10$ .

a)

5

b)

-5

c)

1

d)

-1

35.

If Ahmad bought a ruler and a notebook, the price of the notebook was twice the price of the ruler, and the sum of what he paid was 93 riyals, find the price of the notebook.

a)

16

b)

31

c)

66

d)

62

36.

If $3x = -39$ , then find $-5x$ .

a)

65

b)

-65

c)

-56

d)

56

37.

There are 42 chairs in a meeting room, divided into 3 rows; the chairs in each row is less than the next row by one chair, how many chairs are in the last row?

a)

11

b)

13

c)

15

d)

14

38.

Given $\frac{x}{y} = \frac{1}{10}$ , find $\frac{100x + 100y}{10x}$ .

a)

110

b)

110

c)

100

d)

100

39.

If $\frac{1}{2}x + \frac{1}{4}y = 32$ , then find $2x + y$ .

a)

32

b)

164

c)

128

d)

64

40.

If a number is multiplied by itself, and multiplied by its square, and then 3 is subtracted from it, then what is the equation that represents this expression?

a)

$x^2 - 3$

b)

$x^4 - 3$

c)

$x^2 - 3x$

d)

$3 - x^4$

41.

Two numbers; their difference is 10 and their sum is 74, what is the least number?

a)

42

b)

32

c)

84

d)

36

42.

If one third of the school students like mathematics and 400 students do not like mathematics, then how many students does the school have?

a)

600

b)

800

c)

200

d)

1000

43.

If we have 400 liters of milk, and we want to fill the milk in cans as follows: 100 liters in cans of half a liter capacity, 200 liters in cans of 2 liters capacity, and the rest in cans of one liter capacity, so how many cans do we need?

a)

100

b)

200

c)

400

d)

600

44.

A package of 7 pens and 3 bags or a package of 4 bags, but Ali wants to buy pens only, so what is the largest number of pens can he buy if it is allowed to replace bags by pens?

a)

21

b)

35

c)

27

d)

28

45.

If half of the students left the class, later one third of the students left the class, and finally four students remained in the class, so how many students were in the class?

a)

24

b)

22

c)

23

d)

20

46.

Three consecutive integers; find the difference between squaring the middle number and multiplying the first by the third?

a)

1

b)

0

c)

2

d)

5

47.

A commercial building consists of 10 floors, and in each floor the number of offices was one more than the number of offices in the previous floor. If the number of the offices on the last floor is twenty offices, then how many offices are on the first floor?

a)

10

b)

11

c)

12

d)

15

48.

A package of 7 pens and 3 bags or a package of 4 bags, but Ali wants to buy pens and one bag only, so what is the largest number of pens can he buy if it is allowed to replace bags by pens?

a)

21

b)

35

c)

27

d)

28

49.

Solve for y: $-9 - y = -3$ .

a)

6

b)

-6

c)

-12

d)

12

50.

If the sum of two numbers is 40, and the first number is two third the other number, then what is difference between the two numbers?

a)

12

b)

8

c)

16

d)

24

51.

The length of the lion's tail is half the length of its body, and the length of its body is three times the length of its head. If the length of a lion's head is 40 cm, how tall is the whole lion?

a)

150

b)

160

c)

190

d)

220

52.

A computer worth 4000, and its price is reduced by a fixed value annually. If a person decides to buy it after 3 years, where its price after the reduction will be 2500, how much is the reduction per year?

a)

500

b)

750

c)

900

d)

950

53.

A man bought a number of watches for 18,000 riyals, and his profit was 4,500 riyals, if the profit of each watch was 250 riyals, then how many watches did he buy?

a)

12

b)

17

c)

18

d)

20

54.

There are 5 houses and each house has 5 cages, and each cage contains 5 birds, and each bird eats 5 grains of wheat. How many grains did all the birds eat?

a)

225

b)

400

c)

520

d)

625

55.

There were 25 sheep on the farm at a price of 1,200 each, and 20 camels at a price of 4,200 each, then the farmer sold all the animals. How much is the amount of zakat of the total amount of sale, if you know that the amount of zakat is a quarter of a tenth?

a)

2850

b)

2920

c)

3100

d)

3200

56.

If $x + y = 28$ , and $x - y = 14$ , then find $x \cdot y$ .

a)

145

b)

146

c)

147

d)

148

57.

If the difference between two numbers is 15, and the least number is x, where x does not equal to zero, then find the greatest number.

a)

$15 + x$

b)

$15 - x$

c)

$15x$

d)

$\frac{x}{15}$

58.

A car which price is 90,000 riyals, if a third of its price decreased in the first year, then a quarter of its price decreased in the second year after the first reduction, then find the price of the car after the second year?

a)

60,000

b)

50,000

c)

35,000

d)

45,000

59.

If $\frac{1}{2}x + \frac{1}{5}x + \frac{1}{10}x = 4$ , then find x.

a)

5

b)

6

c)

12

d)

10

60.

A merchant buys two toys at a price of 2.5 riyal, and he sells each toy at a price of 2.5 riyal, so how many toys should he sell so that his profit is 25 riyals?

a)

10

b)

20

c)

15

d)

25

61.

Ahmad runs a jog, so if he runs a distance of 3.4 km on Saturday, and every day he increases 0.4 km, then what is the distance that he will run on Friday?

a)

6

b)

5.8

c)

7.2

d)

6.4

62.

If $x + y = 4$ , $x - y = 2$ , then find $x^4 - y^4$ .

a)

36

b)

60

c)

80

d)

100

63.

What is the number that if divided by 3 and the quotient is added to 5 the sum becomes 14?

a)

21

b)

28

c)

18

d)

27

64.

Ahmad has 15 riyals and he wants to buy two books and a set of pens. If the price of the book is 6 riyals and the price of the pen is 0.75 riyals, then how many pens can he buy?

a)

4

b)

5

c)

7

d)

3

65.

Find x: $\frac{5}{9} + \frac{9}{5} = \frac{9}{x + 1} + \frac{x + 1}{9}$

a)

9

b)

4

c)

5

d)

8

66.

If the sum of three consecutive numbers is twice the greatest number, then what is the greatest number?

a)

6

b)

8

c)

1

d)

3

67.

Find x: $x + (x + 1) + (x + 2) = (x + 1)^2$

a)

1

b)

0

c)

3

d)

2

68.

Find the circumference of the circle.

a)

31.4

b)

314

c)

62.8

d)

6.28

69.

Find the area of shaded region.

a)

48

b)

12

c)

56

d)

64

70.

Find the area of the shaded region if the diameter of the circle is $20$ .

a)

$100-50\pi$

b)

$50\pi$

c)

$50\left(\frac{\pi}{2}-1\right)$

d)

$100\left(\frac{\pi}{2}-1\right)$

71.

Find the area of the rectangle if $AH = BH = 5$ and $CD = 8$ .

a)

24

b)

45

c)

12

d)

20

72.

Find the perimeter of the parallelogram if $\triangle ACD$ is an equilateral triangle.

a)

28

b)

14

c)

20

d)

7.5

73.

Find the area of the shaded area in the rectangle.

a)

42

b)

45

c)

56

d)

48

74.

If $BF$ bisects $AE$ and $CE$ , what is the ratio of $FB$ to $CA$ ?

a)

2 : 1

b)

2 : 3

c)

1 : 2

d)

3 : 2

75.

Find the measure of $\angle UMT$ if the sum of $\angle UMT$ and $\angle UMO$ is 130.

a)

135°

b)

15°

c)

75°

d)

35°

76.

Find $x$ .

a)

72°

b)

62°

c)

78°

d)

68°

77.

Let $CE = 4ED$ , and $AECB$ is a parallelogram; what is the area of the whole shape?

a)

48

b)

54

c)

12

d)

60

78.

Find the perimeter of the shape.

a)

32

b)

38

c)

24

d)

28

79.

Find the measure of the angle "m" if "m" is the center of the circle.

a)

80°

b)

100°

c)

50°

d)

90°

80.

Find $x$ .

a)

99

b)

90

c)

100

d)

150

81.

Find $x$ .

a)

180°

b)

270°

c)

220°

d)

250°

82.

Find $x$ .

a)

55

b)

60

c)

65

d)

70

83.

Find $x$ .

a)

5

b)

4

c)

3

d)

2

84.

Find $m\,\angle y^{\circ}$ .

a)

70°

b)

110°

c)

50°

d)

40°

85.

Find $x$ .

a)

130°

b)

140°

c)

110°

d)

120°

86.

Find the area of the triangle if $AB = 4$ .

a)

8

b)

32

c)

16

d)

48

87.

Find the area of the shaded region.

a)

10.57

b)

12

c)

10.75

d)

20

88.

Find the area of the rectangle if $AB = 4$ , $DB = 2DC$ .

a)

8

b)

32

c)

16

d)

48

89.

Find $x + y$ .

a)

110

b)

100

c)

60

d)

120

90.

Find the measure of angle C if the measure of angle A is $32^{\circ}$ .

a)

110

b)

58

c)

64

d)

48

91.

Find the area of the circle if the area of the triangle is 2.

a)

$2\pi$

b)

$6\pi$

c)

$4\pi$

d)

$8\pi$

92.

If the perimeter of $\triangle ABC = 24$ , find the perimeter of $\triangle ADC$ .

a)

33

b)

32

c)

24

d)

28

93.

If the area of the circle $K = 36\pi$ , find the area of the circle $J$ .

a)

$72\pi$

b)

$144\pi$

c)

$96\pi$

d)

$124\pi$

94.

Find $x$ .

a)

40

b)

90

c)

20

d)

70

95.

Which of the following angles are congruent angles?

a)

A & E

b)

B & F

c)

A & D

d)

D & E

96.

All the angles of triangle ABC are congruent and AC = $5$ , then find the perimeter of the rhombus.

a)

39

b)

23

c)

34

d)

20

97.

Find m ∠x°.

a)

120°

b)

80°

c)

60°

d)

30°

98.

If the area of the outer triangle is 80 cm², then find the area of the shaded triangle.

a)

10 cm²

b)

60 cm²

c)

20 cm²

d)

40 cm²

99.

Find x°.

a)

70°

b)

30°

c)

60°

d)

40°

100.

Find x.

a)

80°

b)

60°

c)

10°

d)

8°

101.

Find the measure of the smallest angle when the two adjacent angles shown are 4x and 2x.

a)

20°

b)

40°

c)

30°

d)

60°

102.

Find x.

a)

74°

b)

50°

c)

100°

d)

77°

103.

Find x.

a)

80°

b)

70°

c)

20°

d)

160°

104.

If the length of the square side is $4$ , find the area of the trapezoid.

a)

3

b)

6

c)

10

d)

15

105.

If the area of the outer square is 24 cm², then find the area of the shaded region.

a)

12 cm²

b)

15 cm²

c)

9 cm²

d)

6 cm²

106.

If the area of the outer square = 24, then find the area of the inner square.

a)

6

b)

8

c)

4

d)

12

107.

Find x.

a)

1

b)

4

c)

3

d)

9

108.

Find y in terms of x.

a)

y = 2x

b)

$y = 2x^2$

c)

y = 3x

d)

$y = 3x^2$

109.

If AB = $8$ and AC = $6$ , find the circumference of the circle.

a)

10π

b)

5π

c)

6π

d)

4π

110.

Find x.

a)

84°

b)

60°

c)

48°

d)

36°

111.

If the area of the shaded region is 18, find the value of x.

a)

60°

b)

30°

c)

45°

d)

35°

112.

If the area of the ABCD rectangle is 24 and the coordinates of point E are (5, 2), then find the coordinates of point B.

a)

(4, 8)

b)

(8, 4)

c)

(10, 4)

d)

(5, 6)

113.

Find x.

a)

80°

b)

50°

c)

70°

d)

20°

114.

Find x if y = 5x.

a)

60°

b)

66°

c)

70°

d)

30°

115.

The unshaded region is made of two quarters of two circles. If the area of the large circle is $64\pi$ , and the area of the small circle is $16\pi$ , then find the area of the shaded region.

a)

20π

b)

4(8 − 5π)

c)

96 − 20π

d)

4(6 − 5π)

116.

Find x (drawing is not to scale).

a)

93°

b)

87°

c)

70°

d)

90°

117.

Find circumference.

a)

13π

b)

7π

c)

5π

d)

10π

118.

Find y + x.

a)

300°

b)

120°

c)

180°

d)

240°

119.

Find x.

a)

120°

b)

130°

c)

100°

d)

110°

120.

Find x if the perimeter of the rectangle is 28.

a)

7

b)

6

c)

9

d)

5

121.

Find y in the rhombus.

a)

54

b)

52

c)

56

d)

58

122.

Find x in the regular hexagon.

a)

30°

b)

40°

c)

60°

d)

70°

123.

Find x.

a)

50°

b)

30°

c)

40°

d)

45°

124.

Find y + x.

a)

200°

b)

180°

c)

145°

d)

215°

125.

Find x.

a)

40

b)

70

c)

50

d)

80

126.

Find x + y.

a)

90

b)

110

c)

80

d)

60

127.

Find x.

a)

120°

b)

165°

c)

100°

d)

110°

128.

Find x.

a)

50

b)

90

c)

60

d)

130

129.

Find x.

a)

90°

b)

145°

c)

15°

d)

155°

130.

Find the measure of ∠x if x is the center of the circle.

a)

60°

b)

120°

c)

70°

d)

90°

131.

In the rectangle, if the number of squares shown is 10% of the rectangle area, how many squares represent the entire area of the rectangle?

a)

180

b)

100

c)

120

d)

60

132.

If the height of the triangle at point B = 6, and the length of the hypotenuse is 10, find the coordinates of point B.

a)

(8, 6)

b)

(7, 6)

c)

(5, 5)

d)

(6, 7)

133.

If a circle is divided by 4 straight lines that they did not intersect or they intersect only at the circumference, then how many regions was the circle divided to?

a)

5

b)

6

c)

4

d)

3

134.

The perimeter of a rectangle is 52 cm, if its length increased by 2 cm and its width decreased by 2 cm, then the new shape becomes a square. Find the area of the square.

a)

196

b)

169

c)

121

d)

144

135.

The dimensions of a rectangle are 300 cm and 100 cm. We want to divide it to small rectangles of 30 × 20 cm. How many small rectangles can we divide it to?

a)

50

b)

70

c)

40

d)

60

136.

Which of the following angles cannot be an angle of a convex polygon?

a)

170°

b)

160°

c)

150°

d)

190°

137.

The length of a rectangle is 54 and its width is 36, if we draw squares in it, what is the largest possible length of the square?

a)

12

b)

6

c)

9

d)

18

138.

If the time passes by 150°, how many minutes have passed?

a)

24

b)

25

c)

10

d)

15

139.

We have a rectangular room with dimensions 5 and 9, and it is furnished with a square carpet, the side of the carpet is 6, what is the area of the unfurnished part?

a)

9

b)

15

c)

14

d)

20

140.

A rectangle formed by five adjacent squares, its perimeter is 72. How long is the side of the square?

a)

4

b)

6

c)

8

d)

10

141.

Find the volume of a cube if the diagonal of one of its faces is 4.

a)

$\sqrt{2}$

b)

$8\sqrt{2}$

c)

$2\sqrt{2}$

d)

$16\sqrt{2}$

142.

If the area of a rectangle is 75 and its length is 3 times its width, then find its perimeter.

a)

40

b)

28

c)

32

d)

50

143.

Which of the following has the greatest area?

a)

Half circle with r = 5

b)

Rectangle with dimension 8 & 12

c)

Square with side equals 7

d)

Equilateral triangle with side equal 10

144.

If the length of two sides in a triangle is 6 cm and the measure of one angle equals 60°, then what is the length of the third side?

a)

6

b)

12

c)

3

d)

5

145.

If the perimeter of a rectangle is 36 cm, and its length is twice its width, then what is the area of the rectangle?

a)

72

b)

32

c)

67

d)

128

146.

Find the area of the circle whose equation is: $\tfrac{1}{2}x^2 + \tfrac{1}{2}y^2 = 6$ .

a)

$6\pi$

b)

$12\pi$

c)

$13\pi$

d)

$9\pi$

147.

Find the perimeter of a square that has a diagonal length equals to $7\sqrt{2}$ .

a)

49

b)

$49\sqrt{2}$

c)

28

d)

$28\sqrt{2}$

148.

A 34-meter wire formed in the shape of a 52-m² rectangle. What is the length of the rectangle?

a)

12

b)

13

c)

14

d)

15

149.

If the radius of a circle is equal to r, and the circle is divided into nine parts, find the area of two parts.

a)

$\tfrac{\pi r}{9}$

b)

$\tfrac{\pi r^2}{9}$

c)

$\tfrac{2\pi r}{9}$

d)

$\tfrac{2\pi r^2}{9}$

150.

A land length of 80 m and width of 40 m, and exactly 4 people can stand in each meter squared land, how many people can stand in the whole land?

a)

1000

b)

960

c)

12800

d)

560

Algebra and Word ProblemGAT25to 60s Worksheet Extraction

Total questions: 150

Worksheet time: 1hrs 15mins

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