Competitive Math for Grade 6 - Problems and Solutions

90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 = ?

a.845

b.945

c.1005

d.1025

e.1045

The sum of two numbers is 234560. If one number is more than the other number by ten thousand ten. Find the greatest number.

a.112275

b.122285

c.132285

d.117280

If a machine produces 150 items in one minute, how many would it produce in 10 seconds?

a.10

b.15

c.20

d.25

e.30

4(299)+3(299)+2(299)+298=

2889

2989

2991

2999

3009

Terry sells eggs by the dozen. After she gathers the eggs, she fills as many 1-dozen containers as she can. She keeps any leftover eggs for herself. Today her hens laid 79 eggs. How many eggs will she keep?

6

7

12

67

72

A ream of paper containing 500 sheets is 5 cm thick. Approximately how many sheets of this type of paper would there be in a stack 7.5cm high?

250

550

667

750

1250

Kelly and Jackie wanted to buy a netball ring. Kelly has saved $125 towards it and Jackie has saved $80. How much more do they need to save to buy a ring worth $280?

$75

$125

$85

$95

$105

The Jones High School Alumni Association ran a theatre party and sold tickets at $5.25 each . If receipts totaled $551.25, how many tickets were sold?

10

1050

10.5

3417

105

Each number below the top row is the product of the number to the right and the number to the left in therow immediately above it. What is the value of x?

8

4

7

5

6

The number 4567 is tripled. The ones digit (units digit) in the resulting number is

5

6

7

3

1

3 x 2006 = 2005 + 2007 + ? . Find the missing number.

2005

2006

2007

2008

2009

Which of the following gives quotient 25 and remainder 13 when divided by 27?

588

788

598

688

A bus runs at a speed of 48 km/h. In how many hours will it travel a distance of 432 km?

8 hrs.

9 hrs.

7 hrs.

6 hrs.

What is the least number to be added in the product of 23 and 32 to make result 1000?

364

464

264

546

Laila writes a list of numbers. Her first number is 4. Each number after the first is 7 more than the previous number. Which of the following numbers appears in Laila’s list?

45

46

47

48

49

The total number of the prime factor of 24 is

8

7

4

9

The number of common factors between 18 and 24 is

1

8

6

4

What is the prime factorization of 37800?

2 x 2 x 3 x 3 x 5 x 5 x 7 x 7

2 x 2 x 2 x 3 x 3 x 5 x 5 x 7

8 x 27 x 25 x 7

2 x 4 x 25 x 27 x 7

Which of the following is a not a factor of 316?

1

8

79

158

The sum of all the prime factors of m is 10. Find the number m.

15

20

28

63

The number of multiples of 3 which are less than 25 is

6

7

8

9

The multiple of 7 between 14 and 77 is

10

9

8

7

What is the sum of first 6 multiples of 16?

336

240

180

192

The sum of first four multiples of 7 is

60

68

70

74

The total numbers from 1 to 100 which are divisible by 7 are:

15

14

13

12

The difference between ten's digit and unit's digit of the sum of the first five multiples of 6 is

6

7

8

9

Which statement is true for 11 and 21?

Both are divisible numbers

Both are even numbers

Both are co-prime numbers

Both are multiples of 3

Unit digit of product of first ten prime numbers is

6

4

2

0

Highest two digits prime number is

93

97

91

99

Find the difference between the fourth multiple of 12 and third multiple of 25.

75

27

48

28

Divide the fifth multiple of 12 by the third multiple of 5.

4

12

10

8

Write all the factors of 48 in ascending order. Find the sum of fifth and ninth factor.

24

18

22

30

The sum of the first four multiples of 6, is

66

56

72

60

Which one of the following is the correct statement for the numbers 56 and 84?

Both the numbers are prime

Both the numbers are co-prime

Both the numbers are multiples of 14

Both the numbers are odd

4 is a common factor of16, 24? 96. What is the largest possible whole number which is less than 60, that can be placed at the place of (?)?

56

60

64

84

Which of the following 1-digit number has 4 factors?

6

5

7

9

20

Number x is a factor of 88. If number x is a two-digit number and the sum of the two digits is 8,what is number x?

80

62

44

17

19

Common multiple for the numbers 4, 8 and 10, within the first 10 multiples is

40

20

50

48

18

The numbers x, x + 2, x + 4 are all prime, so x is

3

2

11

17

Find the prime factors of 330.

a. 2 × 4 × 5 × 11

b. 2 × 3 × 7 × 13

c. 2 × 3 × 5 × 13

d. 2 × 3 × 5 × 11

Find the L.C.M. of 22 × 33 × 5 × 72, 23 × 32 × 52 × 74, 2 × 3 × 53 × 7 × 11

a. 23 × 33 × 53 × 74 ×11

b. 2 × 3 × 5 × 7 ×11

c. 23 × 33 × 53 × 73 ×11

d. 22 × 32 × 52 × 72 ×11

Find the L.C.M. of 16, 24, 36 and 54

a. 216

b. 432

c. 648

d. 972

Find the H.C.F. of 42, 63 and 140

a. 14

b. 7

c. 1

d. 3

Find the H.C.F. of 513, 1134 and 1215.

a. 9

b. 27

c. 81

d. 18

Reduce 391/667 to lowest terms.

a. 39/66

b. 29/31

c. 17/29

d. 29/17

What is the greatest number that exactly divides 105,1001 and 2436?

a. 3

b. 7

c. 11

d. 21

Three different containers contain different quantities of a mixture of milk and water, whose measurements are 403 litres, 434 litres and 465 litres. What biggest measure must be there to measure all the different quantities exactly?

a. 7 litres

b. 1 litres

c. 31 litres

d. 41 litres

Find the greatest number that will divided 3026 and 5053 leaving remainders 11 and 13 respectively?

a. 15

b. 30

c. 45

d. 60

The length and breadth of a room are 16.58 m and 8.32 m respectively. The floor of the room is to be paved with square tiles of uniform size. Find the maximum number of tiles which may cover the floor entirely?

a. 344560

b. 344864

c. 350000

d. 354000

The LCM of  1/3, 5/6,  2/9,  4/27   is

a. 1/54

b. 10/27

c. 20/3

d. 27/3

e.  None of these

Find the GCF of  2/3, 8/9,  16/81,  10/27   is

a . 2/27

b.  2/81

c. 81/163

d. 4/81

e. None of these

The H.C.F. of two numbers is 11 and their L.C.M. is 693. If one of the numbers is 77, find the other.

a. 99

b. 199

c. 81

d. 11

Find the least number which when divided separately by 15,20,48 and 36 will leave a remainder 9 in each case.

a. 639

b. 739

c. 720

d. 729

If the product of two numbers is 324 and their G.C.F. is 3, then their L.C.M. will be

a. 972

b. 327

c. 321

d. 108

The ratio of two numbers is 3: 4 and their G.C.F. is 4. Their L.C.M. is

a. 12

b. 16

c. 24

d. 48

Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm.

a. 55 cm

b. 45 cm

c. 65 cm

d. 25 cm

Three girls start jogging from the same point around a circular track and each one completes one round in 24 seconds, 36 seconds and 48 seconds respectively. After how much time will they meet at one point?

a. 2 minutes 20 seconds

b. 2 minutes 24 seconds

c. 3 minutes 36 seconds

d. 4 minutes 12 seconds

The least number of five digits which is exactly divisible by 12, 15 and 18 is

a. 10010

b. 10015

c. 10020

d. 10080

The greatest number of four digits which is divisible by 15, 25, 40 and 75 is

a. 9000

b. 9400

c. 9600

d. 9800

The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is

a. 3

b. 13

c. 23

d. 33

The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:

a. 1008

b. 1015

c. 1022

d. 1032

Wendy's folder contains 120 sheets of paper, each of weight 0·72 gms. If the empty folder weighs 113·6 gms, what is the total weight of her folder and the paper?

a.200 gms

b.20.0 gms

c.2.00 gms

d.2000 gms

A large thermos flask holds sufficient coffee to exactly fill 2 large cups of capacity 0·24 litres and 4 smaller ones of capacity 0·13 litres. What is the capacity of the flask?

a.100 litres

b.1 litres

c.10 litres

d.1000 litres

1.11 + 11.11 + 111.111 is equal to

a. 123.331

b. 133.331

c. 122.331

d. 123.311

Which one of the following has the same value as

4 + 2/25 + 1/5

a. 4.21

b. 4.28

c. 42.1

d. 421.0

The decimal equivalent to 3/4 +  4/5 +  8/25

a. 1.870

b. 18.70

c. 187

d. 1870

What is the decimal equivalent of 1  5/8  ?

a. 1.58

b. 1.62

c. 1.622

d. 1.625

1/10+2/20+3/30

a..1

b..123

c. .2

d. .3

e. .6

Which of the following is equal to 12?

a. 0.15 x 0.800

b. 0.20 x 0.600

c. 0.15 x 800

d. 0.20 x 60

The product of 1.2 x 0.6 x 3.12 x 0.03 is equal to

a. 0.067392

b. 0.063568

c. 0.4812

d. 0.00392

The product 8×.25×2×.125=

a. 1/8

b. 1/4

c. 1/2

d. 1

e. 2

The sum of the fraction 4/3,   5/9  and   6/18  is

2/5

11/18   

19/9

20/9

The sum 2 1/7 + 3 1/2 + 5 1/9 is between

10 and 10 1/2

10 1/2  and 11

11 and 10 1/2

11 1/2  and 12

The product of two fractions is 6. If one fraction is 5/3. Find the other.

3/5

4/5

18/5

12/5

The difference of 1 3/16 and its reciprocal is equal to

1 1/8

4/3

15/16

None of these

When ( 1/2 - 1/4 + 1/5 - 1/6 ) is divided by ( 2/5 - 5/9 + 3/5 - 7/18 ), the result is

2 1/8

3 1/6

3 3/10

5 1/10

The reciprocal of ( 1/2 + 1/3 ) is

1/6

2/5

6/5

5/2

5

John originally had 15 marbles . He gave 1/3 of his marbles to his friend Jim. How many marbles did John have left?

1. 5

2. 7

3. 10

4. 12

The sum of the fraction2/9,  4/3 and 6/18 is

1. 17/9

2. 16/9

3. 2/5     

4. 11/18

(3/8+7/8)/(4/5) =

1. 1

2. 25/16

3. 2

4. 43/20

5. 47/16

Which of the following fractions has the largest value?

1. 3/7

2. 4/9

3. 17/39

4. 100/201

5. 151/301

The product of two numbers is5/4. If one numbers is  5/6 , what is the other number?

1. 2

2. 1/2

3. 1/3   

4. 2/3

Edward has 2004 marbles. Half of them are blue, one quarter are red, and one sixth are green. How many marbles are of some other colour?

1. 167

2. 334

3. 501

4. 1002

(3×5)/(9×11)  ×(7×9×11)/(3×5×7) 

1. 1

2. 0

3. 49

4. 1/49

5. 50

The value of 5 -(2 1/2 - 3/4)  + (3 1/2-1 1/4) is

1. 4  1/2

2. 5  1/2

3. 5  1/4

4. 3 1/2

In a class of 40, we find that of the students are boys. Furthermore, of the boys are on the basketball team. How many boys from this class are on the basketball team?

1. 10

2. 8

3. 5

4. 12

5. 15

Which fraction should be added to the sum of 53/4, 4 4/5, 7 3/8, to make the result a whole number?

1. 1/40

2. 2/40

3. 3/40

4. 4/40

   
   

Half the people in a room left. One third of those remaining started to dance. There were then people who were not dancing. The original number of people in the room was what?

1. 24

2. 30

3. 36

4. 42

5. 72

The correct arrangement of the fractional numbers 17/25,17/13 , 17/19  and 17/27 in ascending order is

17/19,  17/13,  17/27,  17/25

17/27,  17/25,  17/19,  17/13

17/27,  17/19,  17/13,  17/25

17/13,  17/25,  17/19,  17/27

What fraction of the square is shaded?

1/3

2/5

5/12

3/7

1/2

Which of these five numbers is the largest?

13579+1/2468

13579-1/2468

13579×1/2468

13579÷1/2468

13579.2468

What fraction of the large 12 by 18 rectangular region is shaded?

1/108

1/18

1/12

2/9

1/3

If one third of one fourth of a number is 15, then how much is three-tenth of that number?

35

36

45

54

5/8   of  4/9  of  3/5  of 222= ?

42

43

39

37

If one-eigth of a pencil is black, half of the remaining is yellow and ther remaining  3 1/2 cm is blue, then what is the total length of the pencil?

6 cm

7 cm

8 cm

11 cm

If (2+3+4)/3=(1990+1991+1992)/N    , then N =

3

6

1990

1991

1992

Greg bought 4 notebooks for $6.40.

Which equation can be used to determine the price, p, in dollars, of 1 notebook?

p/4=6.40

p/6.40=4

4p=6.40

6.40p=4

For x=7, which of the following is the smallest?

a.6/x

b.6/(x+1)

c.6/(x-1)

d.x/6

e.(x+1)/6

The formula which expresses the relationship between x and y as showing in the accompanying table is:

y = 100 – 10x

y = 100 5x2

y = 100 – 5x – 5x2

y = 20 – x – x2

None of these

One number is five times another number. The numbers have a difference of 36. What are the numbers?

9,45

9,36

8,40

8,36

One-half of the sum of n and 8 is equal to 7. What is the value of n?

8

14

6

4

If a = -3 and x = 2, find the value of the expression

(3ax+7a-11)/(5ax-3a+1)

2/5

5/2

5/7

5/3

Subtract the sum of 9b2-3c2 and 2b2+bc-2c2 from the sum of 2b2-2bc-c2 and c2+2bc-b2

13b2-5bc+5c2

-10b2-bc+5c2

10b2+bc-5c2

-10b2-5bc-5c2

From the sum of a/2+b/3+c/4  and 2a/3+3b/4+4c/5  , subtract a/6+b/12+c/20 

a/5+b/6+c/2 

a+b+c

2a+b+c

a+2b+3c

(1/5 x-1/6 y)(5x+6y) is equal to

x^2-11xy/30-y^2

x^2+11xy/30-y^2

x^2-11xy/30+y^2

x^2+11xy/30+y^2

(〖3x〗^2-x)÷(-x) is equal to

3x+1

-3x-1

-3x+1

3x-1

(6ab-3abc+9abcd)÷(-1/3 ab) is equal to

2+c+3cd

-2+c-3cd

-18+9c-27cd

18-9c-27cd

What is the sum of (x+1) and the reciprocal of  (x-1)

2x/(x-1)

x^2/(x-1)

(x^2-2)/(x-1)

x^2/(x^2-1)

If a =2, the largest number in the set  -3a, 4a , 24/a , a2, 1  is

-3a

4a

24/a 

A

1 

If a + b = 9 − c and a + b = 5 + c, what is the value of c?

14

2

4

24

Reduced to lowest terms, (a^2-b^2)/ab-(ab-b^2)/(ab-a^2 ) 

a/b 

(a^2-〖2b〗^2)/ab

a^2

a-2b

None of these

Janet has a flower garden with 6 rose bushes, 7 lilac bushes, and 5 azaleas. Which of the following shows the ratio of lilac bushes to the total number of plants in Janet’s garden?

7:11

11:18

7:18

18:5

In a school of 616, there are 6 girls for every 5 boys. How many boys are there?

280

336

56

140

168

The ratio of boys to girls in Mr. Brown's math class is 2:3. If there are 30 students in the class, how many more girls than boys are in the class?

10

5

3

6

2

If 64 is divided into three parts proportional to 2, 4, and 6, the smallest part is:

5 1/3

11

10 2/3

5

None of these

The total number of students in a school is 1224. If the number of girls in the school is 600, then what is the respective ratio of the total number of boys to the total number of girls in the school?

26 : 25

21 : 17

18 : 13

5 : 4

Two numbers are in the ratio 2 : 3. If 9 is added to each, they will be in the ratio 3 : 4 the numbers are

12,28

18,27

8,12

10,15

Divide ₹ 4000 among A, B and C, so that their shares may be in the ratio of 5 : 7 : 8

₹ 1000, ₹ 1400, ₹ 1600

₹ 3000, ₹ 6000, ₹ 9000

₹ 2000, ₹ 4000, ₹ 6000

₹ 1000, ₹ 2000, ₹ 3000

The prices of a cycle and a scooter are the ratio of 9 : 5. If a cycle costs ₹ 4200 more than a scooter, what is the price of scooter?

₹ 5160

₹ 5250

₹ 6000

₹ 6230

A rectangle has perimeter 36 and one side of length 10. The area of this rectangular region is

80 square units

40 square units

260 square units

160 square units

130 square units

A rectangle has perimeter 36 and one side of length 10. The area of this rectangular region is

a. 80 square units

b. 40 square units

c. 260 square units

d. 160 square units

e. 130 square units

The area of the rectangular region is

a. 0.088 m2

b. 0.62 m2

c. 0.88 m2

d. 1.24 m2

e. 4.22 m2

The diagram shows a cube with sides of length 12 cm. An ant is walking across the cube’s surface from A to B on the route shown. How far does it walk?

a. 40 cm

b. 48 cm

c. 60 cm

d. It is impossible to determine

Figures I, II, and III are squares. The perimeter of I is 12 and the perimeter of II is 24. The perimeter of III is

a. 9

b. 18

c. 36

d. 72

e. 81

A living-room floor measures 13 feet by 24 feet. A 12 feet by 18 feet rug is placed on the floor. How many square feet of floor are not covered by the rug?

a. 216

b. 96

c. 312

d. 528

e. None of these

The large rectangle shown here is made up of three squares placed side-by-side. If the perimeter of the large rectangle is 96 centimeters, what is its area in square centimeters?

a. 32 sq.cm

b. 144 sq.cm

c. 432 sq.cm

d. 1024 sq.cm

e. 288 sq.cm

The area of polygon ABCDEF , in square units, is

a. 24

b. 30

c. 46

d. 66

e. 74

A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.2 cm 8.3 cm and 9.5 cm. The area of the square is

a. 24 cm2

b. 36 cm2

c. 48 cm2

d. 64 cm2

e. 144 cm2

All the angles of the polygon pictured below are right angles. The length of each side is given. What is the area?

a. 15 square units

b. 14 square units

c. 13 square units

d. 12 square units

e. 11 square units

Given that the area pf the small square is 1 square unit, what is the area of the pentagon.

a. 12 square units

b. 11 square units

c. 10 1/2  square units

d. 10 square units

e. 9 1/2 square units

The perimeter of one square is 3 times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?

a. 2

b. 3

c. 4

d. 6

e. 9

The perimeter of the polygon shown is

a. 14

b. 20

c. 28

d. 48

Cannot be determined from the information given