Math Olympiad for Class 7-Problem Solving Approach

Use the suitable properties and choose the greatest positive integer.

a.-(+10)

b.-(-2)

c.|-48|

d.+(-101)

The absolute value of -28+12+42-63 is

a.37

b.-36

c.145

d.-145

In a school exam, Rohan’s score was up to 500 points. Then he scored -100 points in the words category. What was his score then?

a.600

b.400

c.-400

d.-600

A flying fish deep under the sea dreams of reaching the clouds one day. The fish is at a depth of 200 feet below sea level right under the clouds. It has to fly 6700 feet to reach the clouds.

How many feet above sea level are the clouds?

a.6900

b.6500

c.-6500

d.-6900

You hungrily remove frozen meat from the fridge. Its temperature is −18° but you can start cooking it only when it reaches 15°. Its temperature is increasing by 3° every minute.

How long will you have to wait before you can start cooking?

a.6

b.5

c.11

d.1

Ram has overdrawn his checking account by Rs.38. The bank debited him Rs.20 for an overdraft fee. Later, he deposited Rs.150. What is his current balance?

a.82

b.92

c.102

d.112

Anna is a microbiology student. She was doing research on optimum temperature for the survival of different strains of bacteria. Studies showed that bacteria X need optimum temperature of -31˚C while bacteria Y need optimum temperature of -56˚C. What is the temperature difference?

a.25

b.-87

c.-25

d.87

A submarine submerges at the rate of 5 m/min. If it descends from 20 m above the sea level, how long will it take to reach 250 m below sea level?

a.54

b.64

c.74

d.44

You hungrily remove frozen meat from the fridge. Its temperature is -−17°. Its temperature is increasing by 3° every five minutes.

What will its temperature be after 30 minutes?

a.1

b.2

c.3

d.4

Death Valley is one of the hottest places on earth with a recorded maximum temperature of 57°. The lowest temperature ever recorded was -−89° in Antarctica.

What is the difference between these two temperatures?

a.-33

b.33

c.-146

d.146

Which of the following fractions is closest to zero?

a.6/13

b.3/5

c.5/6

d.1/4

If _____ +2 37/47=10 9/44, then missing fraction in the box is

a.7 4/11

b.2 10/44

c.8 1/44

d.4 7/11

If x=6/25 and y=3/5, then the value of x/y is

a.6/5

b.18/125

c.2/5

d.1/6

If x=2/3+ 3/4 and y=3/4 "+ " 5/6, then the value of 1/x ÷ 1/y is

a.11/38

b.17/38

c.22/17

d.19/17

What will be the reciprocal of product of improper fractions 2 1/4 and 3 1/2?

a.Proper Fraction

b.Equivalent Fraction

c.Improper Fraction

d.Like Fraction

Pick the odd one out.

a.142/3

b.132/5

c. 16/7

d. 17/24

Which of the following is true with respect to 9/16 and 13/5?

a.9/16 > 13/5

b. 9/16 = 13/5

c.9/16 < 13/5

d.13/5 < 9/16

Which of the following is the improper fraction form of 12 1/5?

a.72/5

b. 61/5

c. 108/5

d. 85/5

What is the sum of 3/4, 7/6 and 1 3/5?

a.3 1/2

b.3 31/60

c.2 13/60

d. 412/120

Among 240 students, it was found that three – fourth of the students preferred to play hockey and one – eighth of the students preferred to play cricket. The number of students whole prefer to play hockey and cricket respectively are

a.180 and 30

b.40 and 180

c.180 and 40

d.None of these

What is the product of 1 1/3, 3 1/4 and 7/8?

a.3 18/24

b.2 19/24

c.3 19/24

d. 18/24

The distance between two cities X and Y is 50 km. Ramesh travels from city X to city Y by scooter with an average speed of 30 km/h.

How long will it take him to reach city Y?

a.12/3h

b.21/3h

c.10h

d.20h

Manav took 4 minutes to complete a race comprising three rounds. the time taken to complete the first and second round is ¾ min and 1½ min respectively.

How much time was taken by Manav to complete the last round?

2½ min

3 min

1¾ min

None of these

One pack of cookies requires 3 cups of flour and 2 cups of sugar. Estimated total quantity of both ingredients used in 10 such packets of cookies will be

less than 50 cups

between 50 cups and 60 cups

between 60 cups and 70 cups

above 60 cups

A flower basket containing 36 flowers is full. How many more flowers are needed to fill it up?

132

108

96

84

The solution of the equation 10 – 3y = 1 is y = ________.

0

1

2

3

5 less than thrice a number and add 7. The result is 14. The number is _________.

5

4

6

2

What is the value of p that makes the following expression true ?

p – {– 4 – (2 – 8 ÷ 4)} = 8

– 12

– 4

4

12

If two third of a number, half of the same number and one-seventh of same number is added to itself, the result is 37. The number is ______.

14 2/97

16 2/97 

18 2/97 

15 2/97 

What is the difference between 3a + 2b and - 2a - 5b?

5a + 7b

5a - 7b

- 5a - 7b

a - 3b

If x + y = 5, y + z = 7 and z + x = 12, what is the value of x + y + z?

12

2

5

24

When a certain number, 'm' is divided by 5 and added to 8, the result is equal to thrice the number subtracted from 4. What is the value of m?

2

4/3

-1/3

-5/4

Which of the given equation does not have 4 as the solution?

p + 5 = 9

14 – p = 10

20/p=4

9p = 36

If 184 is divided into two parts such that one-third of one part exceeds one-seventh of the other part by 8, then the greater part is ______.

72

110

112

114

Twenty-four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. Find each part.

13,11

12,12

10,14

15, 9

lf 3y = 15 and 2x = 16, then 3x + 2y is equal to

• 20

• 18

• 24

• 34

If h = 10, then find the value of 3h + 45 - 12 + (3 x 5) h.

213

243

200

273

The value of the expression ( 2x2 + 2xy- y -1) is 1 at x = 0. What is the value of y?

-2

2

3

4

What is the value of p that makes the following expression true?

p – {– 4 – (2 – 8 ÷ 4)} = 8

– 12

– 4

4

12

What is the value of R that makes the following expression true?

R + { 3 – 4 (25 ÷ 8 + 4) + 1 } = -25

- 4

- 5

5

3

If sum of 'n' natural number is given by n(n+1)/2, then the value of sum of first 20 natural numbers is

210

220

200

190

John is n years older than his sister. His sister's age is 12. What is their total age after 4 years?

24 n years

(32 + n) years

(28 + n)

28 n years

What is the value of R that makes the following expression true?

R + {3 – 4(25 5 + 3) + 1} = -25

-4

-5

5

3

If sum of 'n' natural numbers is given by then the value of sum of first 20 natural numbers is

210

220

200

190

A teacher asks the students of her class to write an equation for the statement Tenth of a number p is 100. Three students wrote the following equations. Which is correct?

(i) p/10=100

(ii) 10/2p=100

(iii) 10p/p=50

• (i) only

• (ii) only

• (iii) only

• Both (i) and (iii)

The breadth of a rectangle is 4 cm less than half of its length. The breadth of the rectangle is 14cm.

If the length of the rectangle is x cm, then which equation represents the given situation?

4-x/2=14

x/2+4=14

x/2-4=14

x-1/2=14

Which of the following does not affect the given equation?

Adding 0 on the L.H.S. and 1 on the R.H.S.

Adding 1 on the L.H.S. and (-1) on the R.H.S.

Adding the same number on both sides of the equation.

Adding 0 on the R.H.S. and 1 on the L.H.S.

Choose the statement that best describes the equation m = 10.

One - fourth of 10 is m.

One - fourth of m is 3 more than 3.

One - fourth of m is 1 0.

Four times m is 10.

Subtract the sum of (12a + 7a2 – 1) and (-4a + 15 – 5a2) from 16 is ________.

2a2 – 8a + 4

2a2 – 8a – 6

-2a2 – 8a + 2

-2a2 + 8a - 2

What is the value of 'x’ in (3x-1)/5- (x+1)/2=3- (x-1)/2

a.9

b.10

c.11

d.12

Which of the following equations can be constructed with x = 2?

a.3x + 4 = 8

b.3x- 4 = 2

c.3x + 4 = 2

d.3x - 4 = 8

If 9/5 of a number is 45, what is 1/5 of the same number?

a.5

b.25

c.30

d.81

If 5 is added to twice a number, the result is 29. Find the number.

a.10

b.12

c.14

d.16

Seven times a number is 12 less than thirteen times the same number. Find the number.

a.1

b.2

c.3

d.4

If x + y = 5, y + z = 7 and z + x = 12, what is the value of x + y + z?

12

2

5

24

Rahul and Chirag had 5184 phone cards. Rahul had seven times as many phone cards as Chirag. How many phone cards did Rahul have?

458

269

858

648

A number is multiplied by 6. If 24 is subtracted from the product and difference is divided by 42, the result is equal to 10. The number is ________.

74

56

19

52

An employer pays ₹ 30 for each day a worker work, and deducts ₹ 5 for each day he is idle. At the end of 50 days, a worker gets ₹ 450. For how many days did the worker remain idle?

40

30

28

45

A man divides ₹ 13050 among 5 sons, 4 daughters and 5 nephews. If each nephew receives three times as much as each daughter and each son receive two times as much as each daughter, how much does each son receive?

₹ 600

₹ 750

₹ 900

₹ 550

When 6 is subtracted from four times a number, the result is 54. What is the number?

16

25

15

35

The sum of three consecutive even numbers is 126. What is the difference between twice the lowest one and one half of the highest one?

68

58

78

48

The difference between a number and its three-fourth is 35. What is the one-fourth of that number?

35

45

55

65

The sum of one-half, one-third and one-fourth of a number exceeds the number by 12.What is the number?

184

164

154

144

Asha was asked to multiply a number by 24. She instead multiplied the number by 42 and got the answer 810 more than the correct answer. The number to be multiplied was ______.

34

25

35

45

Find the value of x 〖 11〗^(6 )÷ 〖 11〗^(4-x )= 〖 11〗^(8 )

a.2

b.4

c.6

d.8

If x =1 and y=2, then x^y+y^x is equal to

a.3

b.4

c.5

d.6

Evaluate and choose the correct option for (a^2 b^3 c)^2/(a^4 b^6 c^2 )

a.0

b.1

c.abc

d.1/abc

Simplify and choose the correct option for (169/225)^(1/2) ×(125/27)^(2/3)× (81/4)^(1/2)

a.0

b.1

c.65/6

d.75/3

(−3)x−2=−243, find the value of x

a.6

b.7

c.8

d.9

If 4x=64, then find the value of 122x−6

a.0

b.1

c.144

d.1728

The value of xy – yx + xy, if x = 6, y = 2 is ______.

• 16

• -16

• 12

• - 12

Find the value of 20 + 30 + 40 + 50 + 60 + 71

• 12

• 234

• 1

• 24

Which of the following is, the equivalent to (1/x^(-4) )?

• 1/x x 1/x x 1/x x 1/x

• x × x × x × x

• 1/x × 1/x × x × x

• None of these

[{(-1/3)^2 }^(-3) ]^1 = ?

• 729

• -1/81

• -729

• 1/81

The simplified value of ((-1)/3)^6/((-1)/3)^5  ÷ (((-1)/27))/(((-1)/9) ) is

• 0

• 1

• -1

• 3

Find the value of b, if (4/5)^3× (4/5)^(b+8)= (5/4)^(-11)

• 0

• 1

• 12

• 11

What is the value of 24 x 53

a. 2453

b. 2000

c. 11200

a. 10000000

Which is greater 43 or 34?

a. both are equal

b. 43

c. 34

d. cannot be determined

Solve (45)x = (44)x ÷ 42

x=4

x=-2

x=-3

x=2

The value of (x^(-4)  × y^(-6))/(x^(-16)  × y^(-7) )

x^(-1)  × y^(-1)

x^12  y^1

1/(x^12   y)

x^12

Mr. Xen asked two of his students to solve the expression 24 /6  (( a^3 b^(-8))/(a^(-5) b^2 ))^(-1/2) and write the answer on blackboard. Andy wrote the answer as 4a^(-4) b^5, whereas Zuck wrote the answer as (4b^5)/a^4 . Who wrote the correct answer?

Andy

Zuck

Both of them

       None of these

The sum of 40% of 70 and 70% of 40 is equal to

a.28

b.36

c.48

d.56

Length and breadth of a rectangle are 3.2m and 150 cm. Then the area is

a.48 sq cm

b.4.8 cm

c.4.8 sq m

d.48 cm

A playground which is 250 m long and 20 m broad is to be fenced with wire. How much wire is needed?

a.440 m

b.540 m

c.270 m

d.500 m

The circumference of the circle is 44 cm. Its area is

a.308 m^2

b.154 m^2

c.77 m^2

d.616 m^2

The difference between circumference and radius of a circle is 37 m. The circumference of the circle is

a.7 m

b.44 m

c.154 m

d.None of these

The length and breadth of a rectangular park are in the ratio 4:3 and its perimeter is 56 m. The area of the filed is

a.192 m^2

b.300 m^2

c.432 m^2

d.228 m^2

The median of the following data 46,64,87,41,58,77,35,90,55,33,92 is

a.87

b.77

c.58

d.60.2

Mean of first six prime numbers is

a.4.83

b.6.83

c.5.83

d.7.83

What is the arithmetic mean of 2,……….,9,10 and 11

a.6,5

b.7

c.7.5

d.8

The runs scored by Indian team in recently held five matches ODI series, are 310,306,288,222 and 374. What is the average score of India in the series?

a.294

b.300

c.288

d.310