Grade 4 : Mathematics Olympiad - Free Sample question paper

Grade 4 : Mathematics Olympiad - Sample question paper

Logical Reasoning

1) Which of the following numbers will continue the given series?

               42 , 45 , 50 , 53 , 58 , 61 , ______

a) 66           c) 64

b) 65           d) 68

2) Among five children Amudhan , Nilan , Mugilan , Priya , Nathiya each of different heights , Amudhan is taller than only Priya and Mugilan is shorter than only Nathiya. Who among them is shortest in height?

3) How many meaningful words can be formed from the third , eighth , tenth , and eighteenth letters of the given alphabet series?

  Z M N Q S V B W X A B U M F W A F R T N O 

a) More than two        c) one

b) none                      d) two

4) If the day before yesterday was Thursday , then what day will be the day after tomorrow?

5) In a birthday party , 7 friends meet . Each friend shook hands with each other exactly once. How many handshakes are there?

6) Find the odd one out

a) book          c) water

b) pen            d) eraser

7) Find the combination of numbers, so that the given letters are arranged accordingly to form a meaningful English word.

     R  C  W  N  O

     1  2   3  4  5 

8) Find the missing number

225 , 275 , 325 , ____ , 425 , 475

9) If 'earth' is called 'sky' , 'sky' is called 'water' , 'water' is called 'light' and 'light' is called 'air' , then if someone is thirsty what should he drink?

10) Find the missing number if same rule is followed in all the three 

patterns

    3    8                5    9                 ?    7

    6    4                3    15               2    14

Mathematical Reasoning

11) Find the sum of (3rd multiple o 11) and the difference between common factors of 8 and 10 )?

12) Amudhan went for playing at 4:15pm and returned home 1 hour 10 mins later. At what time he came back home?

13) Which of the following is incorrect?

a) XL + CVI = 146            c) CD + LXV = 665

b) M-DCL = 350                d) none of these

14) If Amudhan saved a total of Rs 15000 from January to May, then how much did he save in February?

January = 5000  February = ____? March = 4000  April = 3000

May = 3000

15) If AAAAA = 525 ml and AA+BBBB= 270ml then A + B = ______?

16) If Amudhan spent (1/5)th of the amount of money he saved in April which is RS 4000 then how much did he earn in that month?

17) Find the value of Y + X

18) Find the perimeter of the given figure

19) How many one fifths will make one whole?

20) Smallest factor of a number is _____?

Everyday Mathematics

21) Amudhan filled one-fifth of a jar with milk and two-fifth with water. What part of the jar is empty?

22) In an adventure park , Amudhan took a water ride of 20minutes and looping ride of 45 minutes one after another. If he finished the second ride at 6:35pm then when did he start his first ride?

23) Amudhan filled 15L 750ml of petrol in his car. He used 7L 250ml of petrol while going from Chennai to Bengaluru. Find the quantity of petrol left in his car?

24) Amudhan had Rs 7295. He spent Rs 2105 on shopping, Rs 1223 on travelling and Rs 1000 on movie. How much money is left with him now?

25) 100000 cartons were to be transported in 50 trucks. How many cartons could 1 truck carry, if each truck carries equal number of cartons?

26) Amudhan has some animal cards. What fraction of the cards are cat cards?

Number of cat cards = 3

Number of dog cards = 5

Number of fish cards = 2

Number of lion cards = 4

27)Amudhan bought 13 boxes of cold drinks for a party. There were 12 cans  in each box. How many total cans of cold drinks did he buy for the party?

28) On Monday Amudhan drove 2105km, on Tuesday he drove 200km and on wednesday he drove 150km. How many kms he drove on all three days?

29) Amudhan has 675 balls. 278 were cricket balls and rest were footballs. He sold some footballs and found he had 110 foot balls left. How many footballs were sold?

30) A factory manufactures 300 cars each day. How many cars does the factory manufacture in 3 weeks?

Achievers Section

31) Identify the number using given clues.

• Its thousand's digit is three less than its tens digit
• Its hundreds digit is 4th multiple of its ones digit
• Its ones digit is the smallest prime number
• Its tens digit is seven more than its ones digit.

32) Which of the following statements is INCORRECT?

a) 4982/5 , leaves a remainder 2

b) A rectangle has 2 lines of symmetry

c) Sum of 3 1/4 and 4 1/2 is 7 3/4

d) 5 ten thousand + 30 tens + 21 ones written in numerals as 5321

33) Write in ROman Numerals

CMX - DXIV = _______?

34) Select the odd one out.

a)   A     b) H    c)  Q   d) U

35) In a play competition, there are 5 finalists.

Amudhan : He has only one boy behind him

Nilan : He is not the first

Aarush : He is just after Chandru

Mugilan : He is just before Amudhan

Who is at first and last positions respectively?

 

Grade 5 : Mathematics Olympiad (IMO) - Free Sample Questions with detailed answers

Grade 5: Mathematics Olympiad - Sample Question Paper with Detailed Answer

Logical Reasoning

1) A is older than X. Y is younger than X and B. B is not as old as A. Who is the eldest among all?

a) Data inadequate                              c) X
b) A                                                    d) A or X

Solution

Given, A is older than X which means we can ignore X since we need to find the eldest

also given, Y is younger than X which means we can also ignore Y since already X is younger than A which means A is also younger than A

also given, B is not as old as A which means B is also younger than A

Hence A is the eldest among all

The answer is b) A

2) Find the missing number, if a certain rule is followed, either row-wise or column-wise.

                            2  l  20  l  5

                            3  l  42  l  7 

                            5  l   ?   l  7

Solution

Let's check Row wise

             multiply first column with third and then multiply that by 2

     First row ---->  2*5 = 10 then  10 *2 = 20 (getting second column) 

     second row-->  3*7 = 21 then  21 *2 = 42 (getting second column)

Similarly, let's try for third row too --->

   5*7 = 35 then we have multiply 35 by 2

35*2 = 70

Answer is 70

3) Six friends A, B, C, D, E, and F scored different scores in the semester examination. C scored more than A and F only. D scored less than only B. E did not score the least. D scored more than R. Who scored the highest marks?

a) A                 c) B

b) F                 d) C

Solution

here, they have asked us to find the highest score.

Given, C scored more than A and F ONLY.

This means among A, C, F  ---> C scored the highest (ignore A, F), but less than other friends B, D, E. So we can ignore C too.

Also given, D scored less than only B and D scored more than R means

among B, D, R ----> B scored highest

also given, E did not score the least.

There is a chance for B and E to get the highest scores.

But in the options, they haven't given E.

Hence, the answer is c) B.

4) Amudhan's mother remembers that Amudhan's exam is after 21st, but before 26th of September, his sister remembers that his exam is after 22nd but before 25th of September and his father remembers that his exam is on an odd date. On which date in September is  Amudhan's exam?

Solution

According to Amudhan's mom, the exam is after 21st, but before 26th of September

that is,   

• Amudhan's mom  ----> 22,23,24,25
• Amudhan's sister -----> 23,24     [23,24th September is common]
• Amudhan's father -----> an odd date

Among 23 and 24: 23 is an odd date.

Hence, 23rd September is Amudhan's exam.

5) Arrange the following in a meaningful order.

1. Table    2. Tree   3. Wood   4. Seed   5. Plant

Solution

Seed ---> Plant -----> Tree ----> Wood -----> Table

6) In a certain code language, if 'CIRCLE' is coded as 'DISCME', then how will be 'SQUARE' be coded in that language?

Solution

                        C  I  R  C  L  E

                        D  I  S  C  M E

if we observe the above code, the even places remain the same.

                        C  I  R  C  L  E

                        D  I  S  C  M E

if we observe the above code, the odd places change to the next letter.

Now let's try to convert 'SQUARE' to the coded language

The even places remain the same and the odd places change to the next letter.

Hence,             S  Q  U  A  R  E

                      T  Q  V  A  S  E

The answer is 'TQVASE'

7) Amudhan is 10 ranks behind Mugilan who ranks 8 in a class of 20 students. What is Amudhan's rank from the bottom?

Solution

           

8) Which of the given options will complete the given pattern?

3D, 8G, 13J, ? , 23P

Solution

Let's first find out the pattern of the numbers 3, 8, 13,___, 23

here, it increases by 5

3+5 = 8

8+5 = 13

13+5 = 18

18+5 = 23

now lets find the letters pattern D, G, J, ___, P

 

D and (E,F) ---> G

G and (H,I) ---> J

J and (K,L) -----> M

M and (N,O) ----> p

Hence, the answer is 18M

9) Arrange the given words as they occur in a dictionary

1. fright  2. frisk  3. friend  4. fridge   5. frisson

Solution

fridge ---> friend ---> fright ---> frisk ---> frisson

10) Select the odd one out.

              1. Δ           2.◻         3. O         4. U

Solution

1. Triangle is closed figure

2. Square is also closed figure

3. Circle is also a closed figure

4. U is not a closed figure

Hence, 4. U is the odd one out

11) Amudhan is facing the Market. If he turns 2 right angles in an anticlockwise direction, then what will he be facing now?

Solution

Hence the answer is Station

12) Find the missing character, if a certain rule is followed either row-wise or column-wise.

Solution

let's consider first column : 11-6 = 5 = E (5th letter)

                   third column : 12-8 = 4 = D (4th letter)

 Similarly,  Second column : 4-3 = 1 = A (1st letter)

Hence the answer is A

13) Which of the following words cannot be formed from the letters of the given word?  TREASURY

a) STRAYER                c) RESTORE

b) SURETY                  d) ARREST

Solution

The letter O in the word RESTORE is not present in the given word. So, RESTORE cannot be formed from the letters of the given word TREASURY.

Hence the answer is c) RESTORE

14) How many different possible combinations of one fruit and one toy vehicle can be formed from the given fruits and toy vehicles?

 

          Fruits:             Orange     Banana      Mango

Toy Vehicles:  Car    Bus    Train    Bike    Truck

Solution

Total fruits = 3

Total toy vehicles = 5

Total possible combinations = 3 * 5 = 15

Hence the answer is 15

15) In a certain code language, "pen" is called "eraser" , "eraser" is called "pencil" and "pencil" is called "book", then what will be used to erase something?

a) pen             c) pencil

b)book            d) eraser

Solution

To erase something we need an 'eraser', but an eraser is called a 'pencil'.

Hence the answer is c) pencil

Mathematical Reasoning

16) Find the sum of the common prime factors of 120 and 150

Solution

Prime factors of 120 = 2 * 2 * 2 * 3 * 5

Prime factors of 150 =  2 * 3 * 5 * 5 

Common factors are = 2,3,5

Sum of the common prime factors = 2+3+5 = 10

Hence the answer is 10

17) Find the missing value.

3.75 / 3 - (0.2*5.6) + 13/20 = (1+ ____) * 1/2

Hence the answer is 0.56

18) 

Solution

given,  4 squares = 28

           1 square = 28/4 = 7

also given, circle / square = 13

we just found square = 7

so, circle/7  = 13

circle = 13 * 7 = 91

we have to find square + circle = 7 + 91

                                              = 98

hence the answer is 98

19) Amudhan earns Rs 250.75 in a day. He spends Rs 125.05 and saves the rest. How much money will he save in 12 days?

Solution

Amount Amudhan earns in a day = Rs 250.75

Spending amount in a day  = Rs 125.05

Amount saves in a day      =  250.75 - 125.05

                                       =  Rs 125.70  saves in a day

Amount he saves in 12 days = 125.70 * 12

                                          =     Rs 1508.40

Hence the answer is Rs 1508.40

                       

20) Amudhan rented a bike for 210minutes. How much did he pay for it ?

First hour : Rs 8.25. Every additional 1/2 hour : Rs 5.75

Solution

given first hour (first 60mins ) = Rs 8.25

additional 30 mins = 5.75

        he totally rented for 210 mins

                                     210 = 60+ 150 ( 30 + 30 + 30 + 30 + 30 )

                                           = 8.25 + 5.75 + 5.75 +5.75 +5.75 +5.75                                            =   Rs 37 

Hence the amount Amudhan has to pay = Rs 37

21) There are __________ prime numbers between 73 and 94.

Solution

Numbers between 73 and 94 is 

 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 91 , 92 , 93

Among those numbers, we know 2 is the only even prime numbers. So we can strike out all the even numbers present there

 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 91 , 92 , 93

Prime number : If a number is a prime number then that number has only two factors. One of the factor is 1 and the another factor is the number itself

Now we can strike a number whose one's digit is either 5 or 0 ( because that number must be divisible by 5 that means its not a prime number)

 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 91 , 92 , 93

77 is divisible by 7

79 is a prime number (1 and 79 are the only two factors)

81 is divisible by 9

83 is a prime number (1 and 83 are the only two factors)

87 is divisible by 3

89 is a prime number (1 and 89 are the only two factors)

91 is divisible by 7

93 is divisible by 3

Hence the prime numbers present in between 73 and 94 are 79 , 83 , 89

The answer is 3 prime numbers present in between 73 and 94.

22) If 443272 is divided by 268, then _________ is the remainder.

Solution 

If any number is divided by another number then there won't be any remainder

For example, if 4 is divided by 2 then the remainder is 0

Hence the answer is 0

23) Amudhan took 40 minutes to complete his homework. He finished his homework at 16:30. At what time did he start doing his homework?

Solution

Given

Amudhan took 40 minutes to complete his homework

he finished his homework at 16:30 

His start time = 16:30 - 40mins  

       16hours 30mins  -40mins = 15hours + 60mins + 30mins - 40mins 

                                             = 15hours + 90 mins - 40mins

                                             = 15hours + 50 mins

                                             = 15 : 50 

Hence he started his homework by 15:50

24) If a number X is multiplied by 8 and 800 is added, then the answer obtained is 2080. Find the twice of the number X.

Solution

Given,  ( X * 8 )  + 800 = 2080

   we have to find X, so keep X alone on one side and move others to another side

to move 800 to another side we have to subtract 800 on both the sides

         

But we have to find twice of the number X that is 2X = 2*1272

                                                                             = 2544

Hence the answer is 2544 

25) On Amudhan's birthday , his mother gave two-eighth of the cake to each of his 2 neighbours and one-eighth of the cake to each of his 2 friends. What fraction of the cake is left with her?

Solution

2/8 of the cake is left with her

Achievers Section

26) If 17 buckets can be filled by a pipe in 8 1/2 minutes, then how many minutes will be taken by the pipe to fill 45 such buckets?

Solution

17 buckets can be filled by 8 1/2 mins = 17/2  ( converted mixed to an improper fraction)

1 bucket can be filled by (17/2)/17  

 

1 bucket can be filled by 1/2 mins

so, 45 buckets can be filled by 1/2 * 45 = 45/2 = 22 1/2 mins

hence the answer is 22 1/2 mins

27)  CM - CD + CVII + M =________ ( Answer in Roman numerals)

Solution

I - 1             L - 50               M - 1000

V - 5            C - 100

X - 10           D - 500 

CM = 900   (100 - 1000)

CD = 400    ( 100 - 500 )

CVII =  107       (100 + 5 + 1 + 1)

M = 1000

CM - CD + CVII + M =  900 - 400 +107 +1000

                               =   500  + 107 + 1000

                               = 1607

1607 = 1000 + 500 + 100 + 7 (5+1+1)    

         =    M       D         C      V I I 

Hence the answer is MDCVII

28) The smallest number that can be divided by the given numbers without leaving any remainder is _________?

 a) LCM                c) prime numbers

 b) HCF                 d) 1

Solution

LCM is the smallest number that on dividing by the given numbers leaves 0 remainder

Hence the answer is a) LCM

29) Sum of the place values of 5 and 7 in the number 378.125 is _________?

Solution

Place value of 5 is 5/1000 = 0.005

Place value of 7 is 70

Sum of their place values = 70+0.005 = 70.005

Hence the answer is 70.005

30) The value of 30.5 - 30.4 +30.3 -30.2 + 30.1 -30.0 +29.9 -29.8 +29.7-29.6 +29.5 - 29.4 + 29.3 - 29.2 + 29.1 -29.0 = ___________?

Solution

Hence the answer is 0.8

Grade 5: Mathematics Olympiad (IMO) - Free Sample Question Paper

Grade 5: Mathematics Olympiad - Sample Question Paper  

For answer and detail solution:

http://kidsrgr8learners.blogspot.com/2021/09/grade-5-mathematics-olympiad-imo-sample.html

Logical Reasoning

1) A is older than X. Y is younger than X and B. B is not as old as A. Who is the eldest among all?

a) Data inadequate                              c) X

b) A                                                    d) A or X

2) Find the missing number, if a certain rule is followed, either row-wise or column-wise.

                            2  l  20  l  5

                            3  l  42  l  7 

                            5  l   ?   l  7

3) Six friends A, B, C, D, E, and F scored different scores in the semester examination. C scored more than A and F only. D scored less than only B. E did not score the least. D scored more than R. Who scored the highest marks?

a) A                 c) B

b) F                 d) C

4) Amudhan's mother remembers that Amudhan's exam is after 21st, but before 26th of September, his sister remembers that his exam is after 22nd but before 25th of September and his father remembers that his exam is on an odd date. On which date in September is  Amudhan's exam?

5) Arrange the following in a meaningful order.

1. Table    2. Tree   3. Wood   4. Seed   5. Plant

6) In a certain code language, if 'CIRCLE' is coded as 'DISCME', then how will be 'SQUARE' be coded in that language?

7) Amudhan is 10 ranks behind Mugilan who ranks 8 in a class of 20 students. What is Amudhan's rank from the bottom?

8) Which of the given options will complete the given pattern?

3D, 8G, 13J, ? , 23P

9) Arrange the given words as they occur in a dictionary

1. fright  2. frisk  3. friend  4. fridge   5. frisson

10) Select the odd one out.

              1. Δ           2.◻         3. O         4. U

11) Amudhan is facing the Market. If he turns 2 right angles in an anticlockwise direction, then what will he be facing now?

12) Find the missing character, if a certain rule is followed either row-wise or column-wise.

13) Which of the following words cannot be formed from the letters of the given word?  TREASURY

a) STRAYER                c) RESTORE

b) SURETY                  d) ARREST

14) How many different possible combinations of one fruit and one toy vehicle can be formed from the given fruits and toy vehicles? 

          Fruits:             Orange     Banana      Mango

Toy Vehicles:  Car    Bus    Train    Bike    Truck

15) In a certain code language, "pen" is called "eraser", "eraser" is called "pencil" and "pencil" is called "book", then what will be used to erase something?

a) pen             c) pencil

b)book            d) eraser

Mathematical Reasoning

16) Find the sum of the common prime factors of 120 and 150

17) Find the missing value.

3.75 / 3 - (0.2*5.6) + 13/20 = (1+ ____) * 1/2

18) 

19) Amudhan earns Rs 250.75 in a day. He spends Rs 125.05 and saves the rest. How much money will he save in 12 days?

20) Amudhan rented a bike for 380minutes. How much did he pay for it ?

First hour : Rs 8.25. Every additional 1/2 hour : Rs 5.75

21) There are __________ prime numbers between 73 and 94.

22) If 443272 is divided by 268, then _________ is the remainder.

23) Amudhan took 40 minutes to complete his homework. He finished his homework at 16:30. At what time did he start doing his homework?

24) If a number X is multiplied by 8 and 800 is added, then the answer obtained is 2080. Find the twice of the number X.

25) On Amudhan's birthday , his mother gave three-tenth of the cake to each of his 2 neighbours and one-tenth of the cake to each of his friends. What fraction of the cake is left with her?

Achievers Section

26) If 17 buckets can be filled by a pipe in 8 1/2 minutes, then how many minutes will be taken by the pipe to fill 45 such buckets?

27)  CM - CD + CVII + M =________ ( Answer in Roman numerals)

28) The smallest number that can be divided by the given numbers without leaving any remainder is _________?

 a) LCM                c) prime numbers

 b) HCF                 d) 1

29) Sum of the place values of 5 and 7 in the number 378.125 is _________?

30) The value of 30.5 - 30.4 +30.3 -30.2 + 30.1 -30.0 +29.9 -29.8 +29.7-29.6 +29.5 - 29.4 + 29.3 - 29.2 + 29.1 -29.0 = ___________?

For answer and detail solution:

http://kidsrgr8learners.blogspot.com/2021/09/grade-5-mathematics-olympiad-imo-sample.html