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
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)
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
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