Grade 4 : Mathematics Olympiad - Sample question with detailed Answers
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
Solution
First lets find the difference between two numbers
42 , 45 , 50 , 53 , 58 , 61 , _____ ( 45-42=3 , 50-45=5 , 53-50=3...)
3 5 3 5 3 5 (if we observe their differences then the next difference be 5)
61+5 = 66
Hence the answer is a) 66
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?
Solution
Here we have to find the shortest in height
given,
Amudhan is taller than only Priya = Priya, Amudhan (heights in ascending order)
also given,
Mugilan is shorter than only Nathiya = Mugilan , Nathiya (heights in ascending order)
using those two given conditions we can write that as,
Priya , Amudhan, Mugilan , Nathiya (heights in ascending order)
Nilan comes =>
Priya , Amudhan , Nilan , Mugilan , Nathiya (heights in ascending order)
By the above order, the given two conditions satisfies.
hence the answer is Priya
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
Solution
Third letter = N
Eighth letter = W
Tenth letter = A
Eighteenth letter = R
Words formed = WAR , RAN
Hence the answer is Two
4) If the day before yesterday was Thursday , then what day will be the day after tomorrow?
Solution
Daybeforeyesterday Yesterday Today Tomorrow Day before tomorrow
Thursday(given) Friday Saturday Sunday Monday
Hence the answer is Monday
5) In a birthday party , 7 friends meet . Each friend shook hands with each other exactly once. How many handshakes are there?
Solution
Given,
Total number of friends = 7
7th person shook hands with other 6 persons
6th person shook hands with other 5 person
5th person shook hands with other 4 persons
4th person shook hands with other 3 persons
3th person shook hands with other 2 persons
2th person shook hands with other 1 persons
Total number of handshakes = 6+5+4+3+2+1
= 21
Hence the answer is 21
6) Find the odd one out
a) book c) water
b) pen d) eraser
Solution
Book,Pen,Eraser are all stationary items
Hence water is the odd one out
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
Solution
Using the given letters, we can form the word
C R O W N
2 1 5 3 4
Hence the combination of numbers = 21534
8) Find the missing number
225 , 275 , 325 , ____ , 425 , 475
Solution
First lets find the difference between the given numbers
225 , 275 , 325 , ____ , 425 , 475
50 50 50 (difference between two numbers=50)
so, 425-50 = 375
Hence the answer is 375
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?
Solution
If someone is thirsty they drink "water"
"water" is called as "light"
Hence the answer is light
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
Solution
lets take first set Second set
3 8 here, 3*8=24 5 9 here, 5*9=45
6 4 6*4=24 3 15 3 *15 = 45
Similarly, third set ? 7 here, ? * 7 = 28 (4*7=28)
2 14 2*14 = 28
hence the answer is 4
Mathematical Reasoning
11) Find the sum of (3rd multiple of 11) and (the difference between common factors of 8 and 10 )?
Solution
3rd multiple of 11 = 3*11 = 33
Factors of 8 = 1 , 2 , 4 , 8
Factors of 10 = 1 , 2, 5 , 10
Common factor of 8 and 10 = 1 and 2
Their difference = 2-1 = 1
the sum of (3rd multiple of 11) and (the difference between common factors of 8 and 10 ) = 33 + 1 = 34
Hence the answer is 34
12) Amudhan went for playing at 4:15pm and returned home 1 hour 10 mins later. At what time he came back home?
Solution
Amudhan went for playing at 4 : 15 pm
He returned home after 1 hr 10 mins
time he came back home = 5 : 25 pm ( add )
Hence the answer is 5:25pm
13) Which of the following is incorrect?
a) XL + CVI = 146 c) CD + LXV = 665
b) M-DCL = 350 d) none of these
Solution
I - 1 , V - 5 , X - 10 , L - 50 , C - 100 , D - 500 , M- 1000
Given ,XL + CVI = 146
146 = 146
so, option a is correct
Given , M-DCL = 350
1000 - 650 = 350
350 = 350
so, option b is correct
Given , CD + LXV = 665
400 + 65 = 665
465 = 665
The above statement is INCORRECT
Hence the answer is c) CD + LXV = 665 which is INCORRECT
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
Solution
Total amount he saved = Rs 15000
Other than February he saved = 5000+4000+3000+3000
= 15000
Amount he saved in February = total amount - amount he saved other than February
= 15000 - 15000
= 0
Hence the answer is 0
15) If AAAAA = 525 ml and AA+BBBB= 270ml then A + B = ______?
Solution
Given, 5A = 525 ml
A = 525/5 ml = 105 ml
also given 2A + 4B = 270ml
2*105 + 4B = 270
210 +4B = 270
4B = 270 - 210 = 60
B = 60/4 = 15
we have to find A + B = 105 + 15 = 120 ml
Hence the answer is 120 ml
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?
Solution
Amount he spent = 1/5 * 4000 = 800
Amount he saved = 4000
Total amount he earned = 4000+800 = 4800
Hence the answer is Rs 4800
17) Find the value of Y + X
Solution
Hence X = 9 and Y = 2
18) Find the perimeter of the given figure
Perimeter = sum of all the sides
= 12+2+3+3+3+3+3+4+9+5+2
= 49cm
Hence the answer is 49cm
19) How many one fifths will make one whole?
Solution
one fifths = 1/5
we have to make it one whole that is 1
1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1
Hence the answer is 5 one fifths make one whole
20) Smallest factor of a number is _____?
Solution
1 is the smallest factor of any number
Hence the answer is 1
Everyday Mathematics
21) Amudhan filled one-fifth of a jar with milk and two-fifth with water. What part of the jar is empty?
Solution
1/5 + 2/5 = 3/5
there are 5 parts , out of 5 parts 3 parts are filled with milk and water
remaining 2 parts empty
Hence 2/5 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?
Solution
total duration of time for 2 rides=20min+45mins =65mins= 1hour5mins
He finished at 6:35pm - 1hour 5 mins = 5:30pm
Hence the answer is 5:30pm
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?
Solution
Petrol left in his car = 15L 750ml - 7L250ml
= 8L 500ml
Hence the answer is 8L 500ml
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?
Solution
Total amount = Rs 7295
Amount he spent = 2105+1223+1000 = 4328
Amount left with him = 7295 - 4328 = 2967
Hence the answer is Rs 2967
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?
Solution
Total number of cartons = 100000
Total number of trucks = 50
Number of cartons one truck carry = 100000/50 = 2000
Hence the answer is 2000
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
Solution
Total number of cards = 3 cat cards + 5dog + 2 fish + 4 lion
= 14 cards
out of 14 cards 3 are cat cards
hence the answer is 3/14
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?
Solution
Total number of boxes = 13
Number of cans in a box = 12
Total number of cans = 13 * 12
= 156
Hence the answer is 156
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?
Solution
Total Kms on all three days = 2105 + 200 + 150
= 2455 kms
Hence the answer is 2455kms
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?
Solution
Total number of balls = 675
Number of cricket balls = 278
Number of footballs = 675 - 278 = 397
Number of footballs left = 110
Number of footballs sold = 397 - 110=287
Hence the answer is 287 footballs
30) A factory manufactures 300 cars each day. How many cars does the factory manufacture in 3 weeks?
Solution
Number of cars manufactures in a day = 300
number of days in a week = 7
Number of days in 3 weeks = 3*7=21
Number of cars manufactures in 3 weeks = 21*300
= 6300 cars
Hence the answer is 6300 cars
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.
Solution
Given
Its ones digit is the smallest prime number = 2
Its tens digit is seven more than its ones digit = 7+2 = 9
Its hundreds digit is 4th multiple of its ones digit = 4*2=8
Its thousand's digit is three less than its tens digit = 9-3=6
Hence the number is 6892
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
Solution
a) if a number is divisible by 5 then the units place must be either 5 or 0
but here given 4982 (unit place is 2)
that means remainder = 2
option a is correct
b) Rectangle has 2 lines of symmetry
So option b is also correct
c) 3 1/4 = 13/4
4 1/2 = 9/2
13/4 + 9/2 = 13/4 + 18/4 = 41/4 = 10 1/4
but given answer is 7 3/4 which is not correct
Hence the answer is c
33) Write in Roman Numerals
CMX - DXIV = _______?
Solution
CMX = 910
DXIV = 564
CMX - DXIV = 910 - 564 = 346
Hence the answer is 346
34) Select the odd one out.
a) A b) H c) Q d) U
Solution
A , H , U have a line of symmetry but Q doesn't have
Hence the odd one out is c) Q
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?
Solution
using the given information
Amudhan : He has only one boy behind him
1st 2nd 3rd 4th 5th
Amudhan
Mugilan : He is just before Amudhan
1st 2nd 3rd 4th 5th
Mugilan Amudhan
Nilan : He is not the first
Aarush : He is just after Chandru
Which means ( Nilan is not first, also Aarush and Chandru comes next to next), so Nilan must be in fifth position
1st 2nd 3rd 4th 5th
Chandru Aarush Mugilan Amudhan Nilan
Hence the answer is First => Chandru and last=>Nilan
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