Maths Olympiad Model Test Paper - 1 - Math Olympiad for Class 5 PDF Download
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Note: The questions provided in this document are similar to the questions that were asked in the actual Olympiad exam. So, we recommend you study these for your Olympiad preparation
Logical Reasoning
Q1: Sujata is younger than Mehak and older than Sonia. Rekha is younger than Sonia. Palak is older than Mehak, who is older than Sujata. Who is the youngest among them?
(a) Rekha
(b) Sonia
(c) Mehak
(d) Palak
View Answer 
Ans: (a)
- To determine the youngest person, we analyze the relationships:
- Sujata is younger than Mehak but older than Sonia, meaning Sonia is the youngest so far.
- Rekha is younger than Sonia, making Rekha the youngest among them.
- Palak is older than Mehak, who is older than Sujata, confirming that Rekha is indeed the youngest overall.
Q2: Which of the following elements is 6th to the right of the 6th element from the left end in the given arrangement?
M 3 # K I 7 $ N S 1 % J P 5 @ B A
(a) 1
(b) %
(c) J
(d) 5
View Answer Ans: (b)
- First, identify the 6th element from the left in the sequence: M, 3, #, K, I, 7. The 6th element is 7.
- Next, count 6 positions to the right of 7: 7 (1), $ (2), N (3), S (4), 1 (5), % (6).
- Thus, the element that is 6th to the right of the 6th element from the left is %.
Q3: Some letters are given which are numbered 1, 2, 3, 4, 5, and 6 followed by four options containing combinations of these numbers. Find the combination of numbers so that letters are arranged accordingly to form a meaningful English word.
(a) 2, 5, 3, 4, 1, 6
(b) 5, 6, 2, 3, 1, 4
(c) 4, 2, 6, 5, 1, 3
(d) 4, 2, 6, 5, 3, 1
View Answer Ans: (d)
- The letters E, H, N, T, O, R can be rearranged to form the word "THORN".
- The correct combination of numbers that corresponds to this arrangement is 4, 2, 6, 5, 3, 1.
- This means the letters are arranged as follows: T (4), H (2), O (6), R (5), N (3).
- Thus, the answer is option (d) which correctly forms a meaningful word.
Q4: Study the diagram and identify the people who can speak only one language.
(a) E
(b) G
(c) G + F + E
(d) A + B + C
View Answer Ans: (c)
The people who can speak only one language is G + F + E.
Q5: Choose the option which gives the correct order of the letters as indicated by the numbers to form words.
(a) 3, 4, 2, 1, 5
(b) 3, 1, 2, 5, 4
(c) 2, 3, 1, 4, 5
(d) 4, 2, 1, 3, 5
View Answer Ans: (a)
The given letters, when arranged in the order 3, 4, 2, 1, 5 form the word 'LEMON'.
Q6: Shivam has a set of Red, Blue and White marbles.
- The Red marbles make up exactly 1/2 of the set.
- The set has 2 White marbles.
- The number of Blue marbles is twice the n umber of White marbles.
How many marbles are there in Shivam's set?
(a) 12
(b) 6
(c) 8
(d) 4
View Answer Ans: (a)
Number of White marbles = 2
Number of Blue marbles = 2 × 2 = 4
Total number of Blue and White marbles = 4 + 2 = 6
Total marbles (n) = n = 1/2 × n + 6 n = 6 × 2 = 12 marbles.
Q7: Find the mirror image of each of given figure (X).
(a) 
(b) 
(c) 
(d) 
View Answer Ans: (c)
The mirror image is as follows:
Q8: Identify which figure has the following shape hidden in it.
(a) 
(b) 
(c) 
(d) 
View Answer Ans: (b)
Q9: Find the odd letters from the given responses.
(a) ORQP
(b) OLNM
(c) WZYX
(d) PSRQ
View Answer Ans: (b)
As,
Q10: Study the following information and answer the questions based on it.
A, B, C, D and E are five boys sitting in a circle facing the centre. C is seated immediately to the left of E. A is sitting between D and E.
Who is sitting third to the right of E?
(a) A
(b) C
(c) B
(d) D
View Answer Ans: (c)
B is sitting third to the right of E.
Q11: A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
(a) 150
(b) 182
(c) 157
(d) 156
View Answer Ans: (c)
The pattern is as follows:
Q12: Arrange the words according to Dictionary.
1. Knock
2. Kinetic
3. Knockout
4. Knowledge
5. Known
(a) 2, 1, 3, 4, 5
(b) 1, 3, 2, 5, 4
(c) 4, 3, 1, 5, 2
(d) 3, 2, 1, 4, 5
View Answer Ans: (a)
Q13: In the following figure, the boys who are athletes and disciplined are indicated by which number?
(a) 4
(b) 2
(c) 6
(d) 5
View Answer Ans: (b)
The boys who are athletes and disciplined are indicated by number '2'.
Q14: A word is given in capital letters. It is followed by four words. Out of these four words, three cannot be formed from the letters of the word in capital letters. Point out the word that can be formed.
ALTERNATIVES
(a) TELEVISION
(b) RENOVATE
(c) RESPITE
(d) TRAINS
View Answer Ans: (d)
TRAINS can be formed from the letters of the given word.
Q15: One doughnut weighs as much as ___________ blocks.
(a) 10
(b) 15
(c) 17
(d) 12
View Answer Ans: (d)
Here, 1 cylinder weighs as much as 2 boxes, so 3 cylinders weigh as much as 6 boxes. The remaining boxes equal to 6, which is equal to the weight of half a doughnut, so 1 doughnut should weigh around 12 boxes.
Mathematical Reasoning
Q16: I think of a decimal number. Add 3.4 to it. Subtract 2.5 from the sum obtained. Multiply the result obtained by 3, I get 9 as the answer. Find the decimal number.
(a) 0.21
(b) 2.1
(c) 21.0
(d) 0.15
View Answer Ans: (b)
- Let the decimal number be x.
- First, we add 3.4 to x, giving us x + 3.4.
- Next, we subtract 2.5 from this sum: (x + 3.4) - 2.5 = x + 0.9.
- Then, we multiply the result by 3: 3(x + 0.9) = 3x + 2.7.
- According to the problem, this equals 9: 3x + 2.7 = 9.
- Solving for x, we subtract 2.7 from both sides: 3x = 6.3.
- Finally, dividing by 3 gives us x = 2.1.
Q17: Which of the following fractions is listed from largest to smallest?
(a) 3/7, 7/8, 5/6, 2/3
(b) 7/8, 5/6, 2/3, 3/7
(c) 2/3, 3/7, 7/8, 5/6
(d) 3/7, 2/3, 5/6, 7/8
View Answer Ans: (b)
- To determine the largest to smallest fractions, we need to compare their values.
- When comparing, 7/8 is the largest, followed by 5/6, then 2/3, and finally 3/7 as the smallest.
- Thus, the correct order from largest to smallest is 7/8, 5/6, 2/3, 3/7.
- This makes option (b) the correct answer.
Q18: What is the total of all the prime factors of 145?
(a) 35
(b) 41
(c) 34
(d) 29
View Answer Ans: (c)
- The prime factors of 145 are 5 and 29.
- To find the sum, we add these factors: 5 + 29 = 34.
- Thus, the total of all the prime factors of 145 is 34.
- Therefore, the correct answer is (c).
Q19: Compare and fill the box. 
(a) >
(b) <
(c) =
(d) Can’t be determined
View Answer Ans: (b)
- Since 965 is less than 1245, we can conclude that CMLXV is smaller than MCCXLV.
- Thus, the correct symbol to fill in the box is <.
- This means CMLXV is less than MCCXLV.
- To compare CMLXV (which is 965) and MCCXLV (which is 1245), we need to look at their numerical values.
Q20: What is the unknown value in the following mathematical equation?
0.25 × 12 = 0.25 × 3 + 0.25 × 3 + 0.25 × 
(a) 2
(b) 3
(c) 6
(d) 10
View Answer Ans: (c)
- To solve for the missing value, we start with the equation: 0.25 × 12 = 0.25 × 3 + 0.25 × 3 + 0.25 × ?.
- Calculating the left side gives us 0.25 × 12 = 3.
- The right side simplifies to 0.25 × 3 + 0.25 × 3 = 0.75 + 0.25 × ?.
- Setting both sides equal: 3 = 0.75 + 0.25 × ?. Subtracting 0.75 from both sides gives us 2.25 = 0.25 × ?.
- Dividing both sides by 0.25 results in ? = 2.25 / 0.25 = 9, which is incorrect. The correct approach is to realize that 0.25 × 6 = 1.5, thus ? must equal 6 to balance the equation.
Q21: What value should replace (P) in the equation? 
(a) 4 kg 260 g
(b) 4 kg 26 g
(c) 4 kg 206 g
(d) 14 kg 62 g
View Answer Ans: (b)
- To find the value of (P), we first need to add the weights on the left side: 4 kg 312 g and 8 kg 204 g.
- When we add these, we get 12 kg 516 g (since 312 g + 204 g = 516 g).
- Now, we set up the equation: 12 kg 516 g + (P) = 16 kg 542 g.
- To isolate (P), we subtract 12 kg 516 g from 16 kg 542 g, which gives us 4 kg 26 g.
Q22: A bottle contains 350 mL of protein shake. It is distributed equally into several glasses. If each glass holds 50 mL of protein shake, how many glasses can be filled?
(a) 6
(b) 7
(c) 9
(d) 5
View Answer Ans: (b)
- To find out how many glasses can be filled, we need to divide the total volume of the protein shake by the volume of each glass.
- We have 350 mL of protein shake and each glass holds 50 mL.
- So, we calculate: 350 mL ÷ 50 mL = 7 glasses.
- This means we can fill 7 glasses with the protein shake.
Q23: The four angles of a quadrilateral are given as: 108, 65,76, and x. Find the value of x.
(a) 249º
(b) 111º
(c) 200º
(d) 105º
View Answer Ans: (b)
Sum of all interior angles of a quadrilateral is 360º.
⇒ 108º + 65º + 76º + x = 360º
⇒ x = 360º – 249º = 111º
24: Vertical angles are _______ right angles.
(a) always
(b) never
(c) sometimes
(d) can not say
View Answer Ans: (c)
Q25: Write the integer that is greater than 32 by 89
(a) 131
(b) 141
(c) 151
(d) 121
View Answer Ans: (d) 32 + 89 = 121
Q26: The value of 100 + (–75) + (–89) + (69) is _______.
(a) 169
(b) 5
(c) 164
(d) –5
View Answer Ans: (b)
We have, 100 + (–75) + (–89) + 69 Rearranging the terms, we get (100 + 69) + (–75) + (–89) = 169 + (–164) = 169 – 164 = 5
Q27: The absolute value of –58 is
(a) 50
(b) –58
(c) 58
(d) 0
View Answer Ans: (c)
Absolute value of a number is its numerical value with positive sign.
Q28: How many negative integers are there between - 6 and 6?
(a) 5
(b) 6
(c) 11
(d) 12
View Answer Ans: (a)
The negative integers between –6 and 6 are –5, –4, –3, –2, –1.
Q29: Find the value of: –12 + (–98) – (–84) + (–7)
(a) –33
(b) –35
(c) –34
(d) –36
View Answer Ans: (a)
–12 + (–98) – (–84) + (–7)
= –12 – 98 + 84 – 7
= (–12 – 98 – 7) + 84
= –117 + 84 = –33
Q30: What fraction will come in place of *? 
(a) 8/18
(b) 9/100
(c) 10/81
(d) 9/121
View Answer Ans: (b)
In given series, numerators form a series of odd numbers while denominators form a series of squares of even numbers.
Fraction in place of * = 9/102 = 9/100
Q31: Denominator of a fraction is 6 greater than its numerator. If the sum of the denominator and the numerator is 16, find the fraction.
(a) 5/11
(b) 7/13
(c) 8/14
(d) 2/8
View Answer Ans: (a)
Denominator of fraction is 6 greater than numerator.
D = N + 6
The sum of denominator and numerator is 16.
D + N = 16
Adding 6 both side
D + N + 6 = 16 + 6
D + D = 22
2D = 22
D = 22/2 = 11
Since, D + N = 16
11 + N = 16
N = 16 – 11 = 5
Then, denominator = 11 and numerator = 5.
Hence, fraction is 5/11.
Q32: 16.37 and 18.97 are
(a) like decimal fractions
(b) Unlike decimal fractions
(c) equivalent decimal fractions
(d) None of these
View Answer Ans: (a)
Q33: Simplify: 35 – 5 [2 + 3 {2 – 2 (5 – 3) + 5} – 10] ÷ 4
(a) 35
(b) 25
(c) 33.85
(d) 33.75
View Answer Ans: (d)
35 – 5 [2 + 3 {2 – 2 (5 – 3) + 5} – 10] ÷ 4
= 35 – 5 × 1 ÷ 4 = 35 – 5/4
= 35 – 1.25 = 33.75
Q34: The cost of 1 litre milk is ₹ 7.50 then the cost of 30.5 litres milk is
(a) ₹ 225.75
(b) ₹ 223.75
(c) ₹ 228.75
(d) ₹ 243.60
View Answer Ans: (c)
Cost of 1 litre milk = ₹7.50
Cost of 30.5 litres of milk = ₹(7.50 × 30.5)
= ₹ 228.75
Q35: Convert 56098 ml into litre
(a) 56.098 L
(b) 55.980 L
(c) 50.670 L
(d) 51.453 L
View Answer Ans: (a) 56098/1000 = 56.098 litres.
Everyday Mathematics
Q36: Each level of a structure has 20 doors. The building consists of 12 levels. There are 25 buildings in total within a complex. Determine the overall number of doors installed in the complex.
(a) 2400
(b) 3000
(c) 6000
(d) 5000
View Answer Ans: (c)
- To find the total number of doors, first calculate the doors per building: 20 doors/floor * 12 floors = 240 doors/building.
- Next, multiply the number of doors in one building by the total number of buildings: 240 doors/building * 25 buildings = 6000 doors.
- Thus, the total number of doors fitted in the complex is 6000.
Q37: Aira runs 165.395 km in 5 hours. How much distance did she run in 1 hour?
(a) 31.152 km
(b) 33.079 km
(c) 32.065 km
(d) 30.672 km
View Answer Ans: (b)
- To find the distance Aira ran in 1 hour, we need to divide the total distance by the total time.
- The total distance is 165.395 km and the total time is 5 hours.
- So, we calculate: 165.395 km ÷ 5 hours = 33.079 km.
- This means Aira ran 33.079 km in 1 hour.
Q38: Aakash has a photo frame in the shape of a triangle. The measure of its sides are 35 cm, 28 cm, and 32 cm. A design is made with the ribbon around all sides of the frame. Find the total length of the ribbon used to make the design.
(a) 75 cm
(b) 95 cm
(c) 94 cm
(d) 70 cm
View Answer Ans: (b)
- To find the total length of the ribbon, we need to add the lengths of all sides of the triangle.
- The sides are 35 cm, 28 cm, and 32 cm.
- Calculating the total: 35 + 28 + 32 = 95 cm.
- Thus, the total length of the ribbon used is 95 cm.
Q39: Beena saves ₹0.55 every day. What will be her total savings after two weeks?
(a) ₹3.85
(b) ₹5.50
(c) ₹6.60
(d) ₹7.70
View Answer Ans: (d)
- Beena saves ₹0.55 daily.
- In two weeks, there are 14 days.
- Total savings = ₹0.55 × 14 = ₹7.70.
- Thus, her total savings after two weeks will be ₹7.70.
Q40: The number of males in a country is 6,73,248 and the number of females is 5,43,215. If the total population is 14,90,775, then find the number of children in that country.
(a) 3,64,123
(b) 2,74,312
(c) 2,34,712
(d) 3,12,643
View Answer Ans: (b)
- To find the number of children, we first need to calculate the total number of adults (males and females combined).
- The total number of adults is 6,73,248 (males) + 5,43,215 (females) = 12,16,463.
- Now, we subtract the total number of adults from the total population: 14,90,775 - 12,16,463 = 2,74,312.
- Thus, the number of children in the country is 2,74,312.
Q41: Ankita's sister attends Kathak dance classes on Tuesday, Thursday, and Saturday each week. If each class is 50 minutes long, what is the total time she practiced Kathak dance over three weeks?
(a) 7 hrs 30 mins
(b) 7 hrs 35 mins
(c) 6 hrs 35 mins
(d) 8 hrs 45 mins
View Answer Ans: (a)
- She has classes on Tuesday, Thursday, and Saturday, which means she attends 3 classes per week.
- Each class lasts 50 minutes, so in one week, she practices for 3 x 50 = 150 minutes.
- Over three weeks, the total practice time is 3 x 150 = 450 minutes.
- Converting 450 minutes into hours gives us 7 hours and 30 minutes.
Q42: A vendor sold 1 kg of potatoes for ₹40, 1 kg of tomatoes for ₹60, and 1 kg of onions for ₹65. He sold 15 kg of potatoes, 26 kg of tomatoes, and 35 kg of onions in a week. Calculate his total earnings for that week.
(a) ₹3245
(b) ₹4235
(c) ₹3475
(d) ₹4435
View Answer Ans: (d)
- To find the total earnings, we first calculate the earnings from each type of vegetable:
- Potatoes: 15 kg * ₹40 = ₹600
- Tomatoes: 26 kg * ₹60 = ₹1560
- Onions: 35 kg * ₹65 = ₹2275
- Now, we add these amounts together: ₹600 + ₹1560 + ₹2275 = ₹4435.
- Thus, the vendor earned a total of ₹4435 in that week.
Q43: Prachi begins her trip on 28th July at 3:00 P.M. and arrives at her destination on 2nd August at 11:15 A.M. What is the total duration of her journey?
(a) 4 days 20 hrs 15 mins
(b) 5 days 20 hrs 15 mins
(c) 4 days 19 hrs 45 mins
(d) 5 days 19 hrs 45 mins
View Answer Ans: (a)
- To calculate the total time taken, we first find the start and end times: 28th July 3:00 P.M. to 2nd August 11:15 A.M.
- From 28th July to 2nd August is 4 full days.
- From 3:00 P.M. to 11:15 A.M. the next day is 20 hours and 15 minutes.
- Adding these together gives a total of 4 days, 20 hours, and 15 minutes for the journey.
Q44: A monkey climbs up a wall 1.8 km high. He suddenly slips down and falls by 900 m where he finds support. How high is he from the ground?
(a) 27 km
(b) 270 m
(c) 0.9 km
(d) 18 m
View Answer Ans: (c)
Required height =(1.8 – 0.9) km = 0.9 km
Q45: If 50 metre long horizontal line is divided into 4 equal parts using a compass and name of the divided points from starting point are A, B, C, D and E. Find the length AD.
(a) 32.40 m
(b) 37.50 m
(c) 30.75 m
(d) None of these
View Answer Ans: (b)
Since AB = BC = CD = DE
∴ AB = 1/4 AE
= 1/4 × 50m = 12.5m
Hence AD = 3 × AB = 3 × 12.5 m = 37.50 m
Achievers Section
Q46: In a town, there are two car manufacturing companies. The number of cars produced by one company is 4,50,370 and the number of cars produced by the other company is 3,17,398. (a) What is the total number of cars produced by both companies? (b) How many fewer cars does the second company produce than the first one?
(a) 654348
(b) 132972
(c) 767768
(d) 721398
View Answer Ans: (c)
- To find the total number of cars manufactured, we add the cars from both companies: 4,50,370 + 3,17,398 = 7,67,768.
- To determine how many fewer cars the second company manufactures than the first, we subtract: 4,50,370 - 3,17,398 = 1,32,972.
- The total number of cars produced is 767768, which is the correct answer.
- The difference in production between the two companies is 132972, confirming the calculations.
Q47: A brick is broken down into two pieces in such a way that each is 0.937 m long. What would be the total length of the brick?
(a) 2.784 m
(b) 1.349 m
(c) 1.874 m
(d) 1.972 m
View Answer Ans: (c)
Total length of the brick
= 0.937 + 0.937
= 2 × 0.937
= 1.874 m
Q48: Representation of data in tabular form is done by using ______.
(a) Bar graph
(b) Frequency
(c) Tally marks
(d) None of these
View Answer Ans: (c)
Q49: The sum of face values of 4 in 3541 and 7614 is:
(a) 6
(b) 18
(c) 8
(d) 21
View Answer Ans: (c)
Face value of 4 in 3541 is = 4
Face value of 4 in 7614 is = 4
Sum of face values of 4 in 3541 and 7614 = 4 + 4 = 8
Q50: What is the difference between the greatest six digit number and the smallest six digit number?
(a) 999990
(b) 899990
(c) 989990
(d) 899999
View Answer Ans: (d) We know that,
The greater six digit number = 999999
The smallest six digit number = 100000
Required difference = 999999 – 100000 = 899999
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