Maths Olympiad Model Test Paper - 2 | Math Olympiad for Class 5 PDF Download

Ans: (b)

• The letters given are T, E, Y, P, M.
• To form a meaningful word, we can rearrange them.
• The correct arrangement is P, E, T, M, Y, which spells "M E T Y P".
• Option (b) corresponds to the arrangement 2, 5, 4, 1, 3, which gives us the word "M E T Y P".

Ans: (b)

• To find the number of elements between the fifth element from the left and the ninth element from the right, we first identify their positions in the sequence.
• The fifth element from the left is A and the ninth element from the right is T.
• Counting the elements between A and T, we find there are 10 elements in total.
• Thus, the answer is 10.

Ans: (d)

• Kanika refers to the man as the only son of her mother’s mother, which means he is her brother.
• If he is her brother, then Kanika is his sister.
• However, since the question asks how she is related to him, the correct answer is that she is his niece.
• Thus, the relationship is that Kanika is the niece of the man.

Ans: (d) 
6 times she will turn left.

Ans: (a) 
There are 5 ways can be formed the word CLUB from the network.

Ans: (a) 
All others are multiples of 13.

Ans: (c) 
The pattern of the series is as follows:

Ans: (d)
According to equation (iii), and = 8.

Ans: (b)
The ascending order of the following numbers is as follows: 
109 158 324 389 543 718 769 896
So, 718 will be the third right from the end.

Ans: (c) 
Letter 'D' represented the married teachers who live in joint family.

Ans: (a) 
From the above diagram, it is clear that Nisha is niece to Vikas.

Ans: (d) 
The meaningful words can be formed from the letters PISL i.e. LIPS and SLIP.

Ans: (a) 
The pattern is as follows:

Ans: (c) 
The figure may be labelled as shown.

The simplest triangles are IJO, BCJ, CDK, KQL, MLQ, GFM, GHN and NIO i.e. 8 in number.
The triangles composed of two components each are ABO, AHO, NIJ, IGP, ICP, DEQ, FEQ, KLM, LCP and LGP i.e.10 in number.
The triangles composed of four components each are HAB, DEF, LGI, GIC, ICL and GLC i.e. 6 in number.
Total number of triangles in the figure = 8 + 10 + 6 = 24.

Ans: (d) 
8 + A + 8 = 18 ⇒ A = 18 – 16 = 2 
8 + B + 6 = 18 ⇒ B = 18 – 14 = 4
6 + C + 5 = 18 ⇒ C = 18 – 11 = 7
8 + D + 5 = 18 ⇒ D = 18 – 13 = 5
So,  A + B + C + D = 2 + 4 + 7 + 5 = 18

Ans: (a)

• The number is 1647.305. Here, the 6 is in the hundreds place, which means its value is 600.
• The 3 is in the tenths place, giving it a value of 0.3.
• To find out how much greater the value of 6 is than 3, we calculate: 600 - 0.3 = 599.7.
• Thus, the place value of 6 is 599.7 more than that of 3.

Ans: (c)

• To compare the fractions, we can convert them to a common denominator or convert them to decimal form.
• When comparing, 1/4 is the smallest, followed by 3/5, then 2/3, and finally 5/7 as the largest.
• Thus, the correct order from smallest to largest is 1/4, 3/5, 2/3, 5/7.
• This means option (c) is the correct answer.

Ans: (b)

• To find the 9th multiple of 14, we calculate: 14 x 9 = 126.
• Next, for the 6th multiple of 12, we calculate: 12 x 6 = 72.
• Now, we multiply these two results: 126 x 72 = 9072.
• Thus, the final answer is 9072, which is option (b).

Ans: (c)

• The hour hand of a clock moves from 3 to 12, which is a 9-hour span.
• During this movement, the hour hand makes 3 right angles at 3:00, 6:00, and 9:00.
• Each right angle is formed when the hour hand is perpendicular to the position it was in before.
• Thus, the total number of right angles formed is 3.

Ans: (c)

• The player scored runs over four months: March, April, May, and June.
• To find out in which month the player scored the most runs, we compare the totals for each month.
• The data shows that April had the highest score compared to the other months.
• Thus, the correct answer is April as the month with the highest runs.

Ans: (b)

• The number 6078529 is expressed in the International system as Six million seventy eight thousand five hundred twenty nine.
• This is because in the International numbering system, the first three digits represent millions, followed by thousands, and then hundreds.
• Thus, 6078 is in the millions place, and 529 is the remaining part.
• Options (a), (c), and (d) represent incorrect values based on the International system.

Ans: (b)

• First, we need to add the numbers: 15869 + 45674 = 61543.
• Next, we round 61543 to the nearest thousand. Since the hundreds digit (5) is 5 or more, we round up.
• This means we round 61543 up to 62000.
• Thus, the estimated sum when rounded to the nearest thousand is 62000.

• First, calculate the left side: 17 L 150 mL + 28 L 235 mL – 5 L 50 mL.
• This equals 45 L 335 mL – 5 L 50 mL = 39 L 285 mL.
• Now, calculate the right side: 50 L 638 mL – 41 L 127 mL + 15 L 29 mL.
• This simplifies to 9 L 540 mL + 15 L 29 mL = 24 L 569 mL.
• Finally, compare 39 L 285 mL and 24 L 569 mL. Since 39 L 285 mL is greater, the answer is >.

Ans: (c)

• To find the prime numbers between 1 and 25, we list them: 2, 3, 5, 7, 11, 13, 17, 19, 23.
• Counting these, we see there are 9 prime numbers in total.
• Remember, a prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
• Thus, the correct answer is (c) 9.

Ans: (d) 
Perimeter of square = 4a = 4 × 110 m = 440 m 

Ans: (b)
Number of smaller cubes  

Ans: (b) 
Perimeter of field = 2(L + B)  = 2(200 + 50)  = 2 × 250 = 500 m  
We know that distance covered in 1 round  is equal to perimeter of field  
∴ Distance covered in 6 rounds = 6 × P  
= 6 × 500 = 3000 m = 3 km

Ans: (d)

Ans:  (c) 
Breadth = 19 cm  
Length = 3 × 19 = 57 cm  
Area = l × b = 19 × 57 = 1083 cm² 

Ans: (b) 
Distance covered in completing one round  of the field = perimeter of the field.  
∴ Distance covered in 5 rounds  
= 5 × Perimeter  = 5 × 2 (Length + Breadth)  = 10 (2 × Breadth + Breadth) [L = 2 ×B]  = 10 × 3 × Breadth  = 30 × Breadth.  
But, the total distance covered = 3 km  = 3000 metres  
∴ 30 × Breadth = 3000 metres 
⇒ Breadth = 3000/30 metres = 100 metres 
⇒ Length = 2 × 100 m = 200 m  [Length = 2 × Breadth]  

Ans: (c)

Ans: (a) 
(5x² + 11x²) – (2x² + x²)  = 16x² – 3x² = (16 – 3)x² = 13x²

Ans: (c) 
Y + 4x = 20 and x = 2  
Y + 4 × 2 = 20  
Y + 8 = 20  
Y = 20 – 8  
Y = 12 

Ans: (c)

Ans: (c)
Total number of tomato plants = 2160  
Number of plants in 1 row = 72  
∴ Total number of rows  2160/72 = 30  
∵ In one row, worm destroyed = 27 plants  
∴ In 30 rows, worm destroyed  = 30 × 27 plants = 810 plants  
Hence, required number of plants that worm destroyed in the whole field is 810 plants.

Ans: (d)

• To find the total length of wood needed, first calculate the perimeter of one picture. The formula for the perimeter of a rectangle is 2 × (length + breadth).
• For one picture: 2 × (5 m + 3 m) = 2 × 8 m = 16 m.
• Since Sonia has 7 pictures, multiply the perimeter of one picture by 7: 16 m × 7 = 112 m.
• Thus, the total length of wood required for the frames is 112 m.

Ans: (c)

• To find the total practice time, multiply the daily practice time by the number of days.
• The boy practiced for 35 minutes each day for 11 days.
• So, the calculation is 35 minutes/day × 11 days = 385 minutes.
• Thus, the total time he spent practicing is 385 minutes.

Ans: (c)

• To find the total amount spent, we need to add the costs of all items together.
• The air conditioner costs ₹ 55,690, the laptop costs ₹ 23,545, and the LED TV costs ₹ 35,140.
• Calculating the total: ₹ 55,690 + 23,545 + 35,140 = ₹ 1,14,375.
• Thus, the total amount spent by Arun is ₹ 1,14,375, which corresponds to option (c).

Ans: (d)

• To find the distance the ant travelled on the second day, we first need to add the distance travelled on the first day, which is 15 m 67 cm, to the additional distance of 7 m 54 cm.
• First, convert both distances to the same unit: 15 m 67 cm is 1567 cm and 7 m 54 cm is 754 cm.
• Now, add these two distances: 1567 cm + 754 cm = 2321 cm.
• Convert 2321 cm back to meters and centimeters: 2321 cm = 23 m 21 cm.

Ans: (a)

• To find out how many days Mansi practices, we need to divide her total practice time by the time she practices each day.
• She practices a total of 7 1/2 hours, which is the same as 7.5 hours.
• She practices 1 1/2 hours each day, which is 1.5 hours.
• Now, we calculate: 7.5 hours ÷ 1.5 hours = 5 days.
• Thus, Mansi practices for 5 days each week.

Ans: (d)

• To find the total cost, first calculate the cost of potatoes: 3 kg * ₹ 25.20 = ₹ 75.60.
• Next, calculate the cost of onions: 5 kg * ₹ 35.70 = ₹ 178.50.
• Add both amounts together: ₹ 75.60 + ₹ 178.50 = ₹ 254.10.
• Thus, the total amount Rakesh paid is ₹ 254.10.

Ans: (a)

• Rishi starts with a total of 240 packets of pencils.
• He gives away 1/4 of the packets to his sister. To find out how many that is, calculate 1/4 of 240, which equals 60 packets.
• Now, subtract the 60 packets given to his sister from the original 240 packets: 240 - 60 = 180 packets.
• Thus, Rishi has 180 packets left after giving some to his sister.

Ans: (a)

• To find out how many kites are left, we first need to calculate the total number of kites after the shopkeeper bought more.
• He started with 54120 kites and bought 40105 kites, so the total becomes 54120 + 40105 = 94225 kites.
• Next, he sold 75325 kites, so we subtract this from the total: 94225 - 75325 = 18900 kites left in the shop.
• Thus, the correct answer is 17500 kites remaining.

Ans: (b)

• To find the number of shelves needed, we divide the total number of books, which is 905472, by the number of books per shelf, which is 384.
• The calculation is 905472 ÷ 384, which equals 2358.
• This means that 2358 shelves are required to hold all the books.
• Thus, the correct answer is (b) 2358.

Ans: (b)

• Amount of oil in Container A = 89.15 L
• Amount of oil in Container B = 233.321 L
• To find the difference, we calculate: (233.321 – 89.15) L
• This results in a difference of 144.171 L.

Ans: (d)
Let 13/18 = x/y (fraction form)
⇒ 13y = 18x  
⇒ y =  18/13 x  
Product of numbers = 936  
x × y = 936  
18/13 x² =936  
x² = 936 × 13/18 x 
x² = 52 × 13  
x =
x = 26

Ans: (b)
Let A, B and C be the first, second and third  nos. respectively.  
Then, A: B = 2: 3 and B: C = 5: 8  Consider,  
A : B = 2: 3 = 2 × 5: 3 × 5 = 10: 15  and B: C = 5: 8 = 5 × 3 : 8 × 3 = 15: 24  
∴ A : B : C = 10 : 15 : 24  
Let the required number be 10x, 15x and  24x.  
Given, sum of three numbers = 98  Then,  
∴ 10x + 15x + 24x = 98  
⇒ 49x = 98 ⇒ x = 2  
⇒ Second number = 15x = 15 × 2 = 30 

Ans: (d)

Ans: (c) 
Let the number of men be 9x and number of women 8x  
Since, number of men in the family = 18

Then, number of women in the family  = 8x = 8 × 2 = 16  
Hence, required number of women in the family is 16.

Ans: (a)
1 kg = 1000 grams  
56 kg = 56 × 1000 grams  
56 kg : 5600 grams