Maths Olympiad Model Test Paper - 3 | Math Olympiad for Class 5 PDF Download

Ans: (b)

• The correct order of the words based on dictionary arrangement is determined by the first letter of each word.
• Starting with the first letters: S (Sacrifice), S (Scratch), S (Safety), S (Scare), S (Sample).
• Next, we look at the second letters: a (Sacrifice), c (Scratch), a (Safety), c (Scare), a (Sample).
• Following this, we find that Sacrifice comes first, followed by Safety, then Sample, Scare, and finally Scratch.
• Thus, the correct sequence is 1, 3, 5, 4, 2, which corresponds to option (b).

Ans: (c)

• When we reverse the digits of each number, we get:
• 184 becomes 481
• 567 becomes 765
• 764 becomes 467
• 408 becomes 804
• 715 becomes 517
• Among these reversed numbers, 804 (from 408) is the largest.

Ans: (d)

• The word POTASSIUM contains the letters P, O, T, A, S, S, I, U, M.
• When checking the options, STAMP, UPMOST, and MOIST can all be formed using these letters.
• However, the word ADOPT includes the letter D, which is not present in POTASSIUM.
• Thus, ADOPT cannot be formed from the letters of POTASSIUM.

Ans: (a) 
The number of doctors who are both players and artists is 3.

Ans: (a)

Ans: (a)

Ans: (c)

Ans: (d)

Ans: (d)

Ans: (d) 
The correct mirror image is as follows:

Ans: (c)

Single/smallest triangles : 10 
Contains 2 triangles : 8 
Contains 3 triangles : 2 
Contains 4 triangles : 1 
Contains 6 triangles : 1 
Totals : 10 + 8 + 2 + 1 + 1 = 22

Ans: (c) 
Here, 
6 pastries = 126 
1 pastries = 126/6 = 21 
Now, 1 Cup = 1 pastry – 1 
i.e. 1 cup = 21 – 1 = 20 
Therefore, 20 + 20 + 20 + 20 + 20 = 100.

Ans: (a) 
The number at the centre of each triangle equals the sum of the lower two numbers minus the top number.

Ans: (c)

Ans: (d)
As,

and

Ans: (b)

• To find the fraction of the balls that are white, we first need to determine the total number of balls in the bag.
• The total is 18 red balls + 12 white balls = 30 balls.
• Next, we find the fraction of the balls that are white: 12 white balls / 30 total balls.
• This simplifies to 2/5, which is the correct answer.

Ans: (c)

• To find the sum of Five million sixty-three thousand eighty-five (5,063,085) and Two million three thousand forty-nine (2,003,049), we add the two numbers together.
• The calculation is: 5,063,085 + 2,003,049 = 7,066,134.
• Thus, the correct answer is 7,066,134, which corresponds to option (c).
• This shows how simple addition can help us find the total of large numbers.

Ans: (c)

• The Roman numeral MCMLX represents the year 1960. This is calculated by breaking it down: M = 1000, CM = 900, and LX = 60.
• Option (a) is incorrect because MMDXL equals 2540, not 2560.
• Option (b) is wrong as CMLXVI equals 966, not 964.
• Option (d) is also incorrect since MDCIX equals 1609, not 1670.

Ans: (b)

• To find the largest 5-digit even number, we identify it as 99998.
• Next, we need to determine what to add to 99998 to equal 1,000,000.
• Calculating this gives us 1,000,000 - 99998 = 900002.
• Thus, the correct answer is 900002, which is option (b).

Ans: (d)

• To find the common multiples of 18 and 24, we first need to determine their least common multiple (LCM).
• The LCM of 18 and 24 is 72. This means that the common multiples are multiples of 72.
• Next, we find the multiples of 72 that are less than or equal to 100. The multiples are 72 and 144, but only 72 is within the range.
• However, we also need to consider the multiples of 72 that fit within the range of 1 to 100. The only valid multiple is 72 itself.
• Thus, there are 4 common multiples of 18 and 24 between 1 and 100: 72, 144, 216, and 288, but only 72 is counted here.

Ans: (b)

• To find the greatest 6-digit number, we need to arrange the digits 5, 2, 4, 1, 0, 6 in descending order.
• The largest arrangement is 654210. When rounding to the nearest hundred, we look at the last two digits (10), which rounds down to 654200.
• Thus, the answer is 654200, as it is the closest to the original number when rounded.

Ans: (a)

• From the equation R + R + R = 45, we can find R. Since there are three R's, we divide 45 by 3, giving us R = 15.
• Next, using Q × R = 135, we substitute R to find Q: Q × 15 = 135, which gives us Q = 9.
• Now, using P ÷ Q = 9, we can find P: P ÷ 9 = 9, leading to P = 81.
• Finally, we calculate (P × Q) – R: (81 × 9) – 15 = 729 – 15 = 714.

Ans: (b)

• The correct answer is option (b) because the numbers are arranged from the largest to the smallest.
• In this sequence, 8,50,76,745 is greater than 8,50,76,547, which is greater than 8,50,67,574, and finally 8,50,67,547 is the smallest.
• All other options do not maintain a consistent descending order.
• Understanding the concept of descending order means recognizing that each subsequent number must be less than the one before it.

Ans: (a)

• Let the amount of water in Tank B be x liters. Then, Tank A has 5x liters.
• After transferring y liters from Tank A to Tank B, Tank A will have (5x - y) liters and Tank B will have (x + y) liters.
• We want both tanks to have 45 liters, so we set up the equations: 5x - y = 45 and x + y = 45.
• Solving these equations, we find that y = 30 liters, meaning 30 liters must be transferred from Tank A to Tank B.

Ans: (c)

• The question asks for the correct conversion of measurements.
• In option (c), 89 L 75 mL is correctly converted to 89075 mL because 1 L equals 1000 mL.
• Other options either miscalculate or misrepresent the units, making them incorrect.
• Thus, option (c) is the only one that accurately represents the conversion.

Ans: (b)

Multiply by 42 in the ratio A : B : C, then  30 : 42 : 77 

Ans: (d)

Ans: (b)

Ans: (d)
XXXVI, 36.  
XX = 20  
V = 5 

Ans: (c)
Greatest 9 digit number = 999987640  
Smallest 9 digit number = 400006789  
Difference = 999987640 – 400006789  = 599980891

Ans: (c) 
Ten lakh three is written as 10,00,003.  
One million five thousand is written as  1,005,000.  
One million is written as 1,000,000  
One crore is written as 1,00,00,000  
The smallest number is 1,000,000 i.e., 1 million.

Ans: (b)

Ans: (d) 
Division of any whole number by zero is  not defined.

Ans: (d)
Let the numbers be x and y whose HCF is 48  
Then, HCF (x, y) = 48  
Then, numbers x and y will be some  multiples of 48.  
That is, the numbers x and y will be of the  form 48m and 48n respectively for some m  and n.  
Then, product of numbers = x.y = 48 m × 48 n = (48)² (mn)  
Then product of numbers must have (48)² as its factor. Since 4608/48 × 48 = 2 
Therefore, 4608 is the number which have (48)² as its factor.  
Hence, the product of numbers can be 4608. 

Ans: (b)

Ans: (a)

• The population of City Y is 80,51,310, while City X has 19,87,321.
• To find out which city has a larger population, we compare the two numbers.
• City Y is larger, and the difference in population is 80,51,310 - 19,87,321 = 60,63,989.
• Thus, the answer is that City Y has a larger population by 60,63,989.

Ans: (d)

• First, calculate the number of males: 3/7 of 210 equals 90 males.
• Next, to find the number of females, subtract the number of males from the total guests: 210 - 90 = 120 females.
• Thus, the total number of females at the party is 120.
• This means that the correct answer is option (d).

Ans: (c)

• On Monday, Disha studies for 3 hours and 40 minutes, which is 220 minutes in total.
• On Tuesday, she studies 25 minutes more, so that’s 220 + 25 = 245 minutes.
• Now, adding both days together: 220 minutes + 245 minutes = 465 minutes.
• Converting 465 minutes back to hours gives us 7 hours and 45 minutes.

Ans: (b)

• First, convert the total volume of ketchup from liters to milliliters: 4 L = 4000 mL, so 4 L 675 mL = 4675 mL.
• Next, divide the total volume by the daily usage: 4675 mL ÷ 55 mL/day = 85 days.
• This means Rashi will finish the ketchup in 85 days, which is the correct answer.
• Thus, the answer is option (b).

Ans: (d)

• To find out how many bricks were used for each chamber, we need to divide the total number of bricks by the number of chambers.
• So, we calculate: 7695940 bricks ÷ 70 chambers = 109942 bricks per chamber.
• This means that each chamber received an equal share of 109942 bricks.
• Thus, the correct answer is (d) 109942.

Ans: (b)

• The temperatures of the objects are: P = 35°C, Q = 42°C, and R = 21°C.
• To find the coldest object, we compare the temperatures.
• Among the three, R has the lowest temperature at 21°C, making it the coldest.
• Thus, the correct answer is (b) R.

Ans: (c)

• To find out how much more money Mr. Verma needs, we subtract the amount he has from the total cost of the flat.
• The total cost of the flat is ₹35,68,160 and he has ₹21,20,310.
• So, the calculation is: ₹35,68,160 - ₹21,20,310 = ₹14,47,850.
• This means Mr. Verma needs an additional ₹14,47,850 to buy the flat.

Ans: (d)

• The perimeter of a square is calculated by the formula: 4 × side.
• Here, the side of the park is 50 m, so the perimeter is 4 × 50 = 200 m.
• Karan walked around the park 6 times, so the total distance is 200 m × 6 = 1200 m.
• Thus, the total distance Karan walked that day is 1200 m.

Ans: (a)

• To find the total weight, we need to add the weights of onions, potatoes, and tomatoes together.
• Convert all weights to grams: 15 kg 200 g = 15200 g, 10 kg 50 g = 10050 g, and 25 kg 80 g = 25080 g.
• Now, add them: 15200 g + 10050 g + 25080 g = 50230 g.
• Convert back to kilograms and grams: 50230 g = 50 kg 230 g.
• Thus, the total weight is 50 kg 330 g, which is the correct answer.

Ans: (b)

• The Indian numbering system uses lakhs and crores instead of millions.
• The number nine million eighty-five thousand two hundred and forty-one translates to 90 lakh 85 thousand 241 in the Indian system.
• Thus, it is written as ₹90,85,241, which corresponds to option (b).
• Options (a), (c), and (d) do not represent the correct format for the Indian numbering system.

Ans: (b)

• Statement-I is incorrect because the correct sum of CMLIX (959) and MCMVII (1907) is 2866, not 2919.
• Statement-II is also incorrect; when a number is divided by itself, the quotient is 1 and the remainder is 0.
• Thus, both statements are false, making option (b) the correct choice.

Ans: (c)

• The one's digit is the smallest prime number, which is 2.
• The hundreds digit is the H.C.F. (Highest Common Factor) of 5 and 25, which is 5.
• The tens digit is 2 more than the hundreds digit, so it is 7 (5 + 2).
• The thousands digit is twice the lakhs digit. If we assume the lakhs digit is 1, then the thousands digit is 2.
• The ten thousands digit is the largest one-digit number, which is 9.
• The lakhs digit is the smallest factor of 15, which is 1.

Putting these together, we get the number 192572.

Ans: (c)

Ans: (d) Third angle = 180° – (36° + 36°)  
= 180° – 72° = 108° 
∴ Given triangle is an Isosceles obtuse triangle. 

Ans: (c) 
We know that, sum of an integer and its  additive inverse is zero.  
And additive inverse of –9 is 9  
So, P = 9