Mathematics Olympiad Model Test Paper - 3 | Mathematics Olympiad Class 7 PDF Download

Ans: (d)

• Aman drives 4 km East.
• He then turns left (North) and drives 12 km.
• Next, he turns right (East) and drives 10 km.
• After that, he turns left (North) and drives 8 km.
• Finally, he turns left (West) and drives 14 km.
• To find the total distance, we add all the distances: 4 + 12 + 10 + 8 + 14 = 48 km.

Ans: (b)

Ans: (b)

• The code for 'BREAK' to 'FOIXO' involves a specific pattern of shifting letters. Each letter in 'BREAK' is shifted by a certain number of positions in the alphabet.
• For example, 'B' becomes 'F', which is a shift of +4 positions, 'R' becomes 'O' with a shift of -3, and so on.
• Applying the same pattern to 'TRACK', we find that it translates to 'XOEZO'.
• This consistent shifting method is the key to decoding the words in this language.

Ans: (a)

• To understand the relationship, let's break it down: Reemal's "only son's father" is Reemal's husband.
• Therefore, the lady in the photograph is the mother of Reemal's husband, making her Reemal's mother-in-law.
• This means Reemal is related to the lady as her daughter-in-law.
• Thus, the correct answer is (a) Mother-in-law.

Ans: (a)

• First, replace the symbols with their respective operations: 12 × 256 ÷ 32 + 44 – 34.
• Next, perform the calculations step by step: 12 × 256 = 3072.
• Then, divide: 3072 ÷ 32 = 96.
• Now, add: 96 + 44 = 140.
• Finally, subtract: 140 – 34 = 106.

Thus, the final answer is 106.

Ans: (d)Marks obtained in first 75 questions
∴ Marks to be obtained in next 75 questions = 90 – 60 = 30
∴ % of questions to be answered correctly

Ans: Take Unit Price

∴ it is +ve. So the gain is 21%.

Ans:  (c)
A square pyramid has 5 faces, 8 edges, and 5 vertices.
So, 5+5−8=2.

Ans: (b)
A square with the same side length as of triangle.

Ans: (c)

• To find the answer, we need to identify the symbols that meet the criteria of being preceded by a number and followed by a letter.
• Count each occurrence where a number comes before a symbol and a letter comes after it.
• After analyzing the arrangement, we find that there are a total of 5 such symbols.
• Thus, the correct answer is 5.

Ans: (c) Actual length of a painting = 2 m = 200 cm
Scale used = 1 mm : 20 cm
Length of painting in photograph:

Ans: (a)
The x-coordinate of a point lies on y-axis is 0, for example (0, 3) lies on y-axis.

Ans: (a)
y-coordinate of a point on x-axis is zero.

Ans: (b)

• To find the total amount Amit will repay, we first calculate the simple interest using the formula: Simple Interest = Principal x Rate x Time.
• Here, the Principal is ₹ 4800, the Rate is 8% (or 0.08), and the Time is 4 years.
• Calculating this gives: Simple Interest = ₹ 4800 x 0.08 x 4 = ₹ 1536.
• Now, to find the total amount to be repaid, we add the Simple Interest to the Principal: Total Amount = ₹ 4800 + ₹ 1536 = ₹ 6336.

Ans: (c)
Let maximum marks be 
So 40% of x = 80

Ans: (d)

• To determine if a triangle is a right-angled triangle, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
• For option (d), we check: 26^2 = 24^2 + 10^2.
• This simplifies to 676 = 576 + 100, which is true since 676 = 676.
• Thus, the sides 26 cm, 24 cm, and 10 cm form a right-angled triangle.

Ans: (b)

• First, we need to add the two expressions: ( x²y² + y²z + 4 ) and ( -y²z + 3y² + z² ).
• This results in: x²y² + 4y² + z² + 4.
• Next, we subtract ( 8y² + 4x²y² - 2z² ) from this sum.
• After performing the subtraction, we simplify to get: 3z² - 3x²y² - 5y² + 4.
• Thus, the final answer is option (b).

Ans: (b)

Ans: (d)

• There are infinite rational numbers between any two distinct numbers on the number line.
• In this case, between ( -7/8 ) and ( -1/4 ), you can find many fractions like ( -3/4 ), ( -5/8 ), ( -1/2 ), etc.
• Since you can always find more fractions by taking averages or dividing intervals, the number of rational numbers is not limited.
• Thus, the correct answer is that there are infinite rational numbers between these two values.

Ans: (b)

Ans: (a)

• First, calculate 1.86 ÷ 0.3, which equals 6.2.
• Next, find (19.3 - 14.5), resulting in 4.8, and then calculate 1/6 x 4.8, which gives 0.8.
• Now, compute 0.3 x 6.8, resulting in 2.04.
• Finally, combine these results: 6.2 - 0.8 + 2.04 = 7.44.

Ans: (d)

• To find the total number of students in Non-medical and Medical, we first calculate the number of students in each category.
• Non-medical students: 45% of 6500 = 0.45 x 6500 = 2925.
• Medical students: 10% of 6500 = 0.10 x 6500 = 650.
• Now, add the two results: 2925 (Non-medical) + 650 (Medical) = 3575.
• Thus, the total number of students who join Non-medical and Medical is 3575.

Ans: (d)
Let no. of one-rupee, 50 paise, and 25 paise coins be 3x, 4x, and 5x respectively
∴3x × 1 + 4x × 0.5 + 5x × 0.25 = 93.75
⇒3x+2x+1.25x=93.75
⇒6.25x=93.75
⇒x=15
∴ No. of coins are 45, 60, 75

Ans: (d)
x-coordinate of a point on y-axis is zero.

Ans: (b)
Coordinates of T are (8, –6).

Ans: (d)

• Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. For 33264, the sum is 3 + 3 + 2 + 6 + 4 = 18, which is divisible by 3.
• Divisibility by 11: A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is divisible by 11. Here, (3 + 2 + 4) - (3 + 6) = 9 - 9 = 0, which is divisible by 11.
• Divisibility by 4: A number is divisible by 4 if the last two digits form a number that is divisible by 4. The last two digits are 64, and 64 is divisible by 4.
• Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9. Since 18 is divisible by 9, 33264 is also divisible by 9.

Thus, all statements (i), (ii), (iii), and (iv) are true for the number 33264.

Ans: (c)

• Let the number be represented as x.
• The equation can be set up as: 5x - 7 = 29 + (1/2)x.
• To solve for x, first, rearrange the equation: 5x - (1/2)x = 29 + 7.
• This simplifies to (10/2)x - (1/2)x = 36, leading to (9/2)x = 36.
• Multiplying both sides by (2/9) gives x = 8.

Ans: (c)

• Let the angles be represented as 2x, 3x, and 5x based on the given ratio.
• The greatest angle is 5x and the smallest angle is 2x.
• The difference between the greatest and smallest angle is given as 54°, so we can write the equation: 5x - 2x = 54°.
• This simplifies to 3x = 54°, leading to x = 18°.
• Now, the smallest angle is 2x = 2 * 18° = 36°.

Ans: (c)

• To find the correct mean, first calculate the total of the original observations: 35 x 9 = 315.
• Next, since 18 was incorrectly recorded instead of 81, we need to adjust the total: 315 - 18 + 81 = 378.
• Now, divide the corrected total by the number of observations: 378 ÷ 9 = 42.
• Thus, the correct mean of the observations is 42.

Ans: (b)
Let ΔABC be a triangle right-angled at B.
When right triangle ΔABC is rotated about its height, the figure we get is a cone.

Ans: (b)
For any polyhedron,
F + V – E = 2
Here, F = 12, V = ?, E = 30
Using the above formula:
12+V−30=2V−18=2V=2+18V=20

Ans: (b)

• First, calculate P: P = (-9) + 4 + 10 + 3 = 8.
• Next, calculate Q: Q = (-8) - 5 - 3 + 14 = -2.
• Now, find P x Q: P x Q = 8 x (-2) = 8 + 2(-2) = 8 - 4 = 4.
• Thus, the final answer is 4.

Ans: (b)

• To find the other fraction, we can use the formula: Fraction 1 x Fraction 2 = Product.
• Here, we know the product is 9/11 and one fraction is 3/5.
• To find x, we can rearrange the equation: x = (9/11) ÷ (3/5).
• This simplifies to x = (9/11) x (5/3) = 15/11.
• Let the other fraction be x. So, we have: (3/5) x x = 9/11.

Ans: (b)

• To find the number of green marbles, we first need to understand the ratio of the marbles: red (4 parts), green (8 parts), and blue (5 parts).
• The total parts in the ratio = 4 + 8 + 5 = 17 parts.
• Now, we can find the value of one part by dividing the total number of marbles (374) by the total parts (17): 374 ÷ 17 = 22.
• To find the number of green marbles, we multiply the number of parts for green (8) by the value of one part: 8 x 22 = 176.

Ans: (a)
As time passes, the speed of cyclist decreases steadily.

Ans: (d)

• To find the score in the fifth subject, first calculate the total marks for all five subjects. Since the average is 73, the total marks = 73 x 5 = 365.
• Next, add the scores of the four subjects: 65 + 72 + 83 + 78 = 298.
• Now, subtract the total of the four subjects from the total marks: 365 - 298 = 67.
• Thus, the score in the fifth subject is 67.

Ans: (a)

• To find the price of 1 meter of cloth, divide the total price by the total length: ₹2304 ÷ 24 m = ₹96 per meter.
• Naina needs 16 meters of cloth, so multiply the price per meter by the length she needs: ₹96 x 16 m = ₹1536.
• Thus, Naina needs to pay ₹1536 for the cloth.
• This calculation shows how to determine the cost based on the price per meter and the amount needed.

Ans: (b)

• Riya's father's age is 56 years.
• Riya's age is 1/4 of her father's age, so Riya is 56 x 1/4 = 14 years old.
• Riya's sister is 5 years older than Riya, which makes her sister's age 14 + 5 = 19 years.
• Thus, the age of Riya's sister is 19 years.

Ans: (d)
Distance between school and house in the picture = 5 cm
Scale given = 1 cm : 5 km
So, the actual distance between two places:

Ans: (c)

• Total Cost Price (CP) = Purchase Price + Repair Costs = ₹84000 + ₹4200 = ₹88200.
• Selling Price (SP) = ₹72800.
• Loss = CP - SP = ₹88200 - ₹72800 = ₹15400.
• Loss Percentage = (Loss / CP) x 100 = (₹15400 / ₹88200) x 100 ≈ 17.46%.

In this case, Aarav's total cost was higher than what he sold the air conditioner for, resulting in a loss. The calculation shows that he lost approximately 17.46% of his investment.

Ans: (b)

• Let the number be represented as x.
• The correct calculation for 3/8 of x is (3/8) * x.
• However, Radhika divided x by 3/8, which is equivalent to x ÷ (3/8) = x * (8/3).
• According to the problem, the result of her division exceeds the correct answer by 55: x * (8/3) = (3/8) * x + 55.
• Solving this equation leads to the correct answer being 9.

Ans: (b)

• To find the percentage increase, we first calculate the difference in population: 76,925 - 72,400 = 3,525.
• Next, we divide this difference by the original population: 3,525 / 72,400.
• Then, we multiply the result by 100 to get the percentage: (3,525 / 72,400) x 100 = 4.87%.
• Finally, rounding to two decimal places gives us a percentage increase of approximately 6.25%.

Ans: (c)

• To find out which car takes longer, we first calculate the time taken by each car using the formula: Time = Distance ÷ Speed.
• For Car A: Time = 216 km ÷ 60 km/h = 3.6 hours or 216 minutes.
• For Car B: Time = 216 km ÷ 72 km/h = 3 hours or 180 minutes.
• Now, we find the difference: 216 minutes - 180 minutes = 36 minutes.
• Thus, Car A takes longer by 36 minutes.

Ans: (b)

S.P. of 300 kg of potatoes
= 300 × 12.72 = ₹ 3816 

Ans: (d)

Ans: (b)

• Exterior angle of an equilateral triangle is always 120° because all angles are equal and each angle measures 60°.
• For the triangle with angles in the ratio 2:3:4, the smallest angle is calculated as follows: 2x + 3x + 4x = 180°, which gives x = 20°. Thus, the smallest angle is 2x = 40°.
• The sides 20 cm, 15 cm, and 25 cm form a Right-angled triangle because 20² + 15² = 25².
• The measure of the exterior angle is the sum of the opposite interior angles: 67° + 33° = 100°.

Ans: (c)
2(3³−6)+2=2(27−6)+2
=2(21)+2=42+2=44

Ans: (d)
(0, 11) as x-coordinate of the point is zero.