Maths Olympiad Sample Paper 1 - Class 5 MCQ

To find the number of students enrolled at Frederich Elementary School:

• Start with the total number of students at Lakeview Elementary School: 914.
• Frederich Elementary School has 276 fewer students.
• Perform the calculation: 914 - 276 = 638.

Therefore, the number of students enrolled at Frederich Elementary School is 638.

To convert the number 4.026 into words:

• The whole number part is 4, which is written as "Four."
• The decimal part is 026, which is read as "point zero two six."

Thus, 4.026 is written as "Four point zero two six."

A diameter is a straight line passing through the center of the circle, dividing it into two equal halves.
In the figure, point O is the center of the circle.
The correct choice is M and S.
Connecting M and S passes through the center O, forming a straight line across the circle.
This makes MS the diameter of the circle.

The appropriate unit for measuring the amount of liquid needed to fill a small teacup is:

When measuring liquids, it is essential to use the right unit to ensure accuracy. Here are some key points:

• The milliliter (mL) is a metric unit specifically designed for measuring liquid volume.
• A small teacup typically holds around 100 to 200 mL of liquid.
• Other units, like grams and kilograms, are used for measuring weight, not volume.
• Using meters is inappropriate, as it measures length, not volume.

Thus, the most suitable unit for this purpose is the milliliter.

Tom left home at 7:15 a.m. to go to work and returned at 4:45 p.m. The total time he was away from home is calculated as follows:

• From 7:15 a.m. to 12:00 p.m. is 4 hours and 45 minutes.
• From 12:00 p.m. to 4:45 p.m. is another 4 hours and 45 minutes.

Adding these two durations gives:

• 4 hours and 45 minutes + 4 hours and 45 minutes = 9 hours and 30 minutes.

Therefore, Tom was away from home for a total of 9 hours and 30 minutes.

Which of these could be solved by using the open sentence S – 7 = ?

The open sentence S – 7 = represents a relationship that can be understood through the context of seashell collections. Here’s how it applies to the scenarios:

• Rita collected 7 more seashells than Henry. This does not fit the equation, as it focuses on the difference, not a subtraction.
• Bony collected 7 fewer seashells than Kamal. This scenario matches the equation, as it can be expressed as S - 7 (Bony's count = Kamal's count - 7).
• David needs 7 seashells more to complete his collection. This situation does not fit, as it’s about needing more rather than having less.
• Amity filled 7 boxes with seashells. This scenario is about multiplication rather than subtraction, so it does not apply.

Thus, the correct answer is B, as it can be expressed accurately using the open sentence.

Solution:

Shelley has several options for her skirt:

• 2 lengths: short or long
• 3 fabric patterns: stripes, plaid, or flowers

To determine the total number of different skirts she can order, multiply the number of lengths by the number of patterns:

2 (lengths) × 3 (patterns) = 6 different skirts.

Solution:

The correct expression for the number of species of ants is 20 times the number of species of bats.

• Let b represent the number of species of bats.
• Since there are about 20 times as many species of ants as bats, the relationship can be expressed as:
• Number of species of ants = 20 × b

Therefore, the correct answer is 20 × b.

Number of pairs of jeans with Shilpa = 2
Number of tops with her = 4
With 1 pair of jeans, she can opt for any of the 4 tops.
Total combinations with 1 pair of jeans are 4.
Similarly, total combinations with the other pair of jeans are 4.
Hence, total combinations are 8.

Here, REDDISH is coded as TGFFKUJ.
R + 2 = T
E + 2 = G
D + 2 = F
D + 2 = F
I + 2 = K
S + 2 = U
H + 2 = J
Similarly,
For CARROT:
C + 2 = E
A + 2 = C
R + 2 = T
R + 2 = T
O + 2 = Q
T + 2 = V
Hence, CARROT will be coded as ECTTQV.

Step 1: Break the figure into two rectangles

The L-shaped figure consists of two rectangles:

1. Rectangle 1: 4 cm × 8 cm
2. Rectangle 2: 4 cm × 12 cm

Step 2: Calculate the areas of the two rectangles

1. Area of Rectangle 1:

   Area = Length×Width
   = 4 × 8 = 32 cm²

2. Area of Rectangle 2:

   Area = Length × Width
   = 4 × 12 = 48 cm²

Step 3: Add the areas of the two rectangles

Total Area of Shaded Part = 32 + 48 = 80 cm²

Area of the rectangle = l × b
35 cm² = 7 cm × b
b = 35/7 cm
b = 5 cm
Now, perimeter of the rectangle = 2(l + b)
= 2(7 + 5) cm = 2(12) cm = 24 cm

The average mass of 3 boys is 64 kg. To find the mass of the third boy, we can follow these steps:

• First, calculate the total mass of the three boys:
• Total mass = Average mass × Number of boys = 64 kg × 3 = 192 kg.

Next, we know the total mass of two boys:

• Total mass of 2 boys = 119 kg.
• To find the mass of the third boy, subtract the total mass of the two boys from the total mass of all three:
• Mass of the third boy = Total mass - Mass of 2 boys = 192 kg - 119 kg = 73 kg.

Thus, the mass of the third boy is 73 kg.

Prime numbers have only 2 factors: 1 and the number itself.
The prime numbers from the above data are as given below:
47, 31, 17, 13, 3, 29, 11, 7, 23, 19, 37
But 31 and 29 are repeated.
Hence, there are 13 students who got marks that are prime numbers.

Radius of the circle = 17.89 m
Diameter of the circle = 2 × radius
= 2 × 17.89 m = 35.78 m
As 1 m = 100 cm,
So, 35.78 m = 35.78 × 100 cm = 3578 cm

To find the number of kittens in the pet shop:

• Start with the total number of animals: 45.
• The number of puppies is 23.
• The number of parrots is 6.
• Calculate the total number of puppies and parrots: 23 + 6 = 29.
• Subtract this from the total number of animals: 45 - 29 = 16.

Thus, there are 16 kittens in the pet shop.

Number of cards with each player = 52 ÷ 4 = 13
Number of cards of hearts = 4
Required fraction = 4/13

Number of girls = 2400
Number of boys = (4/5) × 2400 = 1920
Total number of pupils = 2400 + 1920 = 4320
Teacher to pupil ratio = 1:40
Number of teachers = 4320 ÷ 40 = 108

100 ÷ 50 = 2, but 2 has been changed to (2 - 1) = 1
270 ÷ 90 = 3, but 3 has been changed to (3 - 1) = 2
So, 500 ÷ 100 = 5, but 5 should be changed to (5 - 1) = 4

Given that there are a total of 30 pupils in the class, let:

• b = number of boys
• g = number of girls

We can express the relationship between boys and girls as:

• b + g = 30

Each boy brings 5 stickers, and each girl brings 4 stickers. Therefore:

• Total stickers from boys = 5b
• Total stickers from girls = 4g

According to the problem, the boys bring 60 more stickers than the girls. This can be expressed as:

• 5b = 4g + 60

Now, we can substitute g from the first equation into the second:

• From b + g = 30, we find g = 30 - b.
• Substituting gives: 5b = 4(30 - b) + 60

Simplifying this:

• 5b = 120 - 4b + 60
• 5b + 4b = 180
• 9b = 180
• b = 20

Thus, the number of boys in the class is 20.

To make it divisible by 9, sum of the digits should be divisible by 9.
Sum of digits = 8 + 1 + 7 + ? + 2 + 1 + 8 = 27 + ?
So, 27 + ? should be divisible by 9. So, ? can be 0 and 9
Hence, 2 digits either 0 or 9 can come in the place of '?'.

Let Joy's weight be x.

Vineet's weight is 10.4 kg heavier than Joy, so Vineet's weight is 10.4 + x.

Govind is 6.9 kg lighter than Vineet, making Govind's weight (10.4 + x) - 6.9.

The total mass of the three adults can be expressed as: x + (10.4 + x) + ((10.4 + x) - 6.9) = 219.4 kg

Simplifying this gives:

• 219.4 = 3x + 13.9
• 205.5 = 3x
• x = 68.5 kg

Finally, to find Govind's weight: Govind = 10.4 + 68.5 - 6.9 = 72 kg

Distance covered in 10 hours = 100 km
Distance covered in 1 hour = 100/10 km = 10 km
Distance covered in 15 hours = 15 × 10 km = 150 km

Let the number of elephants be 3x.
Number of crocodiles = 5x
According to the question,
Number of elephants + Number of crocodiles = Total number of animals
3x + 5x = 160
8x = 160
x = 20
So, number of elephants = 3x = 3 × 20 = 60

A cylindrical tank with a capacity of 32 litres is 4/5 full of water.

The following steps outline how to determine the amount of water remaining in the cylindrical tank after pouring some into a pail:

• The tank's total capacity is 32 litres.
• The amount of water currently in the tank is:
• (4/5) × 32 = 25.6 litres
• One quarter of this water is poured into a pail:
• (1/4) × 25.6 = 6.4 litres
• To find the remaining water in the tank, subtract the amount poured into the pail:
• 25.6 - 6.4 = 19.2 litres

Thus, the amount of water left in the cylindrical tank is 19.2 litres, which is equivalent to 19 1/5 litres.

Length of the rectangle = 10 units
Breadth of the rectangle = 8 units
Perimeter of the rectangle = 2 (length + breadth) = 2 (10 + 8) units = 36 units
According to the question,
Perimeter of the square = Perimeter of the rectangle
So, 4 × Side = 36 units
or, Side = (36 ÷ 4) units = 9 units
So, area of the square = 9 units × 9 units = 81 sq. units.

The least common multiple of 8 and 7 is given by 8 * 7 = 56

We need to determine the number A which is a common multiple of 8 and 9. It is also given that the number A is between 1200 and 1300.

The multiples of 8 between the range 1100 and 1200 is given by

1104, 1112, 1120, 1128, 1136, 1144, 1152, 1160, 1168, 1176, 1184, 1192, 1200.

The multiples of 7 between the range 1100 and 1200 is given by

1106, 1113, 1120, 1127, 1134, 1141, 1148, 1155, 1162, 1169, 1176, 1183, 1190 and 1197

It is obvious from the multiples of 8 and 7, the common multiple is 1120.

Thus, the number A is 1120.

Let, breadth = x metres
Length = (x + 40) metres
Perimeter = 2(length + breadth) = 2 (x + 40 + x) metres = 2(2x + 40) metres
According to the question:
2 (2x + 40) × 30 = 15,000
or, 2x + 40 = 250
or, 2x = 210
or, x = 105
Hence, length = 105 + 40 metres = 145 metres

One cupcake in the figure represents 5 cupcakes.
So, number of cupcakes sold on Saturday and Monday = (10 + 4) × 5 = 14 × 5 = 70
Number of cupcakes sold on Sunday and Thursday = (9 + 3) × 5 = 12 × 5 = 60
Difference between the number of cupcakes sold on Saturday and Monday and that on Sunday and Thursday = 70 - 60 = 10

"CODING" is coded as "DPEJOH".
It implies the following:
C + 1 = D
O + 1 = P
D + 1 = E
I + 1 = J
N + 1 = O
G + 1 = H
Similarly,
P + 1 = Q
A + 1 = B
G + 1 = H
E + 1 = F
So, "PAGE" will be coded as "QBHF".