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All questions of Section - 4 ( Achievers Section) for Class 5 Exam

A number consists of 3 different digits. The ones and tens place digits are both divisible by 4. The hundreds place digit is multiple of 7. Which of the following can be the number?
  • a)
    784
  • b)
    647
  • c)
    864
  • d)
    282
Correct answer is option 'A'. Can you explain this answer?

Dhairya malhotra answered
Understanding the Problem
To determine which number satisfies the given conditions, we need to analyze the criteria:
- The number must consist of 3 different digits.
- The ones and tens place digits must be divisible by 4.
- The hundreds place digit must be a multiple of 7.
Evaluating Each Option
Let's look at each option:
- Option a) 784
- Hundreds place: 7 (multiple of 7)
- Tens place: 8 (divisible by 4)
- Ones place: 4 (divisible by 4)
- Digits: 7, 8, 4 (all different)
This option satisfies all the conditions.
- Option b) 647
- Hundreds place: 6 (not a multiple of 7)
This option fails the hundreds place condition.
- Option c) 864
- Hundreds place: 8 (not a multiple of 7)
This option also fails the hundreds place condition.
- Option d) 282
- Hundreds place: 2 (not a multiple of 7)
This option fails the hundreds place condition as well.
Conclusion
After evaluating all options, only option a) 784 meets all the specified criteria:
- Different Digits: 7, 8, and 4 are all unique.
- Divisibility:
- 8 (tens) is divisible by 4.
- 4 (ones) is divisible by 4.
- Hundreds Place: 7 is a multiple of 7.
Thus, the correct answer is option a) 784.
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Fill in the blanks and select the correct option.
(i) The next even number after 14 is P.
(ii) The sum of 9 and 6 is Q.
(iii) The difference between 20 and 13 is R.
  • a)
    (P)-16, (Q)-14, (R)-7
  • b)
    (P)-16, (Q)-15, (R)-7
  • c)
    (P)-18 (Q)-15, (R)-8
  • d)
    (P)-18, (Q)-14, (R)-8
Correct answer is option 'B'. Can you explain this answer?

Aniket Chaudhary answered
Explanation:

Finding the Next Even Number:
- The next even number after 14 is 16. So, P = 16.

Finding the Sum of 9 and 6:
- The sum of 9 and 6 is 15. So, Q = 15.

Finding the Difference between 20 and 13:
- The difference between 20 and 13 is 7. So, R = 7.
Therefore, the correct option is (P)-16, (Q)-15, (R)-7, which corresponds to option 'B'.

If the perimeter of a square is 36 cm, what is the length of each side?
  • a)
    6 cm
  • b)
    9 cm
  • c)
    12 cm
  • d)
    15 cm
Correct answer is option 'B'. Can you explain this answer?

Bibek Shah answered
Understanding the Perimeter of a Square
The perimeter of a square is the total distance around it. Since all four sides of a square are equal in length, we can calculate the perimeter using the formula:
- Perimeter (P) = 4 × Side Length (s)
Given Information
- The perimeter of the square is 36 cm.
Calculating the Length of Each Side
To find the length of one side, we can rearrange the formula:
- Side Length (s) = Perimeter (P) / 4
Now, substituting the given perimeter:
- Side Length (s) = 36 cm / 4
Performing the Calculation
- Side Length (s) = 9 cm
Conclusion
Therefore, the length of each side of the square is:
- 9 cm
This confirms that the correct answer is option B) 9 cm.
By understanding the relationship between the perimeter and the side length of a square, you can easily solve similar problems in the future!

Fill in the blanks and select the correct option.
(i) The sum of 372 and 648 is P.
(ii) The difference between 987 and 543 is Q.
(iii) The product of 25 and 4 is R.
  • a)
    (P)-1020, (Q)-444, (R)-100
  • b)
    (P)-1021, (Q)-444, (R)-101
  • c)
    (P)-1020, (Q)-445, (R)-101
  • d)
    (P)-1020, (Q)-444, (R)-99
Correct answer is option 'A'. Can you explain this answer?

Shivam Sen answered
Understanding the Problem
To determine the values for P, Q, and R, we need to perform basic arithmetic calculations based on the given numbers.
Calculating P
- Sum of 372 and 648:
- P = 372 + 648
- P = 1020
Calculating Q
- Difference between 987 and 543:
- Q = 987 - 543
- Q = 444
Calculating R
- Product of 25 and 4:
- R = 25 × 4
- R = 100
Final Values
- P = 1020
- Q = 444
- R = 100
Choosing the Correct Option
Now we compare our calculated values with the options given:
- a) (P)-1020, (Q)-444, (R)-100
- b) (P)-1021, (Q)-444, (R)-101
- c) (P)-1020, (Q)-445, (R)-101
- d) (P)-1020, (Q)-444, (R)-99
The only option that matches our calculations is:
- Option A: (P)-1020, (Q)-444, (R)-100
Conclusion
Thus, the correct answer is option 'A' because all calculated values of P, Q, and R align perfectly with this option.

Fill in the blanks and select the correct option.

(i) The next number in the sequence 3, 6, 9, 12, ... is P.

(ii) The total number of minutes in 3 hours is Q.

(iii) The decimal form of 3/4 is R.
  • a)
    (P)-15, (Q)-180, (R)-0.25
  • b)
    (P)-15, (Q)-180, (R)-0.75
  • c)
    (P)-18, (Q)-240, (R)-0.75
  • d)
    (P)-18, (Q)-240, (R)-0.25
Correct answer is option 'B'. Can you explain this answer?

Rahul Kumar answered
(i) The next number in the sequence 3, 6, 9, 12, ... is P:
The sequence increases by 3 each time.
3 + 3 = 6, 6 + 3 = 9, 9 + 3 = 12, so the next number is 12 + 3 = 15.
So, P = 15.
(ii) The total number of minutes in 3 hours is Q:
1 hour = 60 minutes, so 3 hours = 3 × 60 = 180 minutes.
So, Q = 180.
(iii) The decimal form of 3/4 is R:
To convert 3/4 to a decimal, divide 3 by 4:
3 ÷ 4 = 0.75.
So, R = 0.75.
Thus, the correct answer is B: (P)-15, (Q)-180, (R)-0.75.

Fill in the blanks and select the correct option.
(i) The value of 874−349 when rounded to the nearest ten is ___ P.
(ii) The product of 23×45 is ___Q.
(iii) The LCM of 12 and 18 is ___R.
  • a)
    (P)-520, (Q)-1035, (R)-36
  • b)
    (P)-530, (Q)-1035, (R)-36
  • c)
    (P)-520, (Q)-1030, (R)-36
  • d)
    (P)-525, (Q)-1020, (R)-72
Correct answer is option 'B'. Can you explain this answer?

Manisha Joshi answered
Understanding the Problem
In this question, we need to find values for three mathematical operations: rounding, multiplication, and finding the least common multiple (LCM).
Step-by-Step Breakdown
(i) Rounding the Value of 874 - 349
- First, calculate 874 - 349.
- The result is 525.
- Now, to round 525 to the nearest ten, we look at the unit digit (5). Since it is 5 or greater, we round up to 530.
(ii) Calculating the Product of 23 × 45
- Now, multiply 23 by 45.
- The product can be calculated as follows: 23 × 45 = 1035.
(iii) Finding the LCM of 12 and 18
- The LCM (Least Common Multiple) of 12 and 18 can be determined by listing the multiples.
- The multiples of 12 are 12, 24, 36, ...
- The multiples of 18 are 18, 36, 54, ...
- The smallest common multiple is 36.
Final Values
After calculations, we have:
- P = 530 (rounded value)
- Q = 1035 (product)
- R = 36 (LCM)
Selecting the Correct Option
The correct option is b) (P)-530, (Q)-1035, (R)-36.
This option accurately reflects the results of our calculations.

Select the INCORRECT match
  • a)
    1995 = MCMXCV
  • b)
    1561 = MDLXI
  • c)
    1099 = MXCCXI
  • d)
    599 = DXCIX
Correct answer is option 'C'. Can you explain this answer?

Dhairya malhotra answered
Understanding Roman Numerals
Roman numerals are a numeral system originating from ancient Rome, using combinations of letters from the Latin alphabet. Each letter has a specific value, and they can be combined to represent numbers.
Breakdown of Each Year
Let's analyze the Roman numeral representations given in the options:
  • 1995 = MCMXCV
    • M = 1000
    • CM = 900
    • X = 10
    • CV = 5
    • Correct total: 1000 + 900 + 10 + 5 = 1995

  • 1561 = MDLXI
    • M = 1000
    • D = 500
    • L = 50
    • X = 10
    • I = 1
    • Correct total: 1000 + 500 + 50 + 10 + 1 = 1561

  • 1099 = MXCCXI
    • M = 1000
    • X = 10
    • C = 100
    • C = 100
    • X = 10
    • I = 1
    • Incorrect total: 1000 + 10 + 100 + 100 + 10 + 1 = 1221

  • 599 = DXCIX
    • D = 500
    • X = 10
    • C = 100
    • I = 1
    • X = 10
    • Correct total: 500 + 10 + 100 - 1 = 599


Conclusion
The incorrect match is option C, where 1099 is incorrectly represented as MXCCXI instead of the correct representation, which should be MCMXCIX. Hence, the right answer is option 'C'.

Read the given statements carefully and select the correct option.
Statement I: The perimeter of a rectangle with length 5 cm and width 3 cm is 16 cm.
Statement II: The area of the same rectangle is 15 cm².
  • a)
    Both Statement I and Statement II are true.
  • b)
    Both Statement I and Statement II are false.
  • c)
    Statement I is true but Statement II is false.
  • d)
    Statement I is false but Statement II is true.
Correct answer is option 'A'. Can you explain this answer?

Snehal Sengupta answered
Understanding Statement I: Perimeter of the Rectangle
- The formula for the perimeter (P) of a rectangle is given by:
P = 2 × (length + width)
- For the rectangle:
- Length = 5 cm
- Width = 3 cm
- Calculating the perimeter:
P = 2 × (5 cm + 3 cm)
= 2 × 8 cm
= 16 cm
- Conclusion: Statement I is true.
Understanding Statement II: Area of the Rectangle
- The formula for the area (A) of a rectangle is given by:
A = length × width
- For the rectangle:
- Length = 5 cm
- Width = 3 cm
- Calculating the area:
A = 5 cm × 3 cm
= 15 cm²
- Conclusion: Statement II is also true.
Final Analysis
- Both Statement I and Statement II are true based on the calculations above.
- Therefore, the correct answer is option 'A': Both Statement I and Statement II are true.
This illustrates the importance of understanding basic geometric concepts like perimeter and area, which are fundamental in mathematics for Class 5 students.

Read the given statements carefully and select the correct option.
Statement I: The sum of the angles in a triangle is always 180 degrees.
Statement II: A square has 4 sides of different lengths.
  • a)
    Both Statement I and Statement II are true.
  • b)
    Both Statement I and Statement II are false.
  • c)
    Statement I is true but Statement II is false.
  • d)
    Statement I is false but Statement II is true.
Correct answer is option 'C'. Can you explain this answer?

Rohan Joshi answered
Explanation of the Statements
In evaluating the two statements, we need to assess their accuracy based on basic geometry principles.
Statement I: The sum of the angles in a triangle is always 180 degrees.
- This statement is true.
- In any triangle, regardless of the type (scalene, isosceles, or equilateral), the interior angles always add up to 180 degrees. This is a fundamental property in Euclidean geometry.
Statement II: A square has 4 sides of different lengths.
- This statement is false.
- A square is defined as a quadrilateral with all four sides of equal length and all interior angles measuring 90 degrees. Therefore, it cannot have sides of different lengths.
Conclusion
- Given that Statement I is true and Statement II is false, the correct answer is option 'C': "Statement I is true but Statement II is false."
Understanding these fundamental properties of shapes helps in grasping more complex geometrical concepts later on.

Directions: Read the given statements carefully and choose the correct option.
Statement-1: If 17 employees of a company donate Rs. 768 each, then the company collects Rs. 13,054.
Statement-2: If 23 trucks contain 15755 litres of liquid in total, then each truck contains 685 litres of the liquid.
  • a)
    Both Statement-1 and Statement-2 are true.
  • b)
    Statement-1 is true, but Statement-2 is false.
  • c)
    Statement-1 is false, but Statement-2 is true.
  • d)
    Both Statement-1 and Statement-2 are false.
Correct answer is option 'C'. Can you explain this answer?

Tutorpedia Coaching answered
Statement-1: If 17 employees of a company donate Rs. 768 each, then the company collects Rs. 13,054.
  • The total amount collected = 17 employees × Rs. 768 = 17 × 768 = Rs. 13,056.
  • This contradicts the statement, which says Rs. 13,054. So, Statement-1 is false.
Statement-2: If 23 trucks contain 15,755 litres of liquid in total, then each truck contains 685 litres of the liquid.
  • To find the amount of liquid in each truck: 15,755 litres ÷ 23 trucks = 685 litres per truck.
  • This is correct, so Statement-2 is true.
Thus, Statement-1 is false, but Statement-2 is true.

ABC Ltd. suffered a loss of ninety eight crore forty five lakhs seventeen thousand and fifty one rupees in the year 2016 in the business. Company loss can be written in numerals as
  • a)
    Rs. 94,85,17,051
  • b)
    Rs. 9,45,17,051
  • c)
    Rs. 98,45,17,051
  • d)
    Rs. 95,45,77,051
Correct answer is option 'C'. Can you explain this answer?

Subset Academy answered
The loss is described as ninety-eight crore, forty-five lakh, seventeen thousand, and fifty-one rupees.
Let's break it down:
  • Ninety-eight crore = 98,00,00,000
  • Forty-five lakh = 45,00,000
  • Seventeen thousand = 17,000
  • Fifty-one = 51
So, the total loss in numerals is:
98,00,00,000 + 45,00,000 + 17,000 + 51 = 98,45,17,051
Thus, the company’s loss can be written as Rs. 98,45,17,051.

Madhav is thinking of a 5-digit number. The number is a multiple of 5 and the number is not an even number. The ten's place digit is the highest common factor of 18 and 26. The hundred's place digit is the 7. The ten thousands place digit is the biggest one digit prime number. The thousands place digit is sum of the tens place and ones place digit. What number is Madhav thinking of?
  • a)
    77,725
  • b)
    77,752
  • c)
    47,812
  • d)
    98,752
Correct answer is option 'A'. Can you explain this answer?

Yashina Kapoor answered
  • The digit at the ones place = 5: This is given since the number is a multiple of 5 and not even.
  • The tens place digit is the highest common factor of 18 and 26, which is 2.
  • The hundreds place digit = 7.
  • The thousands place digit is the sum of the tens place and ones place digits = 2 + 5 = 7.
  • The ten thousands place digit is the biggest one-digit prime number = 7.
So, the number that Madhav is thinking of is indeed 77,725.

The product of the greatest 3-digit number and the smallest 2-digit number is:
  • a)
    9990
  • b)
    999
  • c)
    8991
  • d)
    8990
Correct answer is option 'A'. Can you explain this answer?

Edu Impact answered
The greatest 3-digit number is 999, and the smallest 2-digit number is 10. The product of 999 and 10 is 9990. Therefore, the correct answer is 9990.

Which of the following statements is INCORRECT?
  • a)
    The face value of 9 in the number 98,745 is 9.
  • b)
    The place value of 1 in the number 56,201 is 1.
  • c)
    The place value of 8 in the number 8955 is 8000.
  • d)
    The place value of 8 in the number 8955 is predecessor of 7999.
Correct answer is option 'D'. Can you explain this answer?

Edu Impact answered
Option A: The face value of 9 in the number 98,745 is 9.
  • This is correct. The face value of a digit is the digit itself. So, the face value of 9 in the number 98,745 is indeed 9.
Option B: The place value of 1 in the number 56,201 is 1.
  • This is incorrect. The place value of 1 in the number 56,201 is 100 because it is in the hundreds place.
Option C: The place value of 8 in the number 8955 is 8000.
  • This is correct. The place value of 8 in the number 8955 is 8000 because it is in the thousands place.
Option D: The place value of 8 in the number 8955 is the predecessor of 7999.
  • This is incorrect. The place value of 8 in the number 8955 is 8000, which is not the predecessor of 7999. The predecessor of 7999 is 7998, not 8000.
Thus, the incorrect statement is Option D.

In a class of 45 students, 3/5 of the students are boys. How many girls are there in the class?
  • a)
    18
  • b)
    27
  • c)
    28
  • d)
    30
Correct answer is option 'A'. Can you explain this answer?

Edu Impact answered
Number of boys = (3/5) × 45 = 27
Number of girls = Total students - Number of boys = 45 - 27 = 18
The correct answer is 18.

What is the sum of the first five multiples of 7?
  • a)
    105
  • b)
    70
  • c)
    35
  • d)
    175
Correct answer is option 'A'. Can you explain this answer?

Edu Impact answered
The first five multiples of 7 are: 7, 14, 21, 28, and 35. The sum is 7 + 14 + 21 + 28 + 35 = 105.
The correct answer is 105.

A library had 7680 books. If 543 books were damaged, how many books are left?
  • a)
    7137
  • b)
    8123
  • c)
    7237
  • d)
    7017
Correct answer is option 'A'. Can you explain this answer?

Torcia Education answered
The number of books left is calculated by subtracting the damaged books from the total number of books.
7680 − 543 = 7137.
So, the library has 7137 books left.

Fill in the blanks and select the correct option.

(i) The average of 8, 12, and 20 is P.

(ii) The median of 4, 15, and 9 is Q.

(iii) The mode of 2, 3, 3, 4, 4, 4, 5 is R.
  • a)
    (P)-10, (Q)-9, (R)-4
  • b)
    (P)-10, (Q)-15, (R)-4
  • c)
    (P)-13, (Q)-9, (R)-3
  • d)
    (P)-13, (Q)-9, (R)-4
Correct answer is option 'D'. Can you explain this answer?

Rahul Kumar answered
(i) The average of 8, 12, and 20 is P:
The average is calculated as:
Average = (Sum of all numbers) / (Number of numbers)
Average = (8 + 12 + 20) / 3 = 40 / 3 = 13
So, P = 13.
(ii) The median of 4, 15, and 9 is Q:
To find the median, we first arrange the numbers in ascending order:
4, 9, 15
The middle number is 9, so Q = 9.
(iii) The mode of 2, 3, 3, 4, 4, 4, 5 is R:
The mode is the number that appears most frequently. In this case, 4 appears three times, more than any other number.
So, R = 4.
Thus, the correct answer is D: (P)-13, (Q)-9, (R)-4.

In March 2018, City A has 812,956 people, City B has 975,792 people, City C has 793,549 people and City D has 789,264 people. Which city has lowest population?
  • a)
    City D
  • b)
    City C
  • c)
    City B
  • d)
    City A
Correct answer is option 'A'. Can you explain this answer?

Edu Impact answered
Let's compare the populations of the cities:
  • City A: 812,956
  • City B: 975,792
  • City C: 793,549
  • City D: 789,264
The city with the lowest population is City D, with 789,264 people.

Aman has six chits with numbers 7, 8, 9, 1, 0 and 3. Saurav asked him to form the greatest 6-digit odd number with the digits written on chits. Find the number Aman could have formed?
  • a)
    301,897
  • b)
    987,301
  • c)
    897,103
  • d)
    978,103
Correct answer is option 'B'. Can you explain this answer?

Subset Academy answered
To form the greatest 6-digit odd number, we need to arrange the digits in such a way that the number is as large as possible, and it must end with an odd digit.
The digits available are: 7, 8, 9, 1, 0, and 3.
  • The last digit must be odd for the number to be odd. The odd digits available are 7, 9, and 3. Among these, 9 is the largest, so we place 9 at the ones place.
  • To form the greatest number, we arrange the remaining digits in descending order: 8, 7, 3, 1, and 0.
So, the largest possible number is 987,301.

Fill in the blanks and select the correct option.

(i) The greatest common divisor of 48 and 64 is P.

(ii) The next prime number after 17 is Q.

(iii) The square of 12 is R.
  • a)
    (P)-16, (Q)-23, (R)-144
  • b)
    (P)-8, (Q)-19, (R)-144
  • c)
    (P)-16, (Q)-19, (R)-144
  • d)
    (P)-8, (Q)-23, (R)-144
Correct answer is option 'C'. Can you explain this answer?

Rahul Kumar answered
(i) The greatest common divisor of 48 and 64 is P:
The divisors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The divisors of 64 are: 1, 2, 4, 8, 16, 32, 64.
The common divisors of 48 and 64 are: 1, 2, 4, 8, and 16.
The greatest of these common divisors is 16.
So, P = 16.
(ii) The next prime number after 17 is Q:
The prime numbers after 17 are 19, 23, etc.
The next prime number after 17 is 19.
So, Q = 19.
(iii) The square of 12 is R:
The square of 12 is 12 × 12 = 144.
So, R = 144.
Thus, the correct answer is C: (P)-16, (Q)-19, (R)-144.

What is the least common multiple (LCM) of 8, 12, and 16?
  • a)
    24
  • b)
    48
  • c)
    96
  • d)
    144
Correct answer is option 'C'. Can you explain this answer?

Learning Education answered
The LCM of 8, 12, and 16 is the smallest number that is a multiple of all three numbers.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, ...
The LCM of 8, 12, and 16 is 96.
The correct answer is 96.

Chapter doubts & questions for Section - 4 ( Achievers Section) - Math Olympiad for Class 5 2025 is part of Class 5 exam preparation. The chapters have been prepared according to the Class 5 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 5 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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