HOTs for Maths Olympiad - 3 - Class 5 MCQ

• The digits in the ones and tens places must be divisible by 4, meaning these digits can be 4 or 8.
• The digit in the hundreds place must be a multiple of 7, so the digit must be 7.

So, the possible valid numbers are:

• Hundreds place = 7, Tens place = 8, Ones place = 4 → 784
• Hundreds place = 7, Tens place = 4, Ones place = 8 → 748

However, you are asking for the number 784, which satisfies all the conditions:

• Hundreds digit = 7 (multiple of 7)
• Tens digit = 8 (divisible by 4)
• Ones digit = 4 (divisible by 4)

Thus, the required number is 784.

Let's go through each option:

Option A: 1995 = MCMXCV

M = 1000

CM = 900

XC = 90

V = 5

Total = 1000 + 900 + 90 + 5 = 1995

This is correct.

Option B: 1561 = MDLXI

M = 1000

D = 500

L = 50

X = 10

I = 1

Total = 1000 + 500 + 60 + 1 = 1561

This is correct.

Option C: 1099 = MXCCXI

M = 1000

X = 10

C = 100

C = 100

X = 10

I = 1

Total = 1000 + 10 + 100 + 100 + 10 + 1 = 1221

This is incorrect. The correct Roman numeral for 1099 is MXCIX (1000 + 90 + 9).

Option D: 599 = DXCIX

D = 500

XC = 90

IX = 9

Total = 500 + 90 + 9 = 599

This is correct.

Thus, the incorrect match is Option C: 1099 = MXCCXI.

• 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.

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.

Third number is 11^thmultiple of 121, i.e. 11 x 121 = 1331
Second number is 5^th multiple of third number, i.e. 5 x 1331 = 6655
First number is successor of the second number 6655 + 1 = 6656

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.

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.

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.

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.

Total amount of water = 67289 litres
Amount of water leaked = 9274 litres
Amount of water left = 67289 - 9274 = 58015 litres
Hence, option (A) is correct.