Test: Number bases - 1 - JAMB MCQ

Pick up the unit digit of each number and multiply them;

Unit digit in (341)⁴⁹¹

= Unit digit in (1)⁴⁹¹ = 1

Unit digit in (625)³¹⁷

= Unit digit in (5)³¹⁷ = 5

Unit digit in (6374)¹⁷⁹³

= (4)¹⁷⁹³

= unit digit in [(4²)⁸⁹⁶ x 4]

= unit digit in 6 x 4 = 4

So, on multiplying the unit digits, we will get -

1 x 5 x 4 = 20 (consider the unit digit in the product)

So, the unit digit in the product of {(341)⁴⁹¹ x (625)³¹⁷ x (6374)¹⁷⁹³} is 0.

A number is divisible by 9 if the sum of its digits is divisible by 9.

The Sum of the digits of the given numbers are;

6 + 7 + 5 + 7 + 8 = 33

5 + 6 + 7 + 8 + 5 = 31

4 + 5 + 6 + 7 + 8 = 30

6 + 5 + 8 + 8 + 9 = 36

The sum of the digits of the number 65889 is 36, which is divisible by 9, so the correct answer is 65889.

To find the unit digit of the product 853 x 452 x 226 x 1346, follow these steps:

• Identify the unit digit of each number:
  • 853: Unit digit is 3
  • 452: Unit digit is 2
  • 226: Unit digit is 6
  • 1346: Unit digit is 6
• Calculate the product of the unit digits:
  • 3 x 2 = 6
  • 6 x 6 = 36
  • Unit digit of 36 is 6

Thus, the unit digit of the entire product is 6.

It is given that

x + y + z = 0

On cubing both sides, we will get

(x + y + z)³ = 0

x³ + y³ + z³ - 3xyz = 0

So, the value of x³ + y³ + z³ = 3xyz

The numbers which can be found on the number line and include both rational and irrational numbers are known as real numbers, e.g., -1.5, √2, 0, 1, 2, 3, π. Almost any number which you can imagine is a real number.

To determine which number is completely divisible by 45, we need to check divisibility by both 9 and 5.

1. Divisibility by 5: The number must end in 0 or 5.

2. Divisibility by 9: The sum of the digits must be a multiple of 9.

Option a) 331145:

• Ends in 5 (divisible by 5).

• Sum of digits: 3 + 3 + 1 + 1 + 4 + 5 = 17 (not divisible by 9).

Option b) 306990:

• Ends in 0 (divisible by 5).

• Sum of digits: 3 + 0 + 6 + 9 + 9 + 0 = 27 (divisible by 9).

Option c) 181660:

• Ends in 0 (divisible by 5).

• Sum of digits: 1 + 8 + 1 + 6 + 6 + 0 = 22 (not divisible by 9).

Since 306990 (option b) is divisible by both 5 and 9, it is divisible by 45. Verification by division confirms 306990 ÷ 45 = 6822, which is an integer.

On dividing 9805 by 8, the remainder is 5. So, 5 is the smallest number which should be subtracted from 9805 to make it divisible by 8.

Number of odd numbers up to 240 = 240/2 = 120

Sum of first n odd numbers = n²

n = 120

Required sum = 120² = 14400

From 1 - 99, the digit 1 occurs 20 times, and from 100 - 199, the digit 1 occurs 120 times.

So, from 1 to 199, the digit 1 occurs -

20 + 120 = 140 times

According to question 1 is occurring only 136 times, which means we need to remove 196, 197, 198, and 199. So, the required number of pages will be 195.

There are infinite rational numbers in between any two numbers.