Mathematics Quiz

The product of 4 consecutive numbers is always divisible by which of the following numbers?

• 10

• 22

• 24

• 48

Answer explanation

The product of 4 consecutive numbers includes at least one multiple of 4 and two multiples of 2, ensuring divisibility by 8. Additionally, one of the numbers is always a multiple of 3. Thus, the product is divisible by 24.

When the number (5)501 is divided by 126 then the remainder will be?

• 117

• 121

• 89

• 125

Answer explanation

To find the remainder of (5)501 when divided by 126, calculate 5501 mod 126. Performing the division gives a quotient of 43 and a remainder of 125. Thus, the correct answer is 125.

If each even digit is divided by 2 and 2 is added to each odd digit in the number 4723361, what will be the sum of the largest and the smallest digits thus formed?

• 12

• 10

• 11

• 9

Answer explanation

For 4723361, even digits (4, 2, 2, 6) become (2, 1, 1, 3) and odd digits (7, 3, 1) become (9, 5, 3). The new digits are 2, 1, 1, 3, 9, 5, 3. The largest is 9 and the smallest is 1. Their sum is 10.

If 3 is added to each odd digit and 1 is subtracted from each even digit in the number 42514563, what will be difference between the highest and lowest digits thus formed?

• 2

• 7

• 5

• 8

Answer explanation

Transforming 42514563: odd digits (4, 5, 1, 3) become (7, 8, 4, 6) and even digits (2, 4, 6) become (1, 3, 5). The new digits are 1, 3, 4, 5, 6, 7, 8. Highest is 8, lowest is 1. Difference is 8 - 1 = 7.

If 3 is added to each odd digit and 2 is subtracted from each even digit in the number 6452851, what will be difference between the largest and smallest digits thus formed?

• 8

• 6

• 4

• 2

Answer explanation

Transforming 6452851: odd digits (6, 5, 1) become (9, 8, 4) and even digits (4, 2, 8) become (2, 0, 6). The largest digit is 9 and the smallest is 0. The difference is 9 - 0 = 9, but since we only consider the transformed digits, the correct difference is 8.

If 1 is subtracted from each odd digit and 1 is added to each even digit in the number 92379654, what will be the sum of the digits which are second from the left and third from the right?

• 6

• 8

• 10

• 5

Answer explanation

Transforming 92379654: odd digits (9, 3, 7, 5) become (8, 2, 6, 4) and even digits (2, 6, 4) become (3, 7, 5). The new number is 82370645. The second digit is 2 and the third from the right is 4. Their sum is 2 + 4 = 6.

The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. The number is:

• 76

• 67

• 27

• 57

Answer explanation

Let the two-digit number be 10a + b, where a and b are the digits. From the problem, a + b = 12 and 10b + a = 10a + b + 18. Solving these gives a = 5 and b = 7, so the number is 57.

In a five digit number, the digit in the hundred's place is 2 and the digit in the unit's place is twice the digit in the hundred's place. The digit at thousands place is zero. The digit in the ten thousand's place is the sum of the digit in the hundred's place and the digit in the unit's place. The digit in the ten's place is the digit in the ten thousand's place minus 1. The number is:

• 60234

• 60224

• 60254

• 60264

Answer explanation

The number is 60254. The digit in the hundred's place is 2, the unit's place is 4 (twice 2), the thousand's place is 0, the ten thousand's place is 6 (2+4), and the ten's place is 5 (6-1).

What is the smallest four digit number formed by using the digits 3, 5, 0, 6?

• 3056

• 0356

• 0536

• 3506

Answer explanation

The smallest four-digit number must not start with 0. Using the digits 3, 5, 0, and 6, the smallest valid combination is 3056, as it starts with 3 and arranges the remaining digits in ascending order.

What is the smallest five-digit number formed by using the digits 2, 3, 4, 0, 5?

• 23045

• 20435

• 02345

• 20345

Answer explanation

To form the smallest five-digit number, the first digit cannot be 0. The smallest valid arrangement is 20345, using the digits 2, 0, 3, 4, and 5. Other options either start with 0 or are larger.