Mathematical Reasoning Quiz

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 (3, 5, 1) become (6, 8, 4) and even digits (4, 2, 6) become (3, 1, 5). The new digits are 6, 8, 4, 3, 1, 5. 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, 4, 2) become (9, 7, 5) and even digits (5, 1) become (8, 3). Largest digit is 9, smallest is 1. Difference is 9 - 1 = 8, which is the correct answer.

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 82370643. The second digit is 2 and the third from the right is 4. Their sum is 2 + 8 = 10.

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 = 7 and b = 6, so the number is 76.

How many times does the digit 5 come in the counting from 1 to 100?

• 21

• 22

• 20

• 19

Answer explanation

The digit 5 appears in the numbers 5, 15, 25, 35, 45, 55, 65, 75, 85, 95 (10 times) and in the tens place of 50-59 (11 times). Thus, it appears a total of 20 times from 1 to 100.

What is the smallest natural number that should be added to 1225 such that a remainder of 3 is left when the resulting number is divided by each of the numbers 12, 18, 21 and 28?

• 41

• 38

• 35

• 43

Find the smallest number from which, if 6 is reduced then, it is completely divisible by 12, 15, 20 and 27.

• 542

• 540

• 546

• 500

Answer explanation

To find the smallest number divisible by 12, 15, 20, and 27, calculate their LCM, which is 540. Adding 6 gives 546, the smallest number that meets the condition.

Find the least number, which when divided by 16, 24, 36 and 54, leaves remainder 12, 20, 32 and 50 respectively?

• 432

• 444

• 428

• 452

Answer explanation

To find the least number, we set up equations based on the remainders. The number can be expressed as: x = 16k + 12, x = 24m + 20, x = 36n + 32, x = 54p + 50. Solving these gives x = 444 as the smallest solution.

What is the smallest number which when divided by 4, 6, 10 and 15, gives remainder 3 in each case?

• 58

• 126

• 37

• 63

Answer explanation

To find the smallest number that gives a remainder of 3 when divided by 4, 6, 10, and 15, we can calculate the least common multiple (LCM) of these numbers, which is 60. Adding 3 gives us 63, the correct answer.

What is the greatest number smaller than 5000 which when divided by 5, 6 and 7, leaves remainders of 4, 5 and 6 respectively?

• 4830

• 4829

• 4845

• 4831

Answer explanation

To find the greatest number less than 5000 that leaves remainders of 4, 5, and 6 when divided by 5, 6, and 7 respectively, we can express it as n = 5k + 4, n = 6m + 5, n = 7p + 6. Solving these gives n = 4829.