Dear Reader,
Below are three simple numeric problems for your practice.

Question 1

Manohar, Kumaresan and Nambiar had heated discussions on different topics. Manohar posed the following quiz to the other two:
“The difference between the reverse and a three digit number is 297. The unit digit of the number is the product of the other two digits. What is the product of the three digits of the number?”

a) 36 b)47 c)23 d)53

Answer : a) 36.

Solution :

The unit digit of the number is the product of the other two digits. This condition is satisfied in the following three digit numbers:
122, 133, 144, 155, 166, 177, 188, 199, 212, 224, 236, 248, 313, 326, 339, 414, 428, 515, 616, 717, 818, 919.
The condition that the difference between the reverse and the three digit number is 297 is satisfied for number 326 (i.e 623 - 326 = 297). The product of all the three digits = 3 x 2 x 6 = 36

Question 2

Rajani and Kamal were having spare time in which they discussed few puzzles/riddles. Kamal posed Rajani the following quiz:
"The product of the first two digits of a three digit number is its unit digit. The difference between this number and its reverse is 594. What is the sum of the three digits of this number? "

a) 15 b) 17 c)19 d) none of these.

Answer : a) 15

Solution :

The number of 177 and the sum of the digits is 15.
The unit digit of the number is the product of the other two digits. This condition is satisfied in the following three digit numbers:
122, 133, 144, 155, 166, 177, 188, 199, 212, 224, 236, 248, 313, 326, 339, 414, 428, 515, 616, 717, 818, 919
The second condition that the difference between the reverse of the number and the number is 594 is satisfied only when the number is taken as 177. The sum of all the digits = 1 + 7 + 7 = 15, which is our answer.

Question 3

Ilayaraja and Gangai Amaran were discussing about various topics including their difficult past. Suddenly Gangai Amaran remembered about a problem which his teacher asked him years ago and he narrated it as follows:
“The average of seven consecutive odd numbers is 63. What is the difference between these highest and lowest numbers?

a. 2 b. 5 c. 8 d. 12

Answer : d) 12

Solution :

Whenever a series of odd numbers with odd number of terms is considered, the middle number would be the average. In our case, since there are seven consecutive numbers, the fourth number should be the average. The average is given to be 63. This should be our fourth term as well. Therefore, the sequence can be written as
57, 59, 61, 63, 65, 67, 69
Difference between the highest and the lowest numbers = 69 - 57 = 12

Note : Tip to Remember: The difference between the highest and lowest numbers – when we take five consecutive odd numbers is always 8. In case nine consecutive odd number are taken – the difference between the highest and the lowest number is always 16.