## Tuesday, 9 May 2017

### CTS Aptitude

Below are few important aptitude questions on lines with CTS.

### Placement Question 1 :

1) Sum of square of three numbers is 95 and the product of these numbers is 101. Find the numbers.
Answer :
This is a tricky question which might consume a lot of time if not read carefully. In the above question, 101 is a prime number which cannot exist as a product of three different numbers. Hence you should immediately tick the option "none of the above" when reading these kinds of questions.

### Placement Question 2 :

2) Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.
Answer:
This question comes under permutations and combinations section. Out of 26 alphabets two distinct letters can be chosen in 26p2 ways. Coming to numbers part, there are 10 ways (any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10 ways to choose the second digit. Hence there are totally 10X10 = 100 ways. Combined with letters there are 6p2 X 100 ways = 65000 ways to choose vehicle numbers.

### Placement Question 3 :

3) Consider the sum of first 70 natural numbers. If every digit '6' is replaced by '8' what would be the net increase and the new sum?
Answer:
To answer this question, you need to know the simple formula for sum of first 'n' natural numbers which is n (n+1)/2.
Hence sum of numbers from 1 to 70 would be 70X71/2 = 2485.
If every '6' digit is replaced by '8' there would be totally 8 replacements at (6,16,26,36,46,56,60,66). Every replacement will add an additional '2' to the net sum. Hence the new sum will be 2485 + 8 X 2 = 2501 and the increase will be 16.

### Placement Question 4 : (For You To Practice)

4) Consider the sum of first 100 odd numbers. If every digit 7 is replaced by 2 what would be net decrease in sum and the new sum ?
This question is for you to try to solve yourselves.