Quantitative Aptitude

Number System and Digits

374 Questions

Number system and digits questions test the ability to manipulate numbers, identify significant digits, and form specific values. These problems often require finding missing digits or determining the properties of large sums. They form a vital component of the quantitative aptitude section.

Number formationMissing digitsSignificant digitsLargest and smallest numbersDigit sum properties

Number System and Digits Questions

Multiple choice

Total number of four digit numbers with at least one 5 in them is

  1. 3600

  2. 3244

  3. 9000

  4. 5932

  5. 3168
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Total number of four digit numbers is 9 X 10 X 10 X 10 = 9000.

Number of four digit numbers with number 5 in them can be found out in the following manner.

First digit can neither be zero nor 5. So, the first digit can be chosen in eight ways, the second,  third and fourth digit each can be chosen in 9 ways as there is no restriction of not choosing 0. Hence, the number of 4 digit numbers with number 5 in them = 8 X 9 X 9 X 9 = 5832.

Total number of four digit numbers with at least one 5 in them = 9000 – 5832 = 3168

Multiple choice

How many numbers can be formed using the digits 2, 3, 4, 5, 6 & 7 if no repetition is allowed?

  1. 1956

  2. 3240

  3. 9122

  4. (6! - 2!)/3!

  5. (6)5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Without repeating we can form 6 one digit numbers. 6 X 5 = 30, two digit numbers. 6 X 5 X 4 = 120, three digit numbers. 6 X 5 X 4 X 3 = 360, four digit numbers. 6 X 5 X 4 X 3 X 2 = 720, five digit numbers and 6 X 5 X 4 X 3 X 2 X 1 = 720 six digit numbers.

Since, this number formation in each case is mutually exclusive we will have to add them all up to arrive at the solution.

So according to problem we can have 6 + 30 + 120 + 360 + 720 + 720 = 1956 numbers.

Multiple choice

What is the largest three-digit number that can be formed by the digits 3, 6, 8, and 7 such that the digits are not repeated?

  1. 837

  2. 863

  3. 873

  4. 836

  5. 876
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The given digits are 3, 6, 8 and 7. Here, 3 < 6 < 7 < 8 In order to form the largest three-digit number, we have to place digits 8, 7, and 6 at the hundreds, tens, and ones place, respectively. Thus, the required largest three-digit number is 876. Hence, the correct option is (5).