Reasoning

Number Systems and Series

164 Questions

Number systems and series questions assess the ability to manipulate numerical values and spot patterns. The focus includes digit arrangements, binary conversions, and identifying largest or smallest numbers. These reasoning tasks are common across major competitive examinations.

Digit manipulationLargest and smallest numbersBinary number systemsPositional numeral systemsNumber series ranking

Number Systems and Series Questions

Multiple choice general knowledge math & puzzles

How many such paires of digits are there in the number 5314698 each of which has as many digits between them in the number as when they have are arranged in descending order?

  1. None

  2. One

  3. Two

  4. More than two
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Number: 5314698. Descending: 865431. Pairs with same gap: 8-6 (0 digits between in both), 5-4 (0 digits between in both), 8-5 (1 digit between in both), 8-4 (2 digits between in both). Total: 4 matching pairs.

Multiple choice general knowledge math & puzzles

The position of the first and the sixth digits in number 5314278906 are interchanged. Similarly the position of the second and the saventh digits are interchanged and so on. Which of the following will be the fourth from the right end after the rearrangemenr?

  1. 3

  2. 1

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original: 5314278906. Swap position 1-6: 7 takes 5's place. Swap 2-7: 8 takes 3's place. Swap 3-8: 0 takes 1's place. Swap 4-9: 9 takes 4's place. Result: 7890534216. Fourth from right (positions 3,2,1,4 from right): 3.

Multiple choice general knowledge math & puzzles

How many such paires of digits are there in the number 5314698 each of which has as many digits between them in the number as when they have are arranged in descending order?

  1. None

  2. One

  3. Two

  4. More than two
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Number: 5314698. Descending: 865431. Pairs with same gap: 8-6 (0 digits between in both), 5-4 (0 digits between in both), 8-5 (1 digit between in both), 8-4 (2 digits between in both). Total: 4 matching pairs.

Multiple choice general knowledge math & puzzles

The position of the first and the sixth digits in number 5314278906 are interchanged. Similarly the position of the second and the saventh digits are interchanged and so on. Which of the following will be the fourth from the right end after the rearrangemenr?

  1. 3

  2. 1

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Swapping the first five digits with the last five digits of 5314278906 gives 7890653142. The fourth digit from the right end is 3 (counting 2, 4, 1, 3). This is a duplicate of question 6019 and follows the same valid logic.

Multiple choice general knowledge math & puzzles

How many such paires of digits are there in the number 5314698 each of which has as many digits between them in the number as when they have are arranged in descending order?

  1. None

  2. One

  3. Two

  4. More than two
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In 5314698, pairs with the same distance as in descending order (98765431). Pairs are (5,4), (5,3), (4,3), (9,8), (6,4). Since there are more than two such pairs (e.g., 5 and 4 have zero digits between them in both), 'More than two' is correct.

Multiple choice general knowledge math & puzzles

The position of the first and the sixth digits in number 5314278906 are interchanged. Similarly the position of the second and the saventh digits are interchanged and so on. Which of the following will be the fourth from the right end after the rearrangemenr?

  1. 3

  2. 1

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The number is 5314278906. Interchanging 1st-6th, 2nd-7th, etc., results in 7890653142. Counting from the right end: 2 (1st), 4 (2nd), 1 (3rd), 3 (4th). Thus, 3 is the fourth digit from the right. The logic follows a simple block swap of the two halves.

Multiple choice general knowledge math & puzzles

5, 9, 1, 2, 2, 3, 5, 9, 1, 2, 2, 3, . . . In the sequence above, the first number is 5. The sequence consists of repetitions of the six numbers 5, 9, 1, 2, 2, and 3. What is the 620th number in the sequence?

  1. 1

  2. 2

  3. 3

  4. 5

  5. 9
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The sequence repeats every 6 numbers. To find the 620th number, divide 620 by 6. The remainder is 2 (620 = 103 * 6 + 2). Therefore, the 620th number is the 2nd number in the repeating sequence, which is 9.

Multiple choice general knowledge

Pick odd one out

  1. 1997

  2. 2017

  3. 1867

  4. 1937
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

1997 is the only number with a repeated digit (the digit 9 appears twice). In 1867, 1937, and 2017, all four digits are unique within their respective numbers. This makes 1997 the odd one out based on digit repetition pattern.

Multiple choice general knowledge math & puzzles

A three digit number consists of 9,5 and one more number . When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. What is the other digit?

  1. 4

  2. 5

  3. 6

  4. 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the 3-digit number be 9 5 x or permutations. Testing x=4: 954 - 459 = 495 (digits 4,9,5 rearranged). The difference 99(9-4) = 495 contains the same digits. This is a classic digit reversal puzzle.

Multiple choice general knowledge math & puzzles

In the following figure:A B C D E F G H IEach of the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 is:a)Represented by a different letter in the figure above.b)Positioned in the figure above so that each of A + B + C,C + D +E,E + F + G, and G + H + I is equal to 13.Which digit does E represent?

  1. 8

  2. 4

  3. 7

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sum of digits 1-9 is 45. In the four sums (each 13), C, E, and G are counted twice. Total sum = 45 + C + E + G = 13 * 4 = 52. Thus C + E + G = 7. Since they are distinct digits, they must be 1, 2, and 4. Trial and error shows E=4 works for the middle intersection.