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Interesting Number Sequences For all Math Lovers and Job Seekers

Puzzle Duniya always put hard efforts to bring exam quality study materials for all students, job-seekers, math-lovers, educationists and other type of interest-category people. Numerical series or sequences is another part of mathematical logic, which adds extra bit of flavor to it’s all existing content and also add a bit more love to it’s potential readers and followers.

Logical Ability Test

Source

Find 10 questions with their proper answers with logical analysis from this section below. Before going to the answer section, please try to solve them yourselves, which will definitely help you to grow your analytical skills and mental sharpness. It will boost your confidence a mile ahead before your appearance in vital competitive exams.

Q1. How many such 5’s are there in the following number sequence each of which is immediately preceded by 3 or 4 but not immediately followed by 8 or 9?

3 5 9 5 4 5 5 3 5 8 4 5 6 7 3 5 7 5 5 4 5 2 3 5 1 0

Answer Option:
a. None
b. 3
c. 4
d. 5

Answer

Answer

d. 5

Explanation

Explanation

As you know, a number which comes after a given number is said to follow it, while the one comes before the given number precedes it. Thus, the numbers satisfying the given conditions may be marked as:
3 5 9 5 4 5 5 3 5 8 4 5 6 7 3 5 7 5 5 4 5 2 3 5 1 0

Q2. In the series given below, how many 8’s are there each of which the middle number is 8 and each of the two numbers on both sides of it is a factor of 8, as shown below:

2 8 3 8 2 4 8 2 4 8 6 8 2 8 2 4 8 3 8 2 8 6

Answer Option:
a. 1
b. 2
c. 3
d. 4

Answer

Answer

b. 2

Explanation

Explanation

Clearly, we may mark such sets of 3 numbers, in which the middle number is 8 and each of the two numbers on both sides of it is a factor of 8, as shown below:
2 8 3 8 2 4 8 2 4 8 6 8 2 8 2 4 8 3 8 2 8 6

Q3. In the series, 6 4 1 2 2 8 7 4 2 1 5 3 8 6 2 1 7 1 4 1 3 2 8 6, how many pairs of successive numbers have a difference of 2 each?

Answer Option:
a. 4
b. 5
c. 6
d. 7

Answer

Answer

c. 6

Explanation

Explanation

Clearly the pair of successive number-shave a difference of 2 can be shown as follows:
6 4 1 2 2 8 7 4 2 1 5 3 8 6 2 1 7 1 4 1 3 2 8 6
Thus, there are 6 such pairs.

Q4. In the following series, how many such odd numbers are there which are divisible by 3 or 5, then followed by odd numbers, and then also followed by even numbers.

12, 19, 21, 3, 25, 18, 35, 20, 22, 21, 45, 46, 47, 48, 9, 50, 52, 54, 55, 56

Answer Option:
a. 0
b. 1
c. 2
d. 3

Answer

Answer

c. 2

Explanation

Explanation

Let’s 1st mare the odd numbers in the given series as bold below:
12, 19, 21, 3, 25, 18, 35, 20, 22, 21, 45, 46, 47, 48, 9, 50, 52, 54, 55, 56
Of these we just strike-through those numbers which are not divisible by 3 or 5.
12, 19, 21, 3, 25, 18, 35, 20, 22, 21, 45, 46, 47, 48, 9, 50, 52, 54, 55, 56
Next, we cross out the numbers which are not immediately followed by an odd number.
12, 19, 21, 3, 25, 18, 35, 20, 22, 21, 45, 46, 47, 48, 9, 50, 52, 54, 55, 56
Finally, we cross out the numbers who don’t have an even number at the second place to their right.
12, 19, 21, 3, 25, 18, 35, 20, 22, 21, 45, 46, 47, 48, 9, 50, 52, 54, 55, 56
Thus, there are 2 such numbers.

Q5. The positions of the 1st and the 2nd digits in the number 94316875 are interchanged. Similarly, the position of the 3rd, and 4th digits are interchanged and so on. Which of the following will be the 3rd to the left of the 7th digit from the left end after the rearrangement?

Answer Option:
a. 4
b. 6
c. 8
d. None of these

Answer

Answer

d. None of these

Explanation

Explanation

Changing the positions of the digits as mentioned, we get the number: 49138657. The 7th digit from the left end of this number is 5. The 3rd digit to the left of 5 is 3. Hence the answer belongs to none of the above

Q6. How many such pairs of digits are there in the number 531268947 each of which has as many digits between them in the number as when they are arranged in descending order?

Answer Option:
a. 1
b. 2
c. 3
d. More than 3

Answer

Answer

d. More than 3

Explanation

Explanation

The given number is: 531268947. Arranging the digits in descending order, we get 987654321. We have the following pairs of digits, satisfying the given conditions:

Digits in given number                          Digits in descending order
5 3 1 2                                                                   5 4 3 2
3 1 2 6                                                                  6 5 4 3
1 2                                                                         2 1
1 2 6 8 9 4 7                                                     7 6 5 4 3 2 1
2 6 8 9 4 7                                                        7 6 5 4 3 2
         8 9                                                                     9 8

Thus, we have 6 such pairs, namely (5, 2), (3, 6), (1, 2), (1, 7), (2, 7) and (8, 9). Hence the answer is more than 3.

Q7. If it’s possible to form a number with the 2nd, the 5th and the 8th digits of the number 31549786, which is the perfect square of two-digit even number, which of the following will be the 2nd digit of the even number?

Answer Option:
a. 1
b. 4
c. 6
d. No such number can be formed

Answer

Answer

b. 4

Explanation

Explanation

The 2nd, 5th and 8th digit of the number 31549786 are 1, 9 and 6 respectively. The perfect square of a two-digit even number, formed using the digits 1, 9 and 6 is 196.
So, 14 * 14 = 196 and the required number is 14. Clearly it’s 2nd digit is 4./toggle]

Q8. If 3 is subtracted from the middle digit of each of the following numbers and then the positions of the digits are reversed, which of the following will be the last digit of the middle number after they are arranged in descending order?

589  362  554  371  442

Answer Option:
a. 1
b. 2
c. 3
d. 5

Answer

Answer

c. 3

Explanation

Explanation

On subtracting 3 from the middle digits, the number becomes:
559  332  524  341  412
Now, on reversing the positions of digits, we have:
955  233  425  143  214
Arranging these numbers in descending order, we have:
955  425  233  214  143
The middle number is 233 and it’s last digit is 3.

Q9. How many numbers from 1 to 100 are there each of which is not only exactly divisible by 4 but also has 4 as a digit?

Answer Option:
a. 7
b. 10
c. 20
d. 21

Answer

Answer

a. 7

Explanation

Explanation

The number from 1 to 100 which are exactly divisible by 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56,60, 64,68, 72, 76, 80, 84, 88, 92, 96, 100.

But each number should have 4 as it’s digit.

So, the required numbers are 4, 24, 40, 44, 48, 64, 84 which are total 7 in numbers.

Q10. Which is the 3rd number to the left of the number which is exactly in the middle of the following sequence of numbers?

1 2 3 4 5 6 7 8 9 7 5 3 1 9 8 7 6 5 4 3 2 1

Answer Option:
a. 2
b. 4
c. 6
d. 8

Answer

Answer

b. 4

Explanation

Explanation

There are 27 numbers in the given sequence. So, middle number = 14th number = 9

Clearly the 3rd number to the left of this 9 is 4.

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