Logical 6 - Number Test

Practice Questions:

Question 1:

If it is possible to form a number with the second, the fifth and the eighth digits of the number 31549786, which is the perfect square of the two digit even number, which of the following will be the second digit of that even number?

The second, fifth and eighth digits of the number 31549786 are 1, 9 and 6 respectively.
The perfect square of the two digit even number formed using the digits 1, 9 and 6 is 196 and 196 = 14².
So, the required even number is 14 and the second digit is 4.

Question 2:

The positions of the first and the second digits in the number 94316875 are interchanged. Similarly, the positions of the third and the fourth digits are interchanged and so on. Which of the following will be the third to the left of the seventh digit from the left end after the rearrangement?

Changing the positions of the digits as mentioned, we get, 49138657
The seventh digit from the left end of this number is 5.
The third digit to the left of 5 is 3.
So, the the third to the left of the seventh digit from the left end after the rearrangement is 3.

Question 3:

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?

The given number is 531268947
Arranging the number in descending order, we get, 987654321
The digits satisfying the given condition are,

5312 - 5432
3126 - 6543
12 - 21
1268947 - 7654321
2268947 - 765432
89 - 98

We have six pairs such as, (5,2), (3, 6), (1, 2), (1, 7), (2, 7), (8, 9).


Question 4:

In a school, the following codes were used during physical exercise. '1' means 'start walking', '2' means 'keep standing', '3' means 'start running at the same spot', '4' means 'sit down'. How many times will a student who performs the following sequence without error from the beginning to the end have to sit down?

1 2 3 4 2 3 1 4 4 3 2 2 1 2 4 3 1 4 4 1 2

The student will have to sit down at the places,
1 2 3 4 2 3 1 4 4 3 2 2 1 2 4 3 1 4 4 1 2
The student has to sit down 4 times.


Question 5:

Thirty six vehicles are parked in a parking lot in a single row. After the first car, there is one scooter. After the second care, there are two scooters. After the third care, there are three scooters and so on. Work out the number of scooters in the second half of the row.

Let C and S denote car and scooter respectively.
The sequence of parking is,
C S C S S C S S S C S S S S C S S S S S C S S S S S S C S S S S S S S C
The parking lot has been divided into two.
C S C S S C S S S C S S S S C S S S || S S C S S S S S S C S S S S S S S C

Thus, the number of scooters in the second half of the row is 15.


Time to Think:

If it is possible to make a number which is perfect square of a two digit odd number with the second, the sixth and the ninth digits of the number 187642539, which of the following is the digit in the unit's place of that two-digit odd Number?