Number System Advance Questions - Aptitude Test

Number System Advance Questions - Aptitude Test:

Q. Oranges can be packed in sets of 10 oranges in box type A or 25 oranges in box type B. A carton comprising of 1000 oranges of type a and b is packed. How many different combinations are possible in the number of type A and type B boxes while organizing the oranges?

Ans. 19


Short Cut: 25 Oranges of Type B can be arranged in this manner: 2,4,6,8,.......38

Since 0 and 40 cannot be possible because in question they have asked to include both types in the carton.

So 2 to 38 will comprises of 19 box.


In Brief: We need to make combinations of Type A [10] and Type B [25] oranges to fill total of 1000 oranges in the carton. We are choosing Type B + Type A combinations to find the factors of 1000.

Combination Number	Combinations
1	25 x 2 + 10 x 95
2	25 x 4 + 10 x 90
3	25 x 6 + 10 x 85
4	25 x 8 + 10 x 80
5	25 x 10 + 10 x 75
6	25 x 12 + 10 x 70
7	25 x 14 + 10 x 65
8	25 x 16 + 10 x 60
9	25 x 18 + 10 x 55
10	25 x 20 + 10 x 50
11	25 x 22 + 10 x 45
12	25 x 24 + 10 x 40
13	25 x 26 + 10 x 35
14	25 x 28 + 10 x 30
15	25 x 30 + 10 x 25
16	25 x 32 + 10 x 20
17	25 x 34 + 10 x 15
18	25 x 36 + 10 x 10
19	25 x 38 + 10 x 5

In this combinations we are choosing both types as mentioned in the question. So the total numbers of possible combination are 19.

Note 1: Since they are asking to include both Type A and Type B we follow above method.
Note 2: If they have asked for Type A or Type B, then we add another two combinations that are:

25 x 40 + 10 x 0

10 x 100 + 25 x 0

In this case 2 more possible combinations add to the above solution 19 + 2 = 21.

Q. By multiplying my birth date by 31 and month by 12, I got a total of 494.  Can you tell me birth date and month?

Ans. Date: 14, Month: 5 (May)

Suppose A is the birth date and B is the month So we can write as, 

31A+ 12B = 494 ---- (1)

31A = 494 - 12B ---- (2)

Now we know that there are 12 month in a year so we check the values of B = 1,2,3......

Since both value must be a positive integer, so the value of B for which A comes as positive integer will satisfy equation (2) and will be our solution.

Case 1: Put  B = 1, than A = 15.54 (Not an integer )

           

Case 2: Put B = 2, than A = 15.16 (Not an integer )

Case 3: Put B = 3, than A = 14.77 (Not an integer )

Case 4: Put B = 4, than A = 14.38 (Not an integer )

Case 5: Put B = 5, than A = 14 (It is  a pure  integer value)

Put these values in equation 1

31(14) + 12(5) = 494

Value satisfies. So the ans is 14 May.

Q. In a hostel there are 1000 students in 1000 rooms.  One day the hostel warden asked the student living in room 1 to close all the doors of the 1000 rooms.  Then he asked the person living in room 2 to go to the rooms which are multiples of his room number 2 and open them.  After he ordered the 3rd student to reverse the condition of the doors which are multiples of his room number 3.  If He ordered all the 1000 students like the same, Finally how many doors of those 1000 rooms are in open condition?

Ans. 969

Suppose we have 10 rooms.

We will follow all conditions as given in the question.

Condition 1: Warden asked student of Room 1 to close all doors.

Condition 2: Warden asked student of Room 2 to open all the door which are multiple of his room number that is 2.

Multiples of 2 between 1 - 10 are = 2, 4, 6, 8, 10

Condition 3: Warden asked student of Room 3 to reverse the conditions (that means close the open rooms and open the closed rooms) which are multiple of 3.

Multiple of 3 between 1 - 10 are = 3, 6, 9

Condition 4: Warden asked all other students to reverse the conditions which are multiple of their room numbers.

First we are checking conditions for first 10 possibilities.

L	1	2	3	4	5	6	7	8	9	10
1  →	C	C	C	C	C	C	C	C	C	C
2  →	C	O	C	O	C	O	C	O	C	O
3  →	C	O	O	O	C	C	C	O	O	O
4  →	C	O	O	C	C	C	C	C	O	O
5  →	C	O	O	C	O	C	C	C	O	C
6  →	C	O	O	C	O	O	C	C	O	C
7  →	C	O	O	C	O	O	O	C	O	C
8  →	C	O	O	C	O	O	O	O	O	C
9  →	C	O	O	C	O	O	O	O	C	C
10  →	C	O	O	C	O	O	O	O	C	O

In above table Open = O & Close = C

After 10th possibility, we find that only perfect square number are in closed condition.

So we need to consider all perfect square under 1000.

Total Perfect squares under 1000 = 31 (Which are in closed condition)

So the number of Open Doors = 1000 - 31 = 969.