Numerical Aptitude

UPSC Prelims 2022 Q) A has some coins. He gives half of the coins and 2 more 2 B.B gives half of the coins and 2 more to C. C gives half of the coins and 2 more to D. The number of coins D has now , is the smallest 2 digit number, how many coins does A have in the beginning ?

Solution:- Hint given is --> The number of coins D has now , is the smallest 2 digit number, which is 10

hence D has 10 coins

coins with C = (coins with D - 2) x 2 = (10 - 2 ) x 2 = 16

coins with B = (coins with C - 2) x 2 = (16 - 2 ) x 2 = 28

coins with A = (coins with B - 2) x 2 = (28 - 2 ) x 2 = 52

Hence the  answer is 52

UPSC Prelims 2022 Q) on one side of a 1.01 km long road, 101 plants are planted at equal distance from each other. what is the total distance between 5 consecutive plants ?

Solution:- Total length = 1.01 Km = 1010 m

Total plants = 101

Total spacing's = 101 -1 = 100

Spacing between each tree = 1010/100 = 10.1m

Now, Distance between 5 trees means (5-1 ) = 4 spaces

Hence answer is 10.1 x 4 = 40.4m

UPSC Prelims 2022 Q) Five friends P,Q,X,Y and Z Purchased some notebooks. The relevant information is given below:

1. Z purchased 8 Notebooks more than X did

2. P and Q together purchased 21 notebooks.

3. Q purchased 5 notebooks less than P did.

4. X and Y together purchased 28 notebooks.

5. P purchased 5 notebooks more than X did.

If each notebook is priced Rs 40, then what is the total cost of all the notebooks?

Solution:- 

We know that, P + Q = 21

Also, P = Q + 5

Hence  Q + 5 + Q = 21

2Q + 5 = 21

Q = 16/2 = 8

Therefore P = Q + 5 = 13

X = 13 - 5 = 8

Y = 28 - 8 = 20

Z = 8 + 8 = 16

So, Total books = 13 + 8 + 8 + 20 + 16 =65

Total cost of books = 65 x 40 = 2600 Rs

UPSC Prelims 2022 Q) There is a numeric lock which has a 3-digits PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in PIN defer by at least 2. How many maximum attempts does one need to find out the PIN with certainty?

Solution:- 3 -digits PIN will be

Possible Attempts Based on conditions given would be

7	5	3
7	5	2
7	5	1
7	4	2
7	4	1
7	3	1
6	4	2
6	4	1
6	3	1
5	3	1

So, the Maximum attempts to find the PIN will be 10.

UPSC Prelims 2022 Q) What is the remainder when 91 X 92 X 93 X 94 X 95 X 96 X 97 X 98 X 99 is divided by 1261 ?

Solution:- 

$$\text{91 X 92 X 93 X 94 X 95 X 96 X 97 X 98 X 99}\over 1261$$

Factorize 1261

$$\text{91 X 92 X 93 X 94 X 95 X 96 X 97 X 98 X 99}\over {\text{13 X 97}}$$

after solving

$$\text{92 X 93 X 94 X 95 X 96 X 98 X 99}\over {\text{1}}$$

each and every number is divisible by 1 hence Remainder will be zero

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:- 

UPSC Prelims 2022 Q) 

Solution:-