Logical Reasoning

 UPSC Prelims 2022--> Q) If the order of the letters in the English alphabet is reversed and each letter represents the letter whose position it occupies, then which one of the following represents 'LUCKNOW'?

^{Solution :- As per Criteria}

 

A

B

C

D

E

F

G

H

I

J

K

L

M

Z

Y

X

W

V

U

T

S

R

Q

P

O

N

 

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

M

L

K

J

I

H

G

F

E

D

C

B

A

 Hence,

L	U	C	K	N	O	W
O	F	X	P	M	L	D

Charts

  UPSC Prelims 2022--> Q) A pie chart gives the expenditure on five different items A,B,C,D and E in a household. If B,C,D and E corresponds to 90^o, 50^o, 45^o  and 75^o respectively, then what is the percentage of expenditure item A?

^{Solution :-} 

^{For Pie chart Total Angle  = 360o}

Angle for B = 90^o

Angle for C = 50^o

Angle for D = 45^o

Angle for E = 75^o

Angle for B = 360^o - 90^o - 50^o - 45^o - 75^o = 100^o

 

 

^{Percentage Expenditure of Item A}

100 x ¹⁰⁰⁄₃₆₀ = ¹⁰⁰⁰⁰⁄₃₆₀  = ¹⁰⁰⁰⁄₃₆ = ²⁵⁰⁄₉ 

Distance and Time

 UPSC Prelims 2022--> Q) X and Y run in a 3 Km race along a circular course of length 300 m . there speeds are in the ratio 3:2 if they start together in the same direction, how many times would the first one pass the other (The start of not counted as passing)?

^{Solution :-} 

                   ^X⁄_Y  =  ³⁄₂

_{Lets assume speed Speed of X is 3 m/s}

Then speed of Y =  2 m/s

_{Now Total Rounds =} ³⁰⁰⁰⁄₃₀₀ = 10 Rounds

_{Time taken by X to complete 1 round =} ³⁰⁰⁄₃ = 10 Seconds

_{Time taken by Y to complete 1 round =} ³⁰⁰⁄₂ = 15 Seconds

Round            X            Y

1                    10            15

2                    20            30

3                    30            45

4                    40            60

5                    50            75

6                    60            90

7                    70            105

8                    80            120

9                    90            135

10                  100          150

They will cross each other 3 times

UPSC Prelims 2022--> Q) Two friends X and Y Start running and they run together for 50m in the same direction and reach a point. X turns Right and Runs 60m while Y turns left and runs 40m. Then X turns left and runs 50m and stops , while Y turns right and runs 50m and then stops. How far are the tow friends from each other now?

Solution :- 

Distance Between X and Y = 60m + 40m = 100 m

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

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Finding Day by Date of Any Year

 UPSC Prelims 2022:- Q) Which Date of June 2099 among the following is Sunday??

Solution:- 

To solve such questions one must know following things

Month Code for day calculations

Month	Normal Year	Leap year
Jan	1	0
Feb	4	3
Mar	4	4
Apr	0	0
May	2	2
June	5	5
July	0	0
Aug	3	3
Sep	6	6
Oct	1	1
Nov	4	4
Dec	6	6

 Century Code

1700	1800	1900	2000
4	2	0	6

Formula = (Date + Year + Month Code + Century Code + No. of Leap Years till that Year)/7 

Year means Last 2 digits of that year i.e. in 1947 it will be 47 only

No. of Leap Years till that Year = Year/4 <-- whatever be the remainder no consideration to it

Days from Remainder obtained from Above equation

Remainder	Day
0	Saturday
1	Sunday
2	Monday
3	Tuesday
4	Wednesday
5	Thursday
6	Friday

so, 

Date=???

Year = 2099 i.e . Year = 99

Month code of June = 5

Century code = 6

No of Leap years = 99/4 = 24

For Sunday, Remainder = 1

Therefore, 

(Date + 99 +5 +6+24)/7

(date + 134)/7 after division Remainder should be  1

from options if date = 7 then 7+134 = 141, so 141 = 20 x 7 +1 hence 

Date = 7

Smallest Or Biggest Number amongst Exponential Numbers

 Q) Prelims 2022 --> Which number among  2⁴⁰ , 3²¹ , 4¹⁸ , and 8¹² is smallest ?

a) 2⁴⁰

b) 3²¹

c) 4¹⁸

d) 8¹²

Solution :- 

Category:- Quantitative Aptitude --> Basic Concept --> Laws of Indices

Common Strategies :- 

    1) Common Base

    2) Common Exponent 

Solving by both Common Exponent method and Common Base method

HCF of 21 , 18 and 12 is 3

-->  21 can be rewritten as 3 x 7 , hence, (3⁷)³= (3x3x3x3x3x3x3)³= (2187)³

-->  18 can be rewritten as 3 x 6 , hence, (4⁶)³= (4x4x4x4x4x4)³= (4096)³

-->  12 can be rewritten as 3 x 4 , hence, (8⁴)³= (8x8x8x8)³= (4096)³

2⁴⁰ can be written as 2 x (2³)¹³= 2 x 8¹³ by common base method it is greater than 8¹²  Hence Out of Option

so from above three Exponents the smallest value is (2187)³ Hence correct option is (b)