Explanation : 
Statement 1: A 20 × 8 sheet can be precisely divided into four square sheets, including two 4×4 squares and two 8×8 squares.

Statement 2: A 20 × 8 sheet can be segmented into 10 triangular sheets, each with an equal area of 16 square units.

Therefore, the correct answer is option (3), which states that both statements 1 and 2 are accurate.

Explanation : 

24 men and 12 women

The answer to this question is d. Data is inadequate to draw any conclusion.

This is because the information given in the question does not specify whether men and women have the same efficiency in doing the work or if their efficiencies are different. Without this information, it’s not possible to determine how long it would take for 12 men and 24 women to do the same piece of work.

Explanation : 

There are two containers X and Y

X contains 100 ml of milk. Y containes 100 ml of water.
20 ml of milk from X is transferred to Y.
Now, we get,
X → Milk = 80 ml
Y → Milk = 20 ml and Water = 100 ml
Total mixture in Y is 120 ml in which ratio of Milk and Water is 1 :5 respectively.

After that 20 ml of the mixture of Y is transferred to X,

Mixture to be transferred from Y = Y → Milk = 20/6, Water = (20/6) × 5 = 100/6
Remaining mixture in Y = Y → Milk = 20 – (20/6) = 100/6, Water = 100 – (100/6) = 500/6

New Mixture in X = X → Milk = 80 + (20/6) = 500/6, Water = 100/6

It is given that m denotes the proportion of milk in X i.e. 500/6
It is given that n denotes the proportion of water in Y i.e. 500/6

It means m = n.

Explanation : 
From statement 1:
At 3 o’clock, the minute hand is 15 minute spaces apart from hour hand.
To be coincident, it must gain 15 minute spaces.
We know that, 55 minutes are gained in 60 minutes.
So, 15 minutes are gained in (60/55) × 15 = 180/11 minutes = 16.36 minutes
Thus, hour hand and minute hand will coincide at 3:16:36, which is between 3:16 pm and 3:17 p.m.
Hence, statement 1 is correct.

From statement 2:
Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide: At any given time, the second hand moves much faster than the minute hand. This means that during any given minute, there will be a moment when both hands coincide.

Thus, both statements 1 and 2 are correct.

Explanation : 

Two candidates X and Y contested an election

Let’s assume the total number of voters in the voter list as “T”.

80% of the voters cast their votes which means the total number of votes cast is (80/100) x T = 0.8T.

Now, we know that X got 56% of the votes cast, which means X got 0.56 x 0.8T = 0.448T votes.

Let’s assume Y got “y” votes. Since there were no invalid votes, the total number of votes cast is the sum of votes received by X and Y, i.e., 0.448T + y = 0.8T.

Solving for y, we get y = 0.352T.

Now, we know that X won by 1440 votes. This means X got 1440 more votes than Y. So, we can write an equation as:

0.448T – 0.352T = 1440

Simplifying the equation, we get 0.096T = 1440, which implies T = 15000.

Therefore, the total number of voters in the voter list is 15000, option (a) is the correct answer.

Explanation : 
2, 12, 36, 80, 150, X

Consider the differences between consecutive terms:

12 – 2 = 10
36 – 12 = 24
80 – 36 = 44
150 – 80 = 70

Now let’s examine the differences between these differences:

24 – 10 = 14
44 – 24 = 20
70 – 44 = 26

We see that the differences between the differences are increasing by 6 each time. Therefore, to find the next difference between consecutive terms, we can add 6 to the last difference between differences:

26 + 6 = 32

Now we can add this difference to the last difference between consecutive terms in the original sequence:

70 + 32 = 102

Finally, to find the value of X, we can add this difference to the last term in the original sequence:

150 + 102 = 252

Thus, the value of X is 252 (option b).

Explanation : 

June 2099 – Sunday

Prelims 2022 – 5-JUN-2022 Sunday.

First, calculate the number of years between 2022 and 2099, which is 2099 – 2022 = 77 years.

Determining Number of Leap Years

Next, determine the number of leap years in this period. Leap years are typically every 4 years, but we must exclude centuries that are not divisible by 400. The years from 2022 to 2099 include the following leap years: 2024, 2028, 2032, 2036, 2040, 2044, 2048, 2052, 2056, 2060, 2064, 2068, 2072, 2076, 2080, 2084, 2088, 2092, 2096. That’s a total of 19 leap years.

Calculating Total Number of Odd Days

Each normal year contributes 1 odd day (365 days = 52 weeks + 1 day), and each leap year contributes 2 odd days (366 days = 52 weeks + 2 days).

So, the total number of odd days in 77 years is:

• Odd days from normal years = 58 normal years × 1 odd day = 58 odd days
• Odd days from leap years = 19 leap years × 2 odd days = 38 odd days
• Total odd days = 58 + 38 = 96 odd days

Determining the Day of the Week

Since each week has 7 days, we find the remainder of 96 divided by 7 to get the number of odd days:

96 mod 7 = 5 odd days

Since June 5, 2022, was a Sunday, adding 5 odd days means:

Sunday + 5 days = Friday

Thus, June 5, 2099, will be a Friday.

Explanation : 

Two friends X and Y start running

After running together for 50 meters in the same direction and reaching a point, X turns right and runs 60 meters while Y turns left and runs 40 meters.

This means that they are now 100 meters apart from each other on a straight line (60 + 40 = 100).

Then X turns left and runs 50 meters and stops while Y turns right and runs 50 meters and then stops.

Since both X and Y ran in the same direction for the same distance (50 meters), their distance from each other remains unchanged at 100 meters.

Explanation :

20,10,10,15,30,75

1 20 x 0.5 = 10
2 10 x 1.0 = 10
3 10 x 1.5 = 15
4 15 x 2.0 = 30
5 30 x 2.5 = 75
6 75 x 3.0 = 225

We can see that to obtain X, we need to multiply the previous term (75) by 3. Therefore, the value of X is:

X = 75 x 3 = 225
Therefore, the correct answer is (d) 225.

Explanation : 

Deciphering the representation of ‘LUCKNOW’ after reversing the order of English alphabet letters.

The English alphabet has 26 letters. If we assign a numerical value to each letter based on its position in the alphabet (A=1, B=2, C=3 and so on), then we can find the reverse of each letter by subtracting its value from 27. This is because when the order of the alphabet is reversed, the first letter (A) becomes the last (Z), the second letter (B) becomes the second last (Y) and so on.

For example: L is the 12th letter in the alphabet. To find its reverse, we subtract its value from 27: 27-12=15. The 15th letter in the alphabet is O. So L becomes O when reversed.

Using this method we can find that: L -> O U -> F C -> X K -> P N -> M O -> L W -> D

So LUCKNOW becomes OFXPMLD when reversed using this method.