Explanation : 

PROBLEM: Can we determine if there are more than 100 figures in the book?

GIVEN:
Statement S1: Not more than 2 figures on any page; 51 pages
Statement S2: At least 1 figure on every page

ANALYSIS:
1. Maximum figures possible:
– 2 figures/page × 51 pages = 102 figures

2. Minimum figures possible:
– 1 figure/page × 51 pages = 51 figures

3. Range of possible total figures:
51 to 102 figures

CONCLUSION: Cannot determine if there are more than 100 figures
REASON: The actual number could be anywhere between 51 and 102 figures

ANSWER: Given information is insufficient to answer the question

Explanation : 

The pattern is a b a b a / b c b c b / c d c d c /d e d e d

Explanation :

A vessel full of water weighs 40 kg

GIVEN:
– Full vessel weighs 40 kg
– One-third filled vessel weighs 20 kg

SOLUTION:
1. Weight difference = 40 – 20 = 20 kg
This is weight of 2/3 water

2. Weight of 1/3 water = 20/2 = 10 kg

3. Empty vessel weight = Weight of 1/3 filled – Weight of 1/3 water
= 20 – 10 = 10 kg

ANSWER: The empty vessel weighs 10 kg

Explanation :

PROBLEM: Find ratio of man’s speed in still water to current speed

FORMULAS:
Time = Distance/Speed
– Downstream time = Distance/(v + c)
– Upstream time = Distance/(v – c)

SOLUTION:
1. Speeds:
– Downstream = v + c
– Upstream = v – c

2. Since downstream time is half:
v + c = 2(v – c)
v + c = 2v – 2c
-v + 3c = 0
v = 3c

3. Therefore:
Man’s speed : Current speed
= v : c
= 3 : 1

ANSWER: The ratio of man’s speed in still water to current speed is 3:1

Explanation :

Minimum number & maximum of points of intersection of a square and circle

Statement 1 is incorrect. The minimum number of points of intersection between a square and a circle can be 0 if the circle is entirely inside or outside the square.

Statement 2 is correct. The maximum number of points of intersection between a square and a circle is 8. This can happen when the circle passes through all four corners of the square and intersects each side once.

So only statement 2 is correct. Therefore, the correct answer is indeed (b) 2 only.

Explanation : 

Digit n > 3 is divisible by 3

Since n is divisible by 3 but not divisible by 6, it means that n must be an odd multiple of 3. Let’s take n=9 as an example.

(a) 2n = 2 * 9 = 18 which is not divisible by 4

(b) 3n = 3 * 9 = 27 which is not divisible by 4

(c) 2n +4 = (2 *9) +4 =22 which is not divisible by 4

(d) 3n +1 = (3 *9)+1=28 which is divisible by 4

So the correct answer is (d) 3n+1.

Explanation :

PROBLEM: Find the final ratio of liquids A and B after two replacements

STEP 1: After First Replacement
– Liquid A = 16 litres
– Liquid B = 4 litres
– Total = 20 litres
– Ratio of A to total = 16/20 = 4/5

STEP 2: Second Replacement
– 4 litres mixture removed
– Liquid A removed = 4 × 4/5 = 3.2 litres
– Liquid A remaining = 16 – 3.2 = 12.8 litres
– Liquid B = 20 – 12.8 = 7.2 litres

STEP 3: Final Ratio
12.8:7.2 simplifies to 16:9

ANSWER: The final ratio of liquid A to liquid B is 16:9

Explanation : 

PROBLEM: Find percentage of married adults in population

GIVEN:
– 40% men are married
– 30% women are married
– Each marriage has one man and one woman

SOLUTION:
Let M = number of men
W = number of women

1. Since married men = married women:
0.4M = 0.3W
W = (4/3)M

2. Total Population N = M + W = M + (4/3)M = (7/3)M

3. Total married adults = 0.4M + 0.3W
= 0.4M + 0.3(4/3)M
= 0.8M

4. Percentage = (0.8M)/(7/3)M = (0.8 × 3)/7 = 2.4/7
= 240/7%
≈ 34.29%

ANSWER: 240/7% or approximately 34.29%

Explanation : 

acpq: besu:: mngi: @

PATTERN: ACPQ → BESU
Letter Shifts:
– 1st letter: +1
– 2nd letter: +2
– 3rd letter: +3
– 4th letter: +4

Starting Word: MNGI
Applying shifts:
M + 1 = N
N + 2 = P
G + 3 = J
I + 4 = M

ANSWER: NPJM

Explanation : 

ghi=1578 def=912 abc= ?

ALPHABETS TO NUMBERS:
ABC = 123
DEF = 456
GHI = 789

DOUBLING THE NUMBERS:
ABC: 123 × 2 = 246
DEF: 456 × 2 = 912
GHI: 789 × 2 = 1578

Pattern: Each three-letter group when doubled gives the result shown on the right side.