Number Sequences and Logic Puzzles

This series operates in triplets where the third number is the product of the first two divided by the second number of the previous triplet. 5×20÷8≈12.5, then 24×6÷12=12, so 2×8÷12≈1.33, but the pattern is actually: each triplet (a,b,c) follows c = a×b÷(previous triplet's second element). Looking simpler: 5×4=20, 20+4=24, 24÷4=6, 6÷3=2, 2×4=8, 8+4=12, 12÷4=3. The answer is 3. Option B is correct.

The pattern is: n² - n = next term. 2²-2=2, 6²-6=30, but that's not 42. Actually: 2×3=6, 6×7=42, 42×43=1806. Each term is multiplied by (term+1). 2×3=6, 6×7=42, 42×43=1806. Option B is correct.

The sequence alternates between two patterns: the 1st, 3rd, and 5th terms (5, 6, 7) increase by 1. The 2nd and 4th terms (10, 9) decrease by 1. Following the second pattern, the next term after 7 should be 9-1=8.

The sequence follows an alternating pattern of adding and subtracting powers of 2: 100-4=96, 96+8=104, 104-16=88, 88+32=120, 120-64=56. The next step is to add 128: 56+128=184. Other options do not follow this geometric progression of differences.

The pattern is 2^n + 2: 2^1+2=4, 2^2+2=6, 2^3+2=10, 2^4+2=18, 2^5+2=34. Wait, that doesn't match. Let's reconsider: pattern is double and add 2: 2×2+2=6, 6×2+2=14, 14×2+2=30, so 30×2+2=62. The correct answer is D (62).

The pattern alternates subtraction and addition with powers of 2: subtract 4, add 8, subtract 16, add 32. The next operation should be subtract 64: 120 - 64 = 56. This correctly continues the alternating pattern with doubling values.

This is the Fibonacci sequence starting from 0, 1: each term is the sum of the previous two terms (0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21). The next term is 13+21=34. Option C is correct.

The pattern alternates subtraction and addition with powers of 2: 100-4=96, 96+8=104, 104-16=88, 88+32=120, 120-64=56. The next operation is add 128: 56+128=184. Option C correctly continues this pattern.

Let current age be x. Then x = (4/5)(x + 7). Solving: 5x = 4x + 28, so x = 28. Verify: in 7 years he will be 35, and 28 is indeed 4/5 of 35.

Let John's current age be x. In 20 years, his age will be x + 20. The problem states x + 20 = 5x. Solving for x gives 4x = 20, so x = 5. Testing other options: if he were 15, in 20 years he would be 35, which is not 5*15.

To find the length, convert speed to m/s: 60 * (5/18) = 50/3 m/s. Distance = Speed * Time, so (50/3) * 9 = 150 meters. 120, 180, and 160 are incorrect results derived from using wrong conversion factors or calculation errors.

The pattern repeats each number twice: 40, 40, 47, 47, 54, 54. Each pair increases by 7 from the previous pair (40 to 47 to 54). Therefore, the next number should be 54 again.

Vijay's mother's only brother is his maternal uncle. That uncle's only nephew is Vijay himself (since Vijay is the son of the uncle's sister). Rani is Vijay's wife, making her his wife.

B and E are brothers and sons of A. C is married to B, and D (C's sister) is married to E. Since D is the wife of A's son E, D is A's daughter-in-law. The option 'Daughter's-in-law' is grammatically poor but identifies the correct relationship.

Abhishek's father's 'only child' is Abhishek himself. The girl is the daughter of this only child, meaning she is Abhishek's daughter. Therefore, Abhishek's wife is the mother of that girl. Distractors like sister or aunt incorrectly identify the generational or marital link.

Salman's grandfather's only son would be Salman's father. Aishwarya is the daughter of that son, making her Salman's sister. They share the same father.

Statement 1 establishes C is D's grandparent. Statement 2 establishes B is D's sister. Both are needed: with only statement 1, we don't know if B is male or female; with only statement 2, we don't know how D relates to C. Combined, B is D's sister and D's granddaughter, making B C's granddaughter.

Sandeep's father has a sister, making her the girl's mother. This means Sandeep and the girl are children of siblings, which is the definition of cousins. Specifically, Sandeep is the girl's cousin (children of siblings are cousins). The gender of the cousin isn't specified in the question.

Sheetal's grandfather's 'only son' is Sheetal's father. The 'son of the only son' is therefore the son of Sheetal's father. Consequently, Vijay is Sheetal's brother. Other options like Uncle or Son do not fit this direct nuclear family lineage.

The woman's statement means: the man is the only son of the woman's mother's mother (her grandmother's only son). This man would be the woman's maternal uncle. Therefore, the woman is this man's niece. A niece is the daughter of one's sibling.