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Family Chart:

As per the given information

Since we don't know the gender of 'C'.

So, we cannot determine how 'C' is related to 'A'

Hence, the correct answer is "Option 4"

The logic follows here,

• 1331 = 113113 11^3
• 2197 = 133133 13^3
• 3375 = 153153 15^3
• 4096 = 163163 16^3
• 1331, 2197, 3375 are cubes of odd numbers
• 4096 is the cube of an even number
• Hence, the correct answer is "Option 3"

The logic follows here, 

Thus, it should be 41 instead of 40.

Hence, the correct answer is "Option 3"

The logic followed here is:

MOUSE is coded as 45291

And,

RAT as 786

Similarly,

STORE is coded as

Hence, the correct answer is "Option 1"

The logic followed here is,

Logic: x $ y = x² + y²

Now,

→ 7 $ 3:

7² + 3² = 49 + 9 = 58 (Matches)

→ 6 $ 2:

6² + 2² = 36 + 4 = 40

Similarly, for 5 $ 1

→ 5² + 1² = 25 + 1 = 26.

Hence, the correct answer is "Option 1".

Decoding symbols for Family Tree:

Step-by-step Relationship Analysis:

Breakdown the statement made by the woman: "She is the daughter of my mother's only daughter."

• "My mother's only daughter" – Since the speaker is a woman, her mother's only daughter is the woman herself.
• Now, replace that part in the sentence: "She is the daughter of "me" (the woman)."

Consolidated Family Structure:

Thus, the girl is the Daughter of the woman.

Hence, the correct answer is "Option 1"

Decoding symbols for Family Tree:

Step-by-step Relationship Analysis:

Breakdown the statement: "This man's son's sister is my daughter."

• "This man's son's sister" – A son's sister is simply the man's Daughter.
• If the same girl is the daughter of the man AND the daughter of the woman, then the man and the woman must be the parents of that girl.

Consolidated Family Structure:

Thus, the woman is the Wife of the man.

Hence, the correct answer is "Option 1"

Shortcut Trick

Total units in the ratio = 7 + 9 = 16 units.

Given Sum = 128, so 16 units = 128 → 1 unit = 128 ÷ 16 = 8.

First number = 7 × 8 = 56.

Second number = 9 × 8 = 72.

∴ The correct answer is 56, 72.

Alternate Method

Given: Ratio of two numbers = 7 : 9 and Sum of numbers = 128.

Formula Used: If a sum S is divided in the ratio a : b, then the parts are (a / (a + b)) × S and (b / (a + b)) × S.

⇒ Let the two numbers be 7x and 9x.

⇒ According to the question, 7x + 9x = 128

⇒ 16x = 128

⇒ x = 128 ÷ 16

⇒ x = 8

⇒ First Number = 7 × 8 = 56

⇒ Second Number = 9 × 8 = 72

∴ The correct answer is 56, 72.

Additional Information

Ratio Definition

A ratio is a comparison of two or more quantities of the same kind by division. For a : b, 'a' is called the antecedent and 'b' is the consequent.

Inverse Ratio

The inverse ratio of a : b is b : a. This is commonly used in speed-time and work-efficiency problems.

Compounded Ratio

For two ratios a : b and c : d, the compounded ratio is (a × c) : (b × d).

Proportion

When two ratios are equal, they are said to be in proportion (a : b :: c : d), implying the product of extremes equals the product of means (ad = bc).

Given:

If 16 + 11 = A and (1)/(9)=B, A % B = (A×B)-1, then find A % B.

Formula used:

A % B = (A×B) - 1

Calculations:

A = 16 + 11 = 27

B = 1/9

A % B = (A×B) - 1

⇒ A % B = (27×1/9) - 1

⇒ A % B = 3 - 1

⇒ A % B = 2

∴ The correct answer is option (3).

Given:

Sum of 28 and 22 = 28 + 22

Multiplier = 8

Formula used:

Total = (Sum) × Multiplier

Calculation:

⇒ Total = (28 + 22) × 8

⇒ Total = 50 × 8

⇒ Total = 400

∴ The correct answer is option (2).