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Question 1 of 5
1. Question
A is married to B. C is the daughter of A. D is the husband of C. E is the father of D. F is the brother of C. G is the wife of F. Then, consider the following-
I. B is the mother of C
II. A is the father-in-law of D
III. E is the father-in-law of C
IV. F is the son of A
V. G is A’s daughter-in-law
VI. E is the grandfather of A’s grandchildrenHow many of the above statements are definitely true?
Correct
Answer: D
Explanation:
- A and B are married
- C is daughter of A → C is child of both A and B
- D is husband of C
- E is father of D
- F is brother of C → Son of A and B
- G is wife of F
Now evaluate:
- B is the mother of C → A married to B, C is their daughter → True
II. A is father-in-law of D → D is C’s husband → A is C’s father → True
III. E is father-in-law of C → D is C’s husband, E is D’s father → True
IV. F is son of A → F is brother of C, and C is daughter of A → True
V. G is A’s daughter-in-law → G is F’s wife, F is A’s son → True
VI. E is grandfather of A’s grandchildren → C (daughter) and F (son) are A’s kids → C is married to D → Their children = A’s grandchildren → E is father of D → E is grandfather of C’s kids → True
Hence, All six statements are true
Incorrect
Answer: D
Explanation:
- A and B are married
- C is daughter of A → C is child of both A and B
- D is husband of C
- E is father of D
- F is brother of C → Son of A and B
- G is wife of F
Now evaluate:
- B is the mother of C → A married to B, C is their daughter → True
II. A is father-in-law of D → D is C’s husband → A is C’s father → True
III. E is father-in-law of C → D is C’s husband, E is D’s father → True
IV. F is son of A → F is brother of C, and C is daughter of A → True
V. G is A’s daughter-in-law → G is F’s wife, F is A’s son → True
VI. E is grandfather of A’s grandchildren → C (daughter) and F (son) are A’s kids → C is married to D → Their children = A’s grandchildren → E is father of D → E is grandfather of C’s kids → True
Hence, All six statements are true
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Question 2 of 5
2. Question
The ratio of the monthly income of Asha and Rekha is 3 : 4.
Question: What is the ratio of their monthly savings?Statement I: Rekha spends 75% of her income.
Statement II: The difference in monthly savings between Rekha and Asha is ₹6,000.
Statement III: The expenditures of Asha and Rekha are in the ratio 9 : 15.Which of the following is correct with respect to above?
Correct
Answer: C
Explanation:
Let incomes:
Asha = 3x, Rekha = 4xFrom Statement I:
Rekha spends 75% → spends = 0.75 × 4x = 3x
Savings = 4x − 3x = xFrom Statement III:
Expenditure ratio Asha : Rekha = 9 : 15 = 3x : 5x
Rekha’s expenditure = 3x (from above)
So, Asha’s expenditure = (9/15) × 3x = 1.8x
Asha’s income = 3x ⇒ savings = 3x − 1.8x = 1.2xNow:
Savings ratio Asha : Rekha = 1.2x : x = 12 : 10 = 6 : 5Statements I and III together are sufficient
Correct answer: (c)Incorrect
Answer: C
Explanation:
Let incomes:
Asha = 3x, Rekha = 4xFrom Statement I:
Rekha spends 75% → spends = 0.75 × 4x = 3x
Savings = 4x − 3x = xFrom Statement III:
Expenditure ratio Asha : Rekha = 9 : 15 = 3x : 5x
Rekha’s expenditure = 3x (from above)
So, Asha’s expenditure = (9/15) × 3x = 1.8x
Asha’s income = 3x ⇒ savings = 3x − 1.8x = 1.2xNow:
Savings ratio Asha : Rekha = 1.2x : x = 12 : 10 = 6 : 5Statements I and III together are sufficient
Correct answer: (c) -
Question 3 of 5
3. Question
A cylindrical drum has base diameter of 7 m and a height of 18 m. It is filled with water to a height of 3 m. If N identical marbles of diameter 1.4 m each are dropped into the drum, then the height of the water in the drum would rise upto 11.4 m. What is the value of N?
Correct
Answer: B
Radius of drum = 7/2 = 3.5 m Radius of each marble = 1.4/2 = 0.7 m
Rise in water level = 11.4 – 3 = 8.4 m
Volume of the water displaced by N marbles = (base area) × (rise in water level)
∴ N {(4π (0.7)3)/3} = π (3.5)2 × 8.4
Or N = [(3.5)2 × 8.4 × 3] / [4 × (0.7)3]
Or N = 225
Hence, option (b) is the right answer.
Incorrect
Answer: B
Radius of drum = 7/2 = 3.5 m Radius of each marble = 1.4/2 = 0.7 m
Rise in water level = 11.4 – 3 = 8.4 m
Volume of the water displaced by N marbles = (base area) × (rise in water level)
∴ N {(4π (0.7)3)/3} = π (3.5)2 × 8.4
Or N = [(3.5)2 × 8.4 × 3] / [4 × (0.7)3]
Or N = 225
Hence, option (b) is the right answer.
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Question 4 of 5
4. Question
A person saves Rs. 5 on Day 1, Rs. 10 on Day 2, Rs. 15 on Day 3, and so on. On which day will his total savings first exceed Rs. 500 and also be a multiple of 25?
Correct
Answer: C
Solution
Daily savings = 5, 10, 15, 20, … (AP with a = 5, d = 5)
Sum of n terms =
We want the smallest n such that sum > 500 and divisible by 25
Try n = 12 → S = 5×12×13 / 2 = 390
→ not > 500
n = 13 → 5×13×14 / 2 = 455
n = 14 → 5×14×15 / 2 = 525 and divisible by 25Hence, option c is correct.
Incorrect
Answer: C
Solution
Daily savings = 5, 10, 15, 20, … (AP with a = 5, d = 5)
Sum of n terms =We want the smallest n such that sum > 500 and divisible by 25
Try n = 12 → S = 5×12×13 / 2 = 390
→ not > 500
n = 13 → 5×13×14 / 2 = 455
n = 14 → 5×14×15 / 2 = 525 and divisible by 25Hence, option c is correct.
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Question 5 of 5
5. Question
What is the number of times the digit ‘1’ is used in numbering a 120-page book?
Correct
Answer: B
Solution:
Units place (ends in 1): 1, 11, …, 111- Last such number ≤ 120 is 111
- Total = [(111−1)/10] + 1 = 12
Tens place:
- 10–19 → 10 numbers
- 110–119 → 10 numbers
→ Total = 20
Hundreds place:
- 100–120 → all have 1 as hundreds → 21 numbers
Total = 12 + 20 + 21 = 53
Incorrect
Answer: B
Solution:
Units place (ends in 1): 1, 11, …, 111- Last such number ≤ 120 is 111
- Total = [(111−1)/10] + 1 = 12
Tens place:
- 10–19 → 10 numbers
- 110–119 → 10 numbers
→ Total = 20
Hundreds place:
- 100–120 → all have 1 as hundreds → 21 numbers
Total = 12 + 20 + 21 = 53
