Data Sufficiency problems
- 1. Question: In which year was Rahul born?
Statements:
- Rahul at present is 25 years younger to his mother.
- Rahul's brother, who was born in 1964, is 35 years younger to his mother.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Both I and II are sufficient
Explanation:
From both I and II, we find that Rahul is (35 - 25) = 10 years older than his brother, who was born in 1964. So, Rahul was born in 1954.
- 2. Question: What will be the total weight of 10 poles, each of the same weight?
Statements:
- One-fourth of the weight of each pole is 5 kg.
- The total weight of three poles is 20 kilograms more than the total weight of two poles.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Either I or II is sufficient
Explanation:
From I, we conclude that weight of each pole = (4x5) kg = 20 kg.
So, total weight of 10 poles = (20 x 10) kg = 200 kg.
From II, we conclude that:
Weight of each pole = (weight of 3 poles) - (weight of 2 poles) = 20 kg.
So, total weight of 10 pojes = (20 x 10) kg = 200 kg.
- 3. Question: How many children does M have?
Statements:
- H is the only daughter of X who is wife of M.
- K and J are brothers of M.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Neither I nor II is sufficient
Explanation:
From I, we conclude that H is the only daughter of M. But this does not indicate that M has no son. The information given in II is immaterial.
- 4. Question: How much was the total sale of the company?
Statements:
- The company sold 8000 units of product A each costing Rs. 25.
- This company has no other product line.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Both I and II are sufficient
Explanation:
From I, total sale of product A = Rs. (8000 x 25) = Rs. 200000.
From II, we know that the company deals only in product A.
This implies that sale of product A is the total sale of the company, which is Rs. 200000.
- 5. Question: The last Sunday of March, 2006 fell on which date?
Statements:
- The first Sunday of that month fell on 5th.
- The last day of that month was Friday.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Either I or II is sufficient
Explanation:
From I, we conclude that 5th, 12th, 19th and 26th of March, 2006 were Sundays.
So, the last Sunday fell on 26th.
From II, we conclude that 31st March, 2006 was Friday. Thus, 26th March, 2006 was the last Sunday of the month.
- 6. Question: What is the code for 'sky' in the code language?
Statements:
- In the code language, 'sky is clear' is written as 'de ra fa'.
- In the same code language, 'make it clear' is written as 'de ga jo'.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Neither I nor II is sufficient
Explanation:
The only word common to I and II is 'clear' and as such, only the code for 'clear' can be ascertained from the given information.
- 7. Question: How many children are there between P and Q in a row of children?
Statements:
- P is fifteenth from the left in the row.
- Q is exactly in the middle and there are ten children towards his right.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Both I and II are sufficient
Explanation:
From II, Q being in the middle, there are 10 children to his right as well as to his left. So, Q is 11th from the left. From I, P is 15th from the left.
Thus, from both I and II, we conclude that there are 3 children between P and Q.
- 8. Question: How is T related to K?
Statements:
- R's sister J has married Ts brother L, who is the only son of his parents.
- K is the only daughter of L and J.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Both I and II are sufficient
Explanation:
From I, we know that L is T's brother and J's husband. Since L is the only son of his parents, T is L's sister.
From II, we know that K is L's daughter.
Thus, from I and II, we conclude that T is the sister of K's father i.e. T is K's aunt.
- 9. Question: How is J related to P?
Statements:
- M is brother of P and T is sister of P.
- P's mother is married to J's husband who has one son and two daughters.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: II alone is sufficient while I alone is not sufficient
Explanation:
From II, we know that P's mother is married to J's husband, which means that J is P's mother.
- 10. Question: How is X related to Y?
Statements:
- Y and Z are children of D who is wife of X.
- R's sister X is married to Ys father.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Either I or II is sufficient
Explanation:
From I, we conclude that Y is the child of D who is wife of X i.e. X is Y's father.
From II, X is married to Y's father. This implies that X is Y's mother.
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