Data Sufficiency problems
- 1. Question: Who is to the immediate right of P among five persons P, Q, R, S and T facing North?
Statements:
- R is third to the left of Q and P is second to the right of R.
- Q is to the immediate left of T who is second to the right of P.
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 have the order: R, -, P, Q.
From II, we have the order: P, Q, T.
Clearly, each one of the above two orders indicates that Q is to the immediate right of P.
- 2. Question: On which date of the month was Anjali born in February 2004?
Statements:
- Anjali was born on an even date of the month.
- Anjali's birth date was a prime number.
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 and II, we conclude that Anjali was born in February 2004 on a date which is an even prime number. Since the only even prime number is 2, so Anjali was born on 2nd February, 2004.
- 3. Question: How is X related to Y?
Statements:
- Y says, "I have only one brother".
- X says, "I have only one sister".
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 statements in I and II do not provide any clue regarding relation between X and Y.
- 4. Question: How is F related to P?
Statements:
- P has two sisters M and N.
- F's mother is sister of M's 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: Both I and II are sufficient
Explanation:
From I and II, we conclude that P is M's brother and so M's father is P's father. So, F is the child of the sister of P's father i.e. F's mother is P's aunt or F is P's cousin.
- 5. Question: B is the brother of A. How is A related to B?
Statements:
- A is the sister of C.
- E is the husband of A.
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:
B is A's brother means A is either brother or sister of B. Now, each one of I and II individually indicates that A is a female, which means that A is B's sister.
- 6. Question: How many children are there in the row of children facing North?
Statements:
- Vishakha who is fifth from the left end is eighth to the left of Ashish who is twelfth from the right end.
- Rohit is fifth to the left of Nisha who is seventh from the right end and eighteenth from the left end.
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:
Since 8th to the left of 12th from the right is 20th from the right, so from I, we know that Vishakha is 5th from left and 20th from right i.e. there are 4 children to the left and 19 to the right of Vishakha. So, there are (4 + 1 + 19) i.e. 24 children in the row.
From II, Nisha is 7th from right and 18th from left end of the row.
So, there are (6 + 1 + 17) = 24 children in the row.
- 7. Question: How many doctors are practising in this town?
Statements:
- There is one doctor per seven hundred residents.
- There are 16 wards with each ward having as many doctors as the number of wards.
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 I, total number of doctors in town = (1/700 x N) , where N = total number of residents in town. But, the value of N is not known.
From II, total number of doctors in town
= (Number of wards in town) x (Number of doctors in each ward)
= 16 x 16 = 256.
- 8. Question: On which day of the week was birthday of Sahil?
Statements:
- Sahil celebrated his birthday the very next day on which Arun celebrated his birthday.
- The sister of Sahil was born on the third day of the week and two days after Sahil was born.
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:
I does not mention the day of the week on the birthday of either Arun or Sahil.
According to II, Sahil's sister was born on Wednesday and Sahil was born two days before Wednesday i.e. on Monday.
- 9. Question: How many pages of book X did Robert read on Sunday?
Statements:
- The book has 300 pages out of which two-thirds were read by him before Sunday.
- Robert read the last 40 pages of the book on the morning of Monday.
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 and II, we find that Robert read (300 x 2/3) i.e. 200 pages before Sunday and the last 40 pages on Monday.
This means that he read [300 - (200 + 40)] i.e. 60 pages on Sunday.
- 10. Question: How is Tanya related to the man in the photograph?
Statements:
- Man in the photograph is the only son of Tanya's grandfather.
- The man in the photograph has no brothers or sisters and his father is Tanya's grandfather.
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 I, we conclude that the man is the only son of Tanya's grandfather i.e. he is Tanya's father or Tanya is the man's daughter.
From II, we conclude that the man's father is Tanya's grandfather. Since the man has no brothers or sisters, so he is Tanya's father or Tanya is the man's daughter.
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