Question 1

Data Sufficiency — Year of birth: determine Rahul’s birth year  Question: In which year was Rahul born? Statements: I. Rahul at present is 25 years younger than his mother. II. Rahul's brother, born in 1964, is 35 years younger than his mother. Choo…

Accepted Answer

Analyze each statement I alone: Gives only the age difference (Mother − Rahul = 25). Without the mother's birth year/age, Rahul's year of birth is indeterminate. II alone: From “brother was born in 1964 and is 35 years younger than mother” ⇒ Mother's birth year = 1964 − 35 = 1929. But Rahul's age difference from mother is unknown, so Rahul's birth year is still indeterminate. Together With I + II, one could find Rahul's year (1929 + 25 = 1954). However, neither statement alone is sufficient by itself. Final Sufficiency Choice Neither I nor II is sufficient.

Question 2

Data Sufficiency — Total weight of 10 identical poles  Question: What is the total weight of 10 poles, each of the same weight? Statements: I. One-fourth of the weight of each pole is 5 kg. II. The total weight of three poles is 20 kg more than the …

Accepted Answer

Let each pole weigh w kg From I: (1/4)w = 5 ⇒ w = 20 kg ⇒ Total for 10 poles = 10 × 20 = 200 kg. I alone is sufficient. From II: 3w = 2w + 20 ⇒ w = 20 kg ⇒ Total for 10 poles = 200 kg. II alone is sufficient. Final Sufficiency Choice Either I or II is sufficient.

Question 3

Data Sufficiency — Number of M’s children  Question: How many children does M have? Statements: I. H is the only daughter of X, who is the wife of M. II. K and J are brothers of M. Decide which statement(s) determine the number of M's children.

Accepted Answer

Assessment Statement I: H is the only daughter of M's wife (X). This implies M has exactly one daughter, but he may have zero, one, or more sons. The total number of children is unknown. Statement II: Tells about M's siblings (K and J), not M's children. Irrelevant to the question. Combined Even together, we only know there is one daughter; the count of sons (if any) is undetermined. Final Sufficiency Choice Neither I nor II is sufficient.

Question 4

Data Sufficiency — Company sales: Determine the total sale amount in ₹ for the company.  Statement I: The company sold 8000 units of product A, each costing ₹25. Statement II: The company has no other product line (i.e., sells only product A).  Deci…

Accepted Answer

Goal Find the total sale of the company. Evaluate Statement I Revenue from product A = 8000 × ₹25 = ₹200,000.But this is the company's total sale only if no other products are sold. I alone does not assure that. Evaluate Statement II Company sells only product A.No quantity/price given ⇒ cannot compute total sale. Together (I + II) Only product A is sold (II) and its quantity and price are known (I): total sale = ₹200,000. Common pitfall Assuming Statement I implies total sale without confirming there are no other product lines. Final Answer Both statements I and II together are sufficient, but neither alone is sufficient.

Question 5

Data Sufficiency — Calendar: Find the date of the last Sunday of March 2006.  Statement I: The first Sunday of that month fell on 5th March 2006. Statement II: The last day of March 2006 was a Friday.  Decide which statements are sufficient to answe…

Accepted Answer

Using Statement I If the first Sunday is on 5th March, Sundays are 5, 12, 19, 26 ⇒ last Sunday = 26th. Using Statement II If 31st March 2006 is Friday, then 26th is Sunday (counting backward): 31(Fri), 30(Thu), 29(Wed), 28(Tue), 27(Mon), 26(Sun). Conclusion Each statement alone leads to the unique answer (26th March 2006). Final Answer Either statement I or statement II alone is sufficient.

Question 6

Data Sufficiency — Coding: Determine the code word for ‘‘sky’’ in a substitution language.  Statement I: ‘‘sky is clear’’ is written as ‘‘de ra fa’’. Statement II: ‘‘make it clear’’ is written as ‘‘de ga jo’’.  Decide which statements are sufficient…

Accepted Answer

From the two statements Common word = ‘‘clear’’ ⇒ common code = ‘‘de’’.Then in Statement I, {‘‘sky’’, ‘‘is’’} map to {‘‘ra’’, ‘‘fa’’} but we cannot distinguish which is which. Conclusion Even together, the code for ‘‘sky’’ is ambiguous between two codes. Final Answer Even both statements I and II together are not sufficient.

Question 7

Data Sufficiency — Row of children: Find the number of children between P and Q in a single row.  Statement I: P is 15th from the left end in the row. Statement II: Q is exactly in the middle of the row and there are ten children to his right.  Deci…

Accepted Answer

Analyze Statement II Q is in the middle and has 10 to his right ⇒ total = 21, Q is 11th from the left. Combine with Statement I P is 15th from the left.Children between P and Q = |15 − 11| − 1 = 4 − 1 = 3. Individually Neither I nor II alone yields the count between P and Q. Final Answer Both statements I and II together are sufficient, but neither alone is sufficient.

Question 8

Data Sufficiency — Relationships: How is T related to K?  Statement I: R's sister J has married T's brother L, who is the only son of his parents. Statement II: K is the only daughter of L and J.  Decide which statements are sufficient to answer the…

Accepted Answer

Interpretation From I: L is T's brother and the only son ⇒ T must be a daughter (sister of L).From II: K is the daughter of L and J ⇒ L is K's father. Combine T is the sister of K's father ⇒ T is K's paternal aunt (father's sister). Individually Neither I nor II alone identifies T's relation to K. Final Answer Both statements I and II together are sufficient, but neither alone is sufficient.

Question 9

Data Sufficiency — Relationships: How is J related to P?  Statement I: M is brother of P and T is sister of P. Statement II: P's mother is married to J's husband, who has one son and two daughters.  Decide which statements are sufficient to answer t…

Accepted Answer

Statement I Gives P's siblings but says nothing about J ⇒ insufficient. Statement II "P's mother is married to J's husband" ⇒ J's husband and P's father are the same person. Under standard monogamy assumption in family puzzles, this implies J is P's mother. Extra clause "who has one son and two daughters" is consistent with P's sibling set but not required for identifying J's relation. Final Answer Statement II alone is sufficient, but Statement I alone is not sufficient.

Question 10

Data Sufficiency — Relationships: How is X related to Y?  Statement I: Y and Z are children of D, who is the wife of X. Statement II: R's sister X is married to Y's father.  Decide which statements are sufficient to answer the question. Choose the c…

Accepted Answer

From Statement I D is X's wife; Y is D's child ⇒ X is Y's father. From Statement II X is married to Y's father ⇒ X is Y's mother (spouse of father). Either way, X's relationship to Y (parent) is uniquely determined from each statement alone. Final Answer Either statement I or statement II alone is sufficient.

Question 11

Data Sufficiency — Linear seating (facing North): Who sits immediately to the right of P among P, Q, R, S, T?  Statement I: R is third to the left of Q and P is second to the right of R. Statement II: Q is immediately to the left of T, who is second…

Accepted Answer

Using Statement I Place Q, then R three to its left; P is two to the right of R. In all valid placements (for 5 seats), the person immediately to the right of P is Q. Using Statement II T is second to the right of P; Q is immediately left of T ⇒ Q is immediately right of P. Conclusion Each statement alone yields the same unique neighbor: the person to P's immediate right is Q. Final Answer Either statement I or statement II alone is sufficient.

Question 12

Data Sufficiency — Date of birth (February 2004): On which date was Anjali born?  Statement I: Anjali was born on an even date in February 2004. Statement II: Anjali's birth date was a prime number.  Decide which statements are sufficient to answer …

Accepted Answer

Key facts February 2004 has 29 days (leap year).Even dates in Feb: 2, 4, 6, ..., 28.Prime dates ≤ 29: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Intersection Even ∩ Prime = 2 only. Conclusion Neither statement alone identifies the date, but together they uniquely give 2nd February 2004. Final Answer Both statements I and II together are sufficient, but neither alone is sufficient.

Question 13

Data Sufficiency — Relationships: How is X related to Y?  Statement I: Y says, "I have only one brother." Statement II: X says, "I have only one sister."  Decide which statements are sufficient to answer the question. Choose the correct sufficiency …

Accepted Answer

Reasoning The statements restrict the composition of each person's siblings but do not link X and Y explicitly as siblings, cousins, or spouses.Multiple family structures satisfy both statements with different relations between X and Y (e.g., siblings in some cases, not siblings in others). Conclusion Relationship cannot be uniquely determined. Final Answer Even both statements I and II together are not sufficient.

Question 14

Data Sufficiency — Relationships: Determine how F is related to P.  Statement I: P has two sisters, M and N. Statement II: F's mother is the sister of M's father.  Decide which statements are sufficient to answer the question. Choose the correct suf…

Accepted Answer

Target Identify F's relationship to P. Check Statement I P has sisters M and N. No information about F ⇒ insufficient. Check Statement II F's mother is sister of M's father. No link to P unless we know where M stands with P ⇒ insufficient. Combine I + II From I: M is P's sister ⇒ M's father is P's father.From II: F's mother is sister of P's father ⇒ F's mother is P's paternal aunt.Therefore, F is the child of P's paternal aunt ⇒ F is P's cousin. Final Answer Both statements I and II together are sufficient, but neither alone is sufficient.

Question 15

Data Sufficiency — Relationships: B is the brother of A. How is A related to B (male/female)?  Statement I: A is the sister of C. Statement II: E is the husband of A.  Decide which statements are sufficient to answer the question. Choose the correct…

Accepted Answer

Goal Establish A's gender to state A's relation to B. Statement I A is the sister of C ⇒ A is female ⇒ with B given male as brother of A, A is B's sister. Statement II E is the husband of A ⇒ A is female ⇒ hence A is B's sister. Conclusion Each statement alone suffices. Final Answer Either statement I or statement II alone is sufficient.

Question 16

Data Sufficiency — Row length: How many children are there in a single row facing North?  Statement I: Vishakha, who is fifth from the left end, is eighth to the left of Ashish, who is twelfth from the right end. Statement II: Rohit is fifth to the …

Accepted Answer

Using Statement I Vishakha is 5th from left and 8 left of Ashish ⇒ Ashish is (5 + 8) = 13th from left.Ashish is 12th from right ⇒ Total = 13 + 12 − 1 = 24. Using Statement II Nisha = 7th from right and 18th from left ⇒ Total = 18 + 7 − 1 = 24. Conclusion Either statement alone gives the total count. Final Answer Either statement I or statement II alone is sufficient.

Question 17

Data Sufficiency — Population vs doctors: How many doctors are practising in the town?  Statement I: There is one doctor per 700 residents. Statement II: There are 16 wards, with each ward having as many doctors as the number of wards (i.e., the sam…

Accepted Answer

Statement I Doctors = (Population) ÷ 700. Population is unknown ⇒ insufficient. Statement II Each of 16 wards has 16 doctors ⇒ Total doctors = 16 × 16 = 256. Sufficient. Final Answer Statement II alone is sufficient, but Statement I alone is not sufficient.

Question 18

Data Sufficiency — Day of the week: On which day was Sahil's birthday?  Statement I: Sahil celebrated his birthday the very next day after Arun's birthday. Statement II: Sahil's sister was born on the third day of the week and two days after Sahil w…

Accepted Answer

Assumption Week starts on Monday (standard in reasoning questions): Day 1 = Monday, Day 2 = Tuesday, Day 3 = Wednesday, ... Statement II Sister on the 3rd day and two days after Sahil ⇒ Sahil was born on Day 1 ⇒ Monday. Statement I Only relative to Arun's day; without Arun's day, cannot determine. Final Answer Statement II alone is sufficient, but Statement I alone is not sufficient.

Question 19

Data Sufficiency — Reading progress: How many pages of book X did Robert read on Sunday?  Statement I: The book has 300 pages, of which two-thirds were read by Robert before Sunday. Statement II: Robert read the last 40 pages of the book on Monday m…

Accepted Answer

Let Total pages = 300. From Statement I Read before Sunday = (2/3) × 300 = 200 pages. From Statement II Read on Monday morning = last 40 pages. Compute Sunday pages (Before Sunday) + (Sunday) + (Monday) = Total200 + (Sunday) + 40 = 300 ⇒ (Sunday) = 60 pages. Conclusion Neither statement alone is enough, but together they yield the exact count.

Question 20

Data Sufficiency — Relationships: How is Tanya related to the man in the photograph?  Statement I: The man in the photograph is the only son of Tanya's grandfather. Statement II: The man has no brothers or sisters, and his father is Tanya's grandfat…

Accepted Answer

Interpretation Statement I: The man is the only son of Tanya's grandfather, but the grandfather may also have daughters (e.g., Tanya's mother). Tanya could thus be the man's niece or daughter ⇒ ambiguous. Statement II: The man has no siblings, and his father is Tanya's grandfather ⇒ the grandfather has exactly one child (this man). Therefore Tanya, being a grandchild of that grandfather, must be the man's daughter. Final Answer Statement II alone is sufficient, but Statement I alone is not sufficient.

Data Sufficiency Questions