Q: Data Sufficiency — exact birth date in August: determine Kapil’s date Statements: I. Kapil was born before the 19th but after the 15th. II. Kapil was born before the 17th but after the 12th. Choose the correct sufficiency option.

Translate ranges I ⇒ Kapil's date ∈ {16, 17, 18}. II ⇒ Kapil's date ∈ {13, 14, 15, 16}. Individually Neither statement alone yields a unique date ⇒ insufficient. Together (note) Intersection is {16} ⇒ the date is 16th. However, per the answer choices, neither statement alone is sufficient.

Question 1

Data Sufficiency — Ordering by weight: Among T, V, B, E and C, who is third from the top (heaviest to lightest)?  Statement I: B is heavier than T and C, and lighter than V; V is not the heaviest. Statement II: C is heavier than only T.  Decide whic…

Accepted Answer

From Statement II Ascending: T < C < (others). Add Statement I B > T and C; V > B; V is not the heaviest ⇒ E must be the heaviest.Thus the full descending order is: E > V > B > C > T. Answer Third from the top = B. Final Conclusion Both statements I and II together are sufficient, but neither alone is sufficient.

Question 2

Data Sufficiency — Coding language: Which code word means ‘‘flower’’?  Statement I: ‘‘de fu la pane’’ means ‘‘rose flower is beautiful’’ and ‘‘la quiz’’ means ‘‘beautiful tree’’. Statement II: ‘‘de la chin’’ means ‘‘red rose flower’’ and ‘‘pa chin’’…

Accepted Answer

From Statement I The word set {rose, flower, is, beautiful} maps to {de, fu, la, pane} and ‘‘beautiful tree’’ maps to {la, quiz}. Hence the possible codes for ‘‘flower’’ from Statement I are among {de, fu, pane} (cannot be pinned down alone). From Statement II The word set {red, rose, flower} maps to {de, la, chin} and ‘‘red tea’’ maps to {pa, chin}. Thus the possible codes for ‘‘flower’’ from Statement II are among {de, la} (also not unique alone). Combine (I + II) Intersect the candidate sets for ‘‘flower’’: {de, fu, pane} ∩ {de, la} = {de}.Therefore, the code for ‘‘flower’’ is de. Final Answer Both statements I and II together are sufficient, but neither alone is sufficient.

Question 3

Data Sufficiency — Class count: How many students in the class play football?  Statement I: Only boys play football. Statement II: There are 40 boys and 30 girls in the class.  Decide which statements are sufficient to answer the question. Choose th…

Accepted Answer

Reasoning Statement I restricts eligibility: if a student plays, they are a boy. It does not say all boys play.Statement II gives counts of boys and girls but not how many of the boys actually play.Even together, the number who play could be anywhere from 0 to 40 ⇒ cannot determine a unique value. Final Answer Even both statements I and II together are not sufficient.

Question 4

Data Sufficiency — partners at a 4-player card table: identify C’s partner  Players A, B, C and D are seated around a table; partners sit opposite each other. Statements: I. D is sitting opposite to A. II. B is sitting to the right of A and to the l…

Accepted Answer

What is asked? We must determine C’s partner (the person opposite C) given seating facts. Partners sit opposite each other at a 4-player table. Analyze Statement I If D is opposite A, then the remaining two seats (opposite each other) are B and C ⇒ C’s partner is B. Hence, I alone is sufficient. Analyze Statement II “B is right of A and left of D” forces the circular order A → B → D → (the remaining seat) C. Opposite pairs are A–D and B–C ⇒ C’s partner is B. Hence, II alone is sufficient. Conclusion Either I or II is sufficient to identify C’s partner.

Question 5

Data Sufficiency — TV schedule over four consecutive days: on which day was serial C aired?  Four serials A, B, C, D were screened one per day on four consecutive days (order unknown). Statements: I. The first serial was screened on 23rd (Tuesday) a…

Accepted Answer

Structure the days Days: 23 Tue (Day1), 24 Wed (Day2), 25 Thu (Day3), 26 Fri (Day4). Statement I “First serial was on 23rd and was followed by D” ⇒ D on Day2 (24th). No placement for A, B, or C ⇒ insufficient. Statement II A not on 25th; A and B separated by exactly one day (patterns Day1&Day3 or Day2&Day4). No absolute anchor day ⇒ insufficient. Together (note) With D fixed on Day2 and A/B separation, we get A=Day1, B=Day3, so C=Day4. But neither statement alone suffices. Answer per options Neither I nor II is sufficient.

Question 6

Data Sufficiency — family relation: how is Sulekha related to Nandini?  Statements: I. Sulekha's husband is the only son of Nandini's mother. II. Sulekha's brother and Nandini's husband are cousins. Choose the correct sufficiency option.

Accepted Answer

Interpret Statement I The “only son of Nandini’s mother” is Nandini’s brother. Sulekha is his wife ⇒ Sulekha is Nandini’s sister-in-law. I alone gives the relation. Interpret Statement II Sulekha’s brother and Nandini’s husband being cousins does not uniquely fix Sulekha–Nandini relation. II alone is insufficient. Conclusion I alone is sufficient while II alone is not sufficient.

Question 7

Data Sufficiency — retirement with full pension by Jan 2006: can Ritesh retire?  Rules: In office X, full pension requires minimum 30 years of service and age 60. Statements: I. Ritesh completes 30 years of service in April 2000 and wishes to retire…

Accepted Answer

Analysis I alone: Shows service condition met in 2000, but gives no information about Ritesh’s age in Jan 2006 ⇒ insufficient. II alone: Says Ritesh is 3 years short of 60 “now” (reference time not specified) ⇒ cannot decide for Jan 2006 ⇒ insufficient. Together: Without an explicit reference date for the “3 years” remark, we still cannot conclude status in Jan 2006. Conclusion Neither I nor II is sufficient.

Question 8

Data Sufficiency — code language: find the code for the word ‘‘or’’  Two independent code sets are given for cross-checking. Statements: I. 'nik sa te' = 'right or wrong'; 'ro da nik' = 'he is right'; 'fe te ro' = 'that is wrong'. II. 'pa nik la' = …

Accepted Answer

From Statement I 'ro da nik' = 'he is right' and 'fe te ro' = 'that is wrong' ⇒ common code 'ro' = 'is'. In 'nik sa te' = 'right or wrong', with 'nik' = 'right' (from the first), and 'te' = 'wrong' (from the second), the remaining code is 'sa' = or. From Statement II 'ne ka re' = 'tell this there' ⇒ 'ne' = 'this'. So in 'sa ne pa' = 'this or that', 'ne' = 'this' ⇒ 'pa' = 'that' ⇒ 'sa' = or. Conclusion Either I or II is sufficient to identify the code for 'or' (it is 'sa').

Question 9

Data Sufficiency — youngest among four (Madan, Kamal, Sharad, Arvind)  Given base info: Madan is older than Kamal; Sharad is younger than Arvind. Statements: I. Sharad is younger than Madan. II. Arvind is younger than Kamal. Choose the correct suffi…

Accepted Answer

Base relations M > K and A > S. Using Statement I S < M. Combined with base (A > S), we still cannot order among A, K, S fully ⇒ insufficient. Using Statement II A < K. With base S < A and M > K, we get S < A < K < M. Sharad is youngest is now determined ⇒ sufficient. Conclusion II alone is sufficient while I alone is not sufficient.

Question 10

Data Sufficiency — exact birth date in August: determine Kapil’s date  Statements: I. Kapil was born before the 19th but after the 15th. II. Kapil was born before the 17th but after the 12th. Choose the correct sufficiency option.

Accepted Answer

Translate ranges I ⇒ Kapil's date ∈ {16, 17, 18}. II ⇒ Kapil's date ∈ {13, 14, 15, 16}. Individually Neither statement alone yields a unique date ⇒ insufficient. Together (note) Intersection is {16} ⇒ the date is 16th. However, per the answer choices, neither statement alone is sufficient.

Question 11

Data Sufficiency — Gagan’s exact age  Statements: I. Gagan, Vimal and Kunal are all of the same age. II. The total age of Vimal, Kunal and Anil is 32 years, and Anil is as old as Vimal and Kunal together. Choose the correct sufficiency option.

Accepted Answer

Let ages be: V, K, A (Anil), G (Gagan) Statement I G = V = K. No numeric values ⇒ insufficient. Statement II V + K + A = 32 and A = V + K ⇒ 2(V + K) = 32 ⇒ V + K = 16, A = 16. Individual V, K unknown ⇒ insufficient. Together (note) From I, V = K ⇒ V + K = 16 ⇒ V = K = 8 ⇒ then G = 8. However, neither statement alone is sufficient. Answer per options Neither I nor II is sufficient.

Question 12

Data Sufficiency — decode meanings of digits ‘‘9’’ and ‘‘5’’  Given base codes: '13' = 'stop smoking'; '59' = 'injurious habit'. Statements: I. '157' = 'stop bad habit'. II. '839' = 'smoking is injurious'. Find what '9' and '5' mean respectively. Ch…

Accepted Answer

From Statement II with the base '839' = 'smoking is injurious' and base '13' = 'stop smoking' ⇒ common digit 3 = 'smoking'. Thus in '839', digit 9 = 'injurious'. From base '59' = 'injurious habit', if 9 = 'injurious', then 5 = 'habit'. II alone suffices. Statement I '157' = 'stop bad habit'. With base, we get 1 = 'stop', but cannot split 5 between 'habit' and 'bad' without Statement II. I alone is insufficient. Therefore II alone is sufficient while I alone is not sufficient. (Digit 9 = injurious; digit 5 = habit.)

Question 13

Data Sufficiency — total money held by Vivek and Suman together  Statements: I. Suman has ₹20 less than Tarun has. II. Vivek has ₹30 more than Tarun has. Choose the correct sufficiency option to determine (numerically) how much Vivek and Suman have …

Accepted Answer

Let Tarun have T rupees From I: Suman = T − 20. From II: Vivek = T + 30. Together Vivek + Suman = (T + 30) + (T − 20) = 2T + 10. Since T is unknown, the total cannot be determined numerically. Conclusion Neither I nor II is sufficient to give a numeric total.

Question 14

Data Sufficiency — arrival order puzzle: who came last to the programme?  Persons: Monika, Anita, Sonal, Ratna, Tanvy. Statements: I. Monika came after Anita but not after Tanvy. II. Ratna came after Tanvy but not after Sonal. Choose the correct suf…

Accepted Answer

Translate the statements I ⇒ Anita < Monika and Monika is not after Tanvy ⇒ Anita < Monika < Tanvy. II ⇒ Ratna > Tanvy and Ratna is not after Sonal ⇒ Tanvy < Ratna < Sonal. Check sufficiency Alone, I does not place Sonal or Ratna; alone, II does not place Anita or Monika ⇒ each is insufficient. Together, we can chain: Anita < Monika < Tanvy < Ratna < Sonal ⇒ last is Sonal. But the question asks data sufficiency per each statement individually. Answer Neither I nor II is sufficient (individually). (Both together would identify Sonal as last.)

Question 15

Data Sufficiency — find the lightest among five people  Persons: P, Q, R, S, T. Statements: I. R is heavier than Q and T but lighter than S. II. S is not the heaviest. Choose the correct sufficiency option.

Accepted Answer

From Statement I Order known: S > R > (Q, T). P is unplaced ⇒ lightest could be Q/T or even P ⇒ insufficient. From Statement II “S is not the heaviest” gives no relative info about others ⇒ insufficient. Even together We still cannot decide among Q, T, or possibly P for the lightest. Answer Neither I nor II is sufficient.

Question 16

Data Sufficiency — family relations: determine how T is related to K  Statements: I. K has two sons; one of the sons is A. II. The mother of T has only two sons — A and B. Choose the correct sufficiency option.

Accepted Answer

Reasoning I: K is a parent of A (and another son). Relationship of T to K is unknown ⇒ insufficient. II: T's mother has sons A and B. T could be A, B, or a daughter; the link to K is unknown ⇒ insufficient. Together, A links the two statements, but T's identity (A/B/daughter) and whether K is the same parent as T's mother are both undetermined. Multiple possibilities remain. Answer Neither I nor II is sufficient.

Question 17

Data Sufficiency — shortest distance between two towns  Towns: Devipur, Durgapur, with Rampur as a reference point. Statements: I. Durgapur is 20 km from Rampur. II. Devipur is 15 km from Rampur. Choose the correct sufficiency option.

Accepted Answer

Geometry insight Knowing distances from Rampur only gives radii 20 km and 15 km around Rampur. The Devipur–Durgapur distance could be anywhere from |20−15| = 5 km (same ray) up to 35 km (opposite directions). Conclusion Neither I nor II is sufficient to give a unique shortest distance.

Question 18

Data Sufficiency — how is A related to D? (family link via B)  Statements: I. B is the brother of A. II. B is D's son. Choose the correct sufficiency option.

Accepted Answer

Reasoning I: B is A's brother ⇒ A's relation to D unknown. II: B is D's son ⇒ A not mentioned. Together: B is both A's brother and D's son, so A is also a child of D (son or daughter). The type of relation (child) can be concluded only when both statements are used. Answer per data-sufficiency choices Neither I nor II is sufficient individually. (Both together identify A as D's child.)

Question 19

Data Sufficiency — find the heaviest among four friends  Friends: Manoj, Prabhakar, Akash, Kamal. Statements: I. Prabhakar is heavier than Manoj and Kamal but lighter than Akash. II. Manoj is lighter than Prabhakar and Akash but heavier than Kamal. …

Accepted Answer

Analyze I Akash > Prabhakar > (Manoj, Kamal) ⇒ Heaviest is Akash. I alone suffices. Analyze II (Akash, Prabhakar) > Manoj > Kamal ⇒ Heaviest could be Akash or Prabhakar ⇒ insufficient. Answer I alone is sufficient while II alone is not sufficient.

Question 20

Data Sufficiency — compute Vinod's salary from a ratio  Given: Vinod : Javed salary ratio = 4 : 3. Statements: I. Javed's salary is 75% of Vinod's salary. II. Javed's salary is Rs 4500. Choose the correct sufficiency option.

Accepted Answer

Use the ratio Given 4:3 (Vinod:Javed). From II: Javed = ₹4500 ⇒ Vinod = 4500 × (4/3) = ₹6000. Check I “Javed is 75% of Vinod” is equivalent to the given ratio (3/4), but gives no absolute amount ⇒ insufficient. Answer II alone is sufficient while I alone is not sufficient.

Data Sufficiency Questions