Practice UPSC CSAT previous year questions from 2011–2026 classified underData Sufficiency. Review the original question, four options, correct answer and explanation for every PYQ.
39 questions • 2011–2026
X receives three coins of different denominations: 1, 2, 5, 10 and 20. If the total amount received by X is m, does X receive a coin of denomination 5? Statement I: m is not a prime number. Statement II: The sum of the digits of m is greater than 5.
Statement I alone is sufficient: among sums of three distinct denominations, a non-prime total forces inclusion of 5; statement II alone does not. Hence A.
For two distinct real numbers x and y, which of them is bigger? Statement I: x² < y < 1. Statement II: y < √x < 1.
Neither statement alone fixes whether x>y or y>x. For example, statement I permits both orderings, and statement II likewise does not uniquely compare x and y. Hence D.
If x and y are integers, then is x even? Statement I: x²y² is even. Statement II: 1 + x² + y² is odd.
Statement I only says at least one of x,y is even. Statement II says x and y have the same parity. Together they must both be even, so x is even. Hence C.
X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the numbers all of which are either from X or from Y. Is every number of T from Y? Statement I: The sum of any two numbers belonging to T is even. Statement II: If both p and q are picked from T, then (p − 1)q is even.
Neither statement establishes that all members of T are even. Statement I allows T to contain only odd numbers, while statement II can also hold without forcing every member to be from Y. Hence D.
If x, y and z are integers, each greater than 1, then is x a prime number? Statement I: xy² = 116. Statement II: xz = 261.
From xy²=116=4×29 and y>1, y=2 and x=29, so x is prime. From xz=261, x could be 29 or 87, so II alone is insufficient. Hence A.
A question is given followed by two Statements I and II. Question: What is the smallest 1-digit number having exactly 4 distinct factors? Statement I: 2 is one of the factors. Statement II: 3 is one of the factors. Which one of the following is correct in respect of the above Question and the Statements?
The base question itself gives 6 as the smallest one-digit number with four factors, so D.
A question is given followed by two Statements I and II. Question: Let P, Q, R, S be distinct non-zero digits. If PP × PQ = RRSS, where P ≤ 3 and Q ≤ 4, then what is Q equal to? Statement I: R = 1. Statement II: S = 2. Which one of the following is correct in respect of the above Question and the Statements?
The unique digit solution is P=3,Q=4,R=1,S=2; either statement alone is sufficient.
A question is given followed by two Statements I and II. Question: How is Q related to P? Statement I: P has two sisters, R and S. Statement II: R’s father is the brother of Q. Which one of the following is correct in respect of the above Question and the Statements?
Together the statements establish Q as P’s paternal uncle; neither alone is sufficient.
A question is given followed by two Statements I and II. Question: In a football match, team P playing against Q was behind by 3 goals with 10 minutes remaining. Does team P win the match? Statement I: Team P scored 4 goals in the last 10 minutes. Statement II: Team Q scored a total of 4 goals in the match. Which one of the following is correct in respect of the above Question and the Statements?
Statement I alone does not control Q’s scoring; statement II does not yield a valid determination of the outcome.
A question is given followed by two Statements I and II. Question: Is (p + q)^2 − 4pq, where p, q are natural numbers, positive? Statement I: p < q. Statement II: p > q. Which one of the following is correct in respect of the above Question and the Statements?
The expression is (p−q)^2; either p<q or p>q guarantees positivity.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question: What are the values of m and n, where m and n are natural numbers? Statement-I: m+n > mn and m > n. Statement-II: The product of m and n is 24. Which one of the following is correct in respect of the above Question and the Statements?
Statement II alone gives many factor pairs of 24; statement I alone also does not uniquely determine m,n. Together they give m=24,n=1, so both are required.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question: What is the time required to download the software? Statement-I: The size of the software is 12 megabytes. Statement-II: The transfer rate is 2–4 kilobytes per second. Which one of the following is correct in respect of the above Question and the Statements?
Download time requires both file size and transfer rate. Neither statement alone is sufficient; together they provide the required information.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question: What are the unique values of x and y, where x, y are distinct natural numbers? Statement-I: x/y is odd. Statement-II: xy = 12. Which one of the following is correct in respect of the above Question and the Statements?
Statement I alone permits many pairs; statement II alone also permits many factor pairs of 12. Together, with distinct natural numbers and x/y odd, the values are uniquely determined.
A certain amount was distributed among X, Y and Z. Question: Who received the least amount? Statement-I: X received 4/5 of what Y and Z together received. Statement-II: Y received 2/7 of what X and Z together received. Which one of the following is correct in respect of the above Question and the Statements?
Neither statement alone identifies the least recipient, but the two equations together determine the relative amounts sufficiently to identify it. Hence both are required.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question: If the average marks in a class are 60, then what is the number of students in the class? Statement-I: The highest marks in the class are 70 and the lowest marks are 50. Statement-II: Exclusion of highest and lowest marks from the class does not change the average. Which one of the following is correct in respect of the above Question and the Statements?
Knowing only the mean, or the highest/lowest marks and unchanged mean after their exclusion, does not determine the class size. Even together the information is insufficient.
There are three distinct prime numbers whose sum is a prime number. Question: What are those three numbers? Statement-I: Their sum is less than 23. Statement-II: One of the numbers is 5. Which one of the following is correct in respect of the above Question and the Statements?
Statement I says the prime sum is less than 23; since the sum of three distinct primes is odd only when one is 2, the prime sum can be 23, but this condition alone is not enough to determine all three. The correct sufficiency relationship is that one statement alone is sufficient in the given setup, while the other is not.
Question: Is (x + y) an integer? Statement-I: (2x + y) is an integer. Statement-II: (x + 2y) is an integer. Which one of the following is correct in respect of the above Question and the Statements?
Even if both 2x+y and x+2y are integers, x+y need not be an integer; for example, solving the two integer expressions can yield non-integral x+y. Thus the data are insufficient.
A person buys three articles p, q and r for ₹50. The price of the article q is ₹16 which is the least. Question: What is the price of the article p? Statement-I: The cost of p is not more than that of r. Statement-II: The cost of r is not more than that of p. Which one of the following is correct in respect of the above Question and the Statements?
Since q=16 is the least and p+r=34, either condition p≤r or r≤p forces p=r=17. Either statement alone is sufficient.
P, Q, R and S appeared in a test. Question: Has P scored more marks than Q? Statement-I: The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S. Statement-II: The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R. Which one of the following is correct in respect of the above Question and the Statements?
The two equations/inequality constrain sums but do not determine whether P>Q. Even together, P−Q can have different signs, so the question cannot be answered.
Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q. Question: What is the difference of their ages? Statement-I: The age of P is greater than the age of Q. Statement-II: The sum of their ages is 11/6 times their difference. Which one of the following is correct in respect of the above Question and the Statements?
Statement I only gives the ordering, not the exact difference. Statement II supplies a numerical relation; combined with the digit-interchange condition it determines the ages and hence the difference. Thus the question can be answered using statement II alone.
Question: Is p greater than q? Statement-1: p×q is greater than zero. Statement-2: p² is greater than q². Which one of the following is correct?
Neither condition, alone or jointly, fixes the sign/order of p and q uniquely.
Question: Is (p+q−r) greater than (p−q+r), where p,q,r are integers? Statement-1: (p−q) is positive. Statement-2: (p−r) is negative. Which is correct?
The comparison is q>r. Statement 1 gives p>q and statement 2 gives p<r; together imply q<r, so the question can be answered using both together but neither alone.
In a party, 75 persons took tea, 60 took coffee and 15 took both. No one taking milk takes tea. Each person takes at least one drink. How many attended? Statement-1: 50 persons took milk. Statement-2: The number attending is five times the number taking milk only. Which is correct?
Statement 1 alone does not fix the total because milk may overlap with coffee. With statement 2 alone, let milk-only=x; the total is 5x, while tea/coffee union is 120 and the remaining people are milk-only, giving 5x=120+x and x=30, total 150. Thus statement 2 alone suffices, not statement 1.
Consider a 3-digit number. Question: What is the number? Statement-1: The sum of the digits equals the product of the digits. Statement-2: The number is divisible by the sum of its digits. Which is correct?
Even together the conditions do not uniquely determine one 3-digit number.
For five children with ages a<b<c<d<e, each successive age differs by 2. Question: What is the youngest age? Statement-1: Eldest is 3 times youngest. Statement-2: Average age is 8 years. Which is correct?
The five ages are x,x+2,x+4,x+6,x+8; statement 2 alone gives x+4=8, hence x=4.
Consider the Question and two Statements given below: Question: Is x an integer? Statement-1: x/3 is not an integer. Statement-2: 3x is an integer. Which one of the following is correct in respect of the Question and the Statements?
Neither statement forces x to be an integer. For example, x=1/2 satisfies both conditions, while an integer x=1 also satisfies both; therefore the data are insufficient.
Consider the Question and two Statements given below: Question: Is Z brother of X? Statement-1: X is a brother of Y and Y is a brother of Z. Statement-2: X, Y and Z are siblings. Which one of the following is correct in respect of the Question and the Statements?
Statement 1 establishes X and Y as brothers and Y as brother of Z, but Z's sex is not fixed. Statement 2 also says only that they are siblings. Neither alone determines whether Z is male.
Consider the Question and two Statements given below in respect of three cities P, Q and R in a State: Question: How far is city P from city Q? Statement-1: City Q is 18 km from city R. Statement-2: City P is 43 km from city R. Which one of the following is correct in respect of the Question and the Statements?
Each statement gives a distance to R but neither gives the relative direction or position of P and Q. Their mutual distance cannot be determined.
Six persons A, B, C, D, E and F are sitting equidistant from each other around a circular table (facing the centre of the table). Consider the Question and two Statements given below: Question: Who is sitting on the immediate left of A? Statement-1: B is sitting opposite to C and D is sitting opposite to E. Statement-2: F is sitting on the immediate left of B. Which one of the following is correct in respect of the Question and the Statements?
Statement 1 fixes two opposite pairs but leaves multiple possibilities. Statement 2 fixes F relative to B but does not locate A. Even together, the immediate-left position of A is not uniquely determined.
Consider the Question and two Statements given below: Question: What is the age of Manisha? Statement-1: Manisha is 24 years younger than her mother. Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3:5. Which one of the following is correct in respect of the Question and the Statements?
Let Manisha be M and mother be M+24. Five years later, (M+5)/(M+29)=3/5, giving 5M+25=3M+87 and M=31. Both statements together determine the age.
Six lectures A, B, C, D, E and F, each of one hour duration, are scheduled between 8:00 a.m. and 2:00 p.m. Consider the Question and Statements given below: Question: Which lecture is in the third period? Statement-1: Lecture F is preceded by A and followed by C. Statement-2: There is no lecture after lecture B. Which one of the following is correct in respect of the Question and the Statements?
Statement 1 only fixes the relative order A-F-C, and statement 2 places B last; neither condition uniquely determines the third lecture, nor do they do so together.
Consider two Statements and a Question: Statement-1: Priya is 4 ranks below Seema and is 31st from the bottom. Statement-2: Ena is 2 ranks above Seema and is 37th from the bottom. Question: What is Seema’s rank from the top in the class of 40 students? Which one of the following is correct in respect of the Statements and the Question?
Statement 1 alone gives Priya as 10th from top and Seema as 6th; statement 2 alone gives Ena as 4th and Seema as 6th. Either suffices.
Consider two Statements and a Question: Statement-1: Each of A and D is heavier than each of B, E and F, but none of them is the heaviest. Statement-2: A is heavier than D, but is lighter than C. Question: Who is the heaviest among A, B, C, D and E? Which one of the following is correct in respect of the Statements and the Question?
Because A and D both exceed B, E and F but neither is the heaviest, C must be the heaviest among the listed persons; statement 1 alone suffices.
Consider two Statements and a Question: Statement 1: The last day of the month is a Wednesday. Statement 2: The third Saturday of the month was the seventeenth day. Question: What day is the fourteenth of the given month? Which one of the following is correct in respect of the Statements and the Question?
The 17th being the third Saturday fixes the 14th as Wednesday, so statement 2 alone suffices.
Two statements S1 and S2 are given below followed by a Question: S1: There are not more than two figures on any page of a 51-page book. S2: There is at least one figure on every page. Question: Are there more than 100 figures in that book? Which one of the following is correct?
S1 gives a maximum of 102 figures; S2 gives a minimum of 51. Even together, the total can range from 51 to 102, so the question cannot be answered uniquely.
Two Statements S1 and S2 are given below with regard to four numbers P, Q, R and S followed by a Question: S1: R is greater than P as well as Q. S2: S is not the largest one. Question: Among four numbers P, Q, R and S which one is the largest?
S1 leaves S as a possible largest number; S2 alone leaves three possibilities. Together, R exceeds P and Q and S is not largest, so R must be largest.
Two Statements S1 and S2 are given below followed by a Question: S1: n is a prime number. S2: n leaves a remainder of 1 when divided by 4. Question: If n is a unique natural number between 10 and 20, then what is n? Which one of the following is correct?
Primes between 10 and 20 are 11, 13, 17 and 19; numbers leaving remainder 1 modulo 4 are 13 and 17. Both statements still leave two possibilities, so they are insufficient.
Two Statements S1 and S2 are given below with regard to two numbers followed by a Question: S1: Their product is 21. S2: Their sum is 10. Question: What are the two numbers? Which one of the following is correct?
Product 21 alone or sum 10 alone allows many pairs, but solving x+y=10 and xy=21 gives x and y as 3 and 7 uniquely (up to order).
Three Statements S1, S2 and S3 are given below followed by a Question: S1: C is younger than D, but older than A and B. S2: D is the oldest. S3: A is older than B. Question: Who among A, B, C and D is the youngest?
S1 tells us C is older than both A and B but does not rank A versus B. Adding S3 establishes A older than B, so B is youngest.
Attempt questions one by one with UPSC-style marking and immediate explanations.