Question 1

Directions (Q91-Q95): In the following questions, determine which statement or statements are redundant for finding the answer to the given question, or can be dispensed with. Q91. A trader sells a homogeneous mixture of A and B at the rate of Rs. 32 per kg. What is the profit earned by th

Accepted Answer

I, II and III together are not sufficient. The selling price is given, but the cost price of the homogeneous mixture depends on the prices and proportion of A and B. Even with all three statements, the ratio of A and B in the mixture is not fixed, so the profit cannot be uniquely determined.

Question 2

Find the difference between the incomes of D and E. (I) The difference between the expense of D in November and the saving of E in April is Rs. 3200. (II) The difference between the saving of D in April and the expense of E in November is Rs. 8000.

Accepted Answer

Statements (I) and (II) taken together are not sufficient to answer the question.. Each statement gives only a difference between one person's expense and another person's saving. Even together, they do not uniquely determine the individual incomes of D and E. Therefore, the income difference cannot be found from the given information.

Question 3

Q153. A man has two articles A and B. To find the selling price of article B, which statement or statements are required to answer the question? A. The total amount received by a man after selling six articles A and four articles B is Rs. 240. From this total amount, he could buy either ni

Accepted Answer

Either A and C together or B and C together are sufficient to answer the question. Statement C alone gives the difference between selling prices and cost prices of A and B, but not the exact value of SP of B. When combined with A, the total amount relation allows solving both prices; when combined with B, the equal profit-percentage condition plus the price difference also determines SP of B. Hence either A and C or B and C is sufficient.

Question 4

Q154. The question is followed by three statements I, II and III. Determine which statement or statements are sufficient to answer the question. The slant height of a cone is x cm. If the side of a square is (x+5) cm, then find the area of the square. I. The ratio of the diameter of the co

Accepted Answer

Either statement I and II together or statement III alone is sufficient to answer the question. The area of the square depends on x, so we need x. Statement I alone is not enough, but I and II together can determine the cone’s dimensions and hence x. Statement III alone gives enough information to find the cone’s radius and slant height directly, so either I and II together or III alone is sufficient.

Question 5

Q155. Two containers A and B contain a mixture of milk and water. Container A contains milk and water in the ratio 3:5, and milk in container B is 75%. The total quantity of mixture in container A and B is 500x liters and 400y liters. If mixture A is mixed with mixture B, then which statem

Accepted Answer

Both (I) and (II). Container A has milk:water = 3:5, so its milk and water quantities are fixed fractions of its total. Container B has 75% milk, so its milk and water quantities are also fixed fractions of its total. Statement I gives one equation involving the two totals, and statement II gives another independent equation, so together they are sufficient.

Question 6

A, B, and C entered into a partnership. After eight months, B and C left the business. Find the total profit at the end of the year. A. Annual profit of B is Rs. 400 more than that of A and Rs. 200 more than that of C. B. Amount invested by C is 50% of the total amount invested by A and B

Accepted Answer

None of the given statements can answer the question. Each statement gives only partial information about the partnership. None of the statements, alone or in the listed combinations, is sufficient to determine the total profit uniquely because the actual capital contributions and profit distribution cannot be fixed completely.

Question 7

Find the two-digit number. A. The sum of the squares of the two digits of the two-digit number is 26. B. The ratio between the two-digit number and the sum of its digits is 5:2. C. The digit in the tens place is 4 less than the digit in the units place. Which of the following is sufficient

Accepted Answer

Only B and C together are sufficient. Statement B gives a relation between the number and the sum of its digits, while C gives a direct relation between the tens and units digits. Together they are enough to determine a unique two-digit number. A alone is not sufficient because multiple digit pairs can satisfy the sum of squares condition.

Question 8

Let the students who take art and science be $4b$ and $b$ respectively. The total students who take commerce = $(2a + 16) - (4b + b) = 2a + 16 - 5b$. From A: $A - 4b - (2a + 16 - 5b) = 8 \Rightarrow -2a + 9b = 24$. Also, $(2a + 16) - 2a + 8b = 16 \Rightarrow b = 8$. Total students in class

Accepted Answer

Statement A alone is sufficient. Statement A provides enough equations to determine the required quantity uniquely. Statement B does not add anything necessary for the final value in this setup. Hence, statement A alone is sufficient.

Question 9

Find the height of the cylinder. I) A rectangular piece of paper of breadth 22 cm is rolled along its breadth to form a cylinder. If the curved surface area of the cylinder is 264 cm². II) The volume of the cylinder is 462 cm³.

Accepted Answer

The statement I alone is sufficient to answer the question, but the statement II alone is not sufficient.. Statement I gives the breadth as the circumference of the base, so the radius can be found. Using curved surface area, the height can then be determined uniquely. Statement II alone gives only volume, which is not enough to determine both radius and height.

Question 10

In how many days can men and women complete the work together? A. The ratio between the efficiency of men and women is 3:1. B. Men and child can do $\tfrac{1}{3}$ of the work in 9 days. C. Women can do $\tfrac{2}{3}$ of the work in 14 days. Which of the following statements is sufficie

Accepted Answer

Only A and C together. Statement A gives only the ratio of efficiencies, not the actual rates. Statement C provides the work rate of women, so using A and C together we can find the rate of men and then the combined time. Hence, only A and C together are sufficient.

Question 11

Find the ratio of the speeds of Train A and Train B. Statement I: If the length of Train A is 100 m and it crosses a platform double its length in 10 s, and Train B crosses the same platform in 20 s. Statement II: The sum of the speeds of Train A and Train B is 200 m/s, and the difference

Accepted Answer

The statement II alone is sufficient to answer the question, but the statement I alone is not sufficient.. Statement II gives the sum and difference of the two speeds, so the individual speeds can be found uniquely and hence their ratio can be determined. Statement I does not give enough information to determine both speeds uniquely because the crossing times alone do not fix the exact speeds without additional details.

Question 12

From statement A: X and Y are integers and multiples of 24, and X is 50% more than Y. From statement B: X/24 and Y/24 are natural numbers. From A and B together: X and Y can be (720, 480), (2160, 1440), etc. So, statements A and B taken together are not sufficient. What is the correct opti

Accepted Answer

Data insufficient. Statement A gives a proportional relation and divisibility condition, but many pairs satisfy it. Statement B also allows many pairs. Even together, they do not lead to a unique answer, so the data is insufficient.

Question 13

Find the volume of the cylinder. (I) The curved surface area of the cylinder is 1760 cm², and the total surface area of the cylinder is 70% more than its curved surface area. (II) The volume of the cylinder is twice that of a cone. The radius of the cylinder and cone is equal, and the rati

Accepted Answer

Statement (I) alone is sufficient to answer the question but statement (II) alone is not sufficient to answer the question.. Statement (I) gives curved surface area and total surface area, which are enough to determine the radius and height of the cylinder uniquely. Statement (II) does not provide enough independent information to fix the cylinder's volume on its own.

Question 14

A path of width $x$ metres is carved around a rectangular field. If the length of the rectangular field is 3 m more than its breadth, find the value of $x$. Statement I: There is a square whose side is 2 m more than the breadth of the rectangular field, and the area of the square is 50

Accepted Answer

The data in both statements I and II together are necessary to answer the question.. Statement I gives a relation between the breadth and the area difference, but not enough to determine the path width uniquely. Statement II gives the area of the path, but without the field dimensions it is still insufficient. Together, they provide enough equations to determine $x$.

Question 15

I. $x^2 + x - 240 = 0$ II. $y^2 = 256$ A) $x \ge y$ B) $x \le y$ C) if $x = y$ or no relation can be established between $x$ and $y$. D) $x < y$

Accepted Answer

if $x = y$ or no relation can be established between $x$ and $y$.. From $x^2+x-240=0$, we get $(x+16)(x-15)=0$, so $x=15$ or $x=-16$. From $y^2=256$, we get $y=16$ or $y=-16$. Since the possible values overlap and vary, a definite relation cannot always be established; in one case $x=y=-16$.

Question 16

Is $w$ an integer? (A) $3w$ is an odd number. (B) $2w$ is an even number.

Accepted Answer

if the Statement 'A' alone is sufficient to answer the question but the Statement 'B' alone is not sufficient. From (A), if 3w is odd, then w must be an odd integer, so A alone is sufficient. From (B), 2w being even does not ensure w is an integer, since non-integers can also satisfy it in some contexts; thus B alone is not sufficient.

Question 17

Directions: The question below is followed by three statements I, II, and III. Decide whether the statements are sufficient to answer the question. Question: Find the average weight of the boys. Statement I: The number of boys and girls in the class is 26 and 24 respectively, and the avera

Accepted Answer

All the statements together are not sufficient.. Statement I gives total students and overall average, but not boys' and girls' individual averages. Statement III gives a relation between boys and girls and a combined average of boys and teachers, but the number of teachers is missing, so boys' average cannot be uniquely found. Therefore, even all statements together are insufficient.

Question 18

Study the following information carefully and answer the question given below. There are four floors in a building, and there are three flats on each floor: Flat 1, Flat 2 and Flat 3. Flat 3 is to the east of Flat 2, and Flat 2 is to the east of Flat 1. In each flat, a certain number of pe

Accepted Answer

66.67%. The arrangement conditions determine the total persons on each floor, and hence the number of persons on the ground floor. Since 40% of the building are females and 20% of the first floor are females, the ground-floor female count works out to be two-thirds of the total females in the building. Therefore, the required percentage is 66.67%.

Question 19

Find the number. Statement I: The sum of the two digits of the number is 8. Statement II: After exchanging the places of the digits, the new number becomes 18 greater than the original number. Which of the following is correct?

Accepted Answer

If the data given in both statements I and II are necessary to answer the question.. Statement I alone gives many possible numbers, and statement II alone also gives many possible numbers. Together, they form two equations that uniquely determine the digits, so both statements are necessary.

Question 20

The following question is accompanied by two statements, I and II. Determine which statement(s) is/are sufficient to answer the question. Q63. Two equations are given below: (i) $\sqrt{A}\,b \times (C + 1) = 24$ where $C$ is the largest even prime number. (ii) $(A + X - Y)^2 = 49$ Fi

Accepted Answer

Statement (II) alone is sufficient to answer the question but statement (I) alone is not sufficient to answer the question.. Statement II provides enough relations to determine the variables uniquely when used with the given equations, while Statement I does not lead to a unique value for the required sum. Therefore, only Statement II is sufficient.

Question 21

How many balls are in the bag? The bag contains only three types of coloured balls. I. The ratio of blue balls to red balls is 4:5. The number of white balls is one more than the number of red balls. II. The number of ways of selecting 2 red balls from the bag is 10.

Accepted Answer

Both statements together are necessary to answer. From statement II, $\binom{r}{2}=10$, so $r=5$. Using statement I, blue:red = 4:5, hence blue = 4 and white = 6. Therefore total balls = 4 + 5 + 6 = 15. Neither statement alone is sufficient, but together they are sufficient.

Question 22

Let the incomes of D and E be $x$ and $y$ respectively. Find $x-y$. (I) $0.72x - 0.5y = 3200$ (II) $0.4x - 0.4y = 8000$ A) Only I B) Only II C) Both I and II D) Either I or II

Accepted Answer

Only II. Statement I alone gives one equation in two variables, so it cannot determine $x-y$ uniquely. Statement II simplifies to $0.4(x-y)=8000$, which gives $x-y=20000$ directly. Hence, only II is sufficient.

Question 23

There are (2a + 16) students in a class with three streams: arts, science, and commerce. The ratio of students who take arts to science is 4:1. Find the total number of students in the class. A. The number of arts students is 8 more than the number of commerce students, and the probability

Accepted Answer

Statement A alone is sufficient to answer the question but Statement B alone is not sufficient to answer the question.. The ratio arts:science = 4:1 gives one relation, but not enough to determine the total. Statement A adds enough information to solve for the numbers uniquely, while Statement B only gives another proportional relation and still leaves the total undetermined.

Question 24

Find the area of rectangle ABCD. I. The perimeter of rectangle ABCD is 4.5 times its breadth. II. The difference between the squares of the adjacent sides of rectangle ABCD is 5.4 times its breadth.

Accepted Answer

Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.. Statement I gives 2(l+b)=4.5b, which is one equation in two unknowns and is not sufficient alone. Statement II gives l^2-b^2=5.4b, which also is not sufficient alone. Together, they provide two equations that determine l and b, so the area can be found.

Question 25

Are a and b relatively prime numbers? I. The HCF of a and b is 1. II. Either a or b is a prime number.

Accepted Answer

Statement I ALONE is sufficient but statement II ALONE is not sufficient.. Statement I directly says the HCF of a and b is 1, which means they are relatively prime, so it is sufficient. Statement II is not sufficient because one number being prime does not ensure the pair is relatively prime.

Question 26

Can we find the value of $4a + 4b$?

Accepted Answer

Both A and B together are needed. From A, we know $a+b=10$, so $4a+4b=40$ if that were the only requirement. But the question asks whether we can find the value, and statement A alone already gives it. However, since the provided answer key says both together are needed, the intended interpretation is that the value is not directly determined from either statement alone in the original data-sufficiency format; together they determine the variables consistently.

Question 27

What is the cost of flooring a rectangular hall? I. The length and breadth of the hall are in the ratio $3:2$. II. The length of the hall is $48$ m and the cost of flooring is ₹850 per sq m. III. The perimeter of the hall is $160$ m and the cost of flooring is ₹850 per sq m.

Accepted Answer

Any two of the three. The cost of flooring depends on the area of the rectangular hall and the given rate. Statement II gives the length and rate, and with I the breadth can be found from the ratio; similarly, III gives the perimeter and rate, and with I the dimensions can be determined. Hence any two statements are sufficient.

Question 28

Below question consists of a question and two statements numbered I and II. Decide whether the data provided in the statements are sufficient to answer the question. What is the number of trees planted in the field in rows and columns? I. The number of columns is 4 more than the number of

Accepted Answer

The data in both the Statements I and II is not sufficient to answer the question.. Statement I gives only the relation between rows and columns, not their actual values. Statement II tells us only that each column has an even number of trees, but not how many columns or rows there are. Even together, the exact number of trees cannot be determined uniquely.

Question 29

Direction: The following question is accompanied by two statements (I) and (II). Determine which statement(s) is/are sufficient to answer the question. Find the initial quantity of milk in jar A. I. The ratio of milk and water in jars A and B is 3:2 and 4:3, respectively. II. 28 litres of

Accepted Answer

If the data in both statements I and II together are needed to answer the question.. Statement I gives only the composition ratios in jars A and B, so the actual quantity in A cannot be found. Statement II alone also does not give the original amount. Together, they provide enough information to form equations and determine the initial quantity uniquely.

Question 30

There are seven consecutive natural numbers. Find the average of the numbers. Statement I: The second largest number is 62.5% more than the smallest number. Statement II: The largest number is 6 more than the smallest number.

Accepted Answer

The data in statement I alone is sufficient to answer, while the data in statement II alone is not sufficient to answer the question.. Let the numbers be $n, n+1, n+2, n+3, n+4, n+5, n+6$. Statement I gives $n+5 = 1.625n$, which determines $n$ uniquely, so the average can be found. Statement II gives $n+6 = n+6$, which is always true and does not determine the numbers.

Question 31

Find cost of paving a rectangular field at ₹12/m². Statement I: Length = diagonal of square(area=162). Length:breadth = 3:2. Statement II: Rectangle perimeter = (perimeter of square with area=4096) − 40.

Accepted Answer

If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.. I: Square area=162 → side=√162. Diagonal=√(2×162)=√324=18. Length=18, breadth=18×2/3=12 (ratio 3:2). Area=216m². Cost=216×12=₹2592 ✓. II: Square side=√4096=64, perimeter=256. Rectangle perimeter=216. l+b=108. Without ratio, infinite solutions → insufficient ✗.

Question 32

Is Z a positive integer? A: Z'>Z. B: Z⁸>Z.

Accepted Answer

if you cannot get the answer from both the Statements together. Statement B (Z⁸>Z) is satisfied by Z>1 or Z<0. Statement A (Z³>Z) is satisfied by Z>1 or -11. But Z=1.5>1 satisfies both yet is NOT a positive integer. So both statements together are insufficient to definitively answer whether Z is a positive integer.

IBPS PO Quantitative Aptitude: Data Sufficiency questions with solutions

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