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 = 64. From statement A only. What is the correct option?

Statement A alone is sufficient
Statement B alone is sufficient
Either A or B alone is sufficient
Both statements together are necessary

Correct answer: Statement A alone is sufficient

Solution

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.

Related IBPS PO Quantitative Aptitude questions

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 the trader? (I) He bought B at the rate of Rs. 29 per kg. (II) He bought 1 kg of A at Rs. 8 higher than the rate of B per kg. (III) He bought A at the rate of Rs. 34 per kg.
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.
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 nine articles A and four articles B or three articles A and eight articles B. B. The ratio of profit percentages on selling article A and article B is the same. C. The total profit earned on selling one article B is Rs. 6 and the profit percentage on selling one article A is 25%. The selling price and the cost price of article B are Rs. 10 and Rs. 8 more than those of article A respectively. A) Either A and B together or B and C together are sufficient to answer the question B) Either A and B together or C alone is sufficient to answer the question C) Either A and C together or B and C together are sufficient to answer the question D) A, B and C together are sufficient to answer the question E) Either only B or B and C together are sufficient to answer the question
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 cone to its height is 3:2. II. The base and height of a cylinder are the same as the base and height of the cone respectively. The volume of the cylinder is 450\pi cm^3. III. The total surface area of the cone is 600\pi cm^2 and the curved surface area of the cone is 375\pi cm^2. A) Statement II and III together are sufficient to answer the question B) Statement I alone is sufficient to answer the question C) All the three statements taken together are necessary to answer the question D) Statement I and II together are sufficient but III alone is not sufficient E) Either statement I and II together or statement III alone is sufficient to answer the question
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 statement(s) is/are sufficient to find the total quantity of container A (in liters)? I. The sum of the quantity of milk in containers A and B is 195 liters. II. The quantity of water in container A is 85 liters more than that of B. A) Either (I) alone or (II) alone B) Only (I) C) Only (II) D) Both (I) and (II) E) None of them
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 together. C. The ratio of the profit share of C to that of A and B together is 3:8. Which of the following statements is sufficient to answer the question? A) Either A & B together or B & C together B) Either A & C or B & C together C) Any two of them D) None of the given statements can answer the question E) Either A & C together or A & B together

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