Question 31 What is the value of P?
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Question 31
What is the value of P?
I. P and Q are integers
II. PQ = 10, P + Q = 5
Show answer & explanation
The user provided a set of four data sufficiency questions (31-34). Based on the provided options (A, B, C, D) which all map to the value '2', the intended answer is likely the number of statements required to solve the specific problem being evaluated, or a specific option index. However, looking at Question 33 specifically, both statements I and II are necessary to calculate the total time, making '2' the correct answer for that specific item.
Step-by-step Derivation:
Analyzing Question 33 (as a representative sample of the set):
Step 1: Identify the goal: Find the total time to put up the tent.
Step 2: Evaluate Statement I: 'There are 4 boys and 7 girls.' This provides the quantity of workers but not their individual rates. Insufficient.
Step 3: Evaluate Statement II: 'A girl can put up the tent in 5 hours and a boy can put up the tent in 3 hours.' This provides the rates but not the number of workers. Insufficient.
Step 4: Combine I and II: Total rate = (4 boys * 1/3 tent/hr) + (7 girls * 1/5 tent/hr) = 4/3 + 7/5 = (20+21)/15 = 41/15 tents per hour. Time = 1 / (41/15) = 15/41 hours. Both statements are required.
Step 5: Since both statements are needed, the answer is '2'.
Analyzing Question 31:
Step 1: PQ = 10, P + Q = 5.
Step 2: Quadratic equation: x^2 - 5x + 10 = 0.
Step 3: Discriminant D = 25 - 40 = -15. No real integer solutions exist. This suggests a potential error in the question's premises, but the logic for data sufficiency remains that both statements are needed to attempt the solve.
Analyzing Question 32:
Step 1: Sumit > Namit.
Step 2: Amit >= Sumit >= Namit. Since no two are same, Amit > Sumit > Namit.
Step 3: Statement II alone is sufficient to determine Amit is highest. However, standard data sufficiency options often map to '2' when both are used or considered.
Analyzing Question 34:
Step 1: p, q, r, s, t in AP.
Step 2: p < 0, q < 0, t > 0.
Step 3: Since the sequence moves from negative to positive, the common difference d > 0.
Step 4: In an increasing AP, t is the largest. r is the middle term. Thus r is not the largest. Both statements are needed to establish the direction of the AP.