You have to decide whether the data given in the statements is sufficient to…
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You have to decide whether the data given in the statements is sufficient to answer the question or draw the conclusion of the statement in the question.
What is the total population of town A ?
A. 40% of total population of town A are males.
B. Total numbers of females in town A is 6000
Answer: C. if both statements A and B are needed — CONCEPT: In a data-sufficiency question, a statement (or combination of statements) is sufficient only when it fixes ONE unique value for the quantity asked —…
- A.
if statement A alone is sufficient but B alone is not sufficient
- B.
if statement B alone is sufficient but statement A alone is not sufficient
- C.
if both statements A and B are needed
- D.
if either of statement A or statement B alone is sufficient.
Attempted by 309 students.
Show answer & explanation
Correct answer: C
CONCEPT: In a data-sufficiency question, a statement (or combination of statements) is sufficient only when it fixes ONE unique value for the quantity asked — here, the total population of town A. A percentage/ratio alone cannot fix a unique total without an absolute count to anchor it, and an absolute count alone cannot fix a unique total without a percentage/ratio to convert it.
Statement A alone: 40% of the population are males, so 60% are females. This is only a proportion — with no absolute number attached, the actual total population could be any value consistent with that 60:40 split, so Statement A alone is not sufficient.
Statement B alone: the number of females is 6000. This is only an absolute count — with no percentage or ratio linking it to the total, the total population could again be any value that has 6000 females, so Statement B alone is not sufficient.
Combining both statements: from Statement A, females = 60% of the total population. From Statement B, females = 6000. Equating the two: 60% of total population = 6000, so total population = 6000 / 0.6 = 10000.
CROSS-CHECK: if the total population is 10000, males = 40% of 10000 = 4000, so females = 10000 − 4000 = 6000, which matches Statement B exactly — confirming the total is uniquely fixed only once both statements are used together.
Neither statement alone fixes a unique total population; only the two statements combined do. So both statements A and B together are needed.