Directions: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) 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; Give answer (b) if the data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question; Give answer (c) if the data either in statement I or in statement II alone are sufficient to answer the question; Give answer (d) if the data even in both statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both statements I and II together are necessary to answer the question. 55% of all teachers in a school are females. If 8% of the female teachers in that school teach 5 classes a day, what is the number of female teachers who do not teach 5 classes a day? I. There are 135 male teachers in the school. II. There are 27 male teachers in the school who do not teach 5 classes a day.

Concept & Logic In data sufficiency, we only need to verify if a unique numerical value can be derived. To find the exact number of female teachers who do not teach 5 classes, we need the total number of female teachers (or the total number of teachers, from which the female count can be derived). Step-by-Step Solution * Given: $55\%$ of all teachers are female. Therefore, $45\%$ of all teachers are male. * Given: $8\%$ of female teachers teach 5 classes a day. This means $92\%$ of female teachers do NOT teach 5 classes a day. * To find the final answer, we just need to evaluate $92\%$ of the total number of female teachers. Calculation / Deduction: * Analyzing Statement I: There are $135$ male teachers. Since males constitute $45\%$ of the total teachers, we can set up the equation: $0.45 \times \text{Total} = 135$. This allows us to calculate the total number of teachers. From the total, we can find the exact number of female teachers, and subsequently, $92\%$ of that number. Statement I alone is sufficient. * Analyzing Statement II: There are $27$ male teachers who do not teach 5 classes a day. This gives us a subset of male teachers but provides no link to the total number of male teachers, total teachers, or female teachers. Statement II alone is insufficient. Exam Strategy & Shortcut Stop calculating the moment you realize you have enough pieces of the puzzle! In Statement I, recognizing that $45\% = 135$ immediately unlocks the total population variable. Once the total is known, every other subset can be calculated. Do not waste time computing the actual final answer ($0.92 \times 165$) during the exam. Common Pitfall A major trap is actually performing the full calculation when only the logical path is required. Students might calculate Total $= 300$, Females $= 165$, and then struggle with $0.92 \times 165 = 151.8$ (since teachers must be whole numbers, this indicates the source numbers are slightly contrived, but the logical sufficiency remains valid). Calculating wastes time. Final Answer **Therefore, the correct answer is If the data in statement I alone are sufficient.**