UPSC Prelims 2024 · CSAT (Paper II): A Question is given followed by two Statements I and II. Consider the Question…
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
Question : If the average marks in a class are 60, then what is the number of students in the class?
Statement-I : The highest marks in the class are 70 and the lowest marks are 50.
Statement-II : Exclusion of highest and lowest marks from the class does not change the average.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (d) & explanation
Even both statements together are not enough (d). Step 1: we need the number of students, given the average is 60. Step 2: statement I gives the highest (70) and lowest (50) marks. Statement II says removing them does not change the average. But 70 and 50 themselves average 60, so removing them keeps the average at 60 for any class size. Step 3: so the statements are always consistent but never fix the number. Options (a), (b) and (c) fail.
Tip: when a statement is true for every possible value, it gives no information. Check whether a fact actually narrows the answer.
Answer as per the official UPSC answer key.
Same theme in UPSC Mains
Related questions from other years
Question : X receives three coins of different denominations : 1, 2, 5, 10 and 20. If the total amount received by X is m, does X receive a coin of denomination 5?
Statement I : m is not a prime number.
Statement II : The sum of the digits of m is greater than 5.
Answer (a) & explanation
Statement II alone is enough; Statement I alone is not (a). Step 1: three different coins from 1, 2, 5, 10, 20 give ten totals. With a 5: 8, 16, 17, 26, 27, 35. Without a 5: 13, 23, 31, 32. Step 2: Statement I (m not prime): 8, 16, 26, 27, 35 have a 5, but 32 (2 + 10 + 20) does not. Mixed answers, so I fails. Step 3: Statement II (digit sum above 5): 8, 16, 17, 26, 27, 35 qualify, and every one has a 5. (13, 23, 31, 32 have digit sums 4, 5, 4, 5.) So II answers "yes". Options (b), (c) and (d) fail.
Tip: when cases are few, list them all. Then check each statement against the full list.
don't assume both statements are needed. Listing all ten cases takes thirty seconds and settles it.
Answer as per the official UPSC answer key.
Read the passage
How is deflation done? Most countries use a method called ‘double deflation’, where input and output prices are deflated separately. Consider a manufacturer importing oil for use in production. If oil prices fall, output prices do not and quantities remain the same, real value added should not change. But if the same deflator is used for inputs and outputs, as in India, it would look as if the manufacturer had become more productive.
Which of the following assumptions is/are valid?
- 1. Deflation strategies can be used to make manufacturers appear to be doing better than they actually are.
- 2. When input and output prices are both deflated against a single input price, it is referred to as ‘double deflation’.
Select the answer using the code given below.
Answer (a) & explanation
Only assumption 1 is valid (a). Step 1: the passage says that using one deflator for inputs and outputs, as in India, makes it "look as if the manufacturer had become more productive". So deflation methods can make firms appear better than they are (1). Step 2: assumption 2 says double deflation means deflating both against a single price. But the passage defines double deflation as deflating inputs and outputs separately. So 2 reverses the definition. Step 3: options (b), (c) and (d) fail.
Tip: check definitions word for word against the passage. Deflating means removing the effect of price changes to find real growth, as in real GDP.
Answer as per the official UPSC answer key.
P, Q, R, S and T are ranked 1 to 5 (not necessarily in that order). The rank of P is 4, the rank of Q is not 5, the rank of R is 1, the rank of S is not 2, the rank of T is not 3. Then which of the following is/are correct?
- I. If the rank of S is 3, then that of T is 2.
- II. If the rank of Q is 3, then that of T is 5.
Select the answer using the code given below.
Answer (d) & explanation
Neither statement is correct (d). Step 1: P = 4 and R = 1 are fixed. Ranks 2, 3 and 5 remain for Q, S and T, with rules: Q is not 5, S is not 2, T is not 3. Step 2: statement I: if S = 3, then Q and T share 2 and 5. Q cannot be 5, so Q = 2 and T = 5, not 2. I is wrong. Step 3: statement II: if Q = 3, then S and T share 2 and 5. S cannot be 2, so S = 5 and T = 2, not 5. II is wrong. Options (a), (b) and (c) fail.
Tip: fix the known ranks first, then apply each "if" condition and let the "not" rules decide the rest. Write the small table on paper.
Answer as per the official UPSC answer key.
How many times does 5 appear in all two-digit positive integers?
Answer (b) & explanation
The digit 5 appears 19 times (b). Step 1: 5 in the tens place: 50, 51, …, 59 = 10 times. Step 2: 5 in the units place: 15, 25, 35, 45, 55, 65, 75, 85, 95 = 9 times (05 is not a two-digit number). Step 3: total = 10 + 9 = 19. The number 55 has two 5s, and both are counted. Option (a), 18, counts 55 once. Options (c) and (d) wrongly add 05 or 5.
Tip: count place by place. The question asks how many times the digit appears, not how many numbers contain it (that would be 18).
Answer as per the official UPSC answer key.