Solving a digit substitution puzzle for a specific multiplier
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.
Options
The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
The Question can be answered by using either Statement alone
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
The Question cannot be answered even by using both the Statements together
Explanation
Evaluate the parameters needed to calculate the exact student population n:
Statement I limits the boundary values (Max = 70, Min = 50). This provides no details on how the scores are distributed or clustered between those values. Insufficient.
Statement II states that removing the Max and Min endpoints leaves the average unchanged at 60. This mathematically implies that the mean of those two extreme scores matches the class average: 70 + 50/2 = 60. While this confirms internal structural symmetry, it provides absolutely zero scale information regarding the total number of intermediate data entries.
Even when combined, the system could accommodate an arbitrary number of students (e.g., 3 students scoring 50, 60, 70, or 50 students all scoring 60). The population remains undetermined.
Answer: (d).
Question details
Year
2024
Paper
CSAT
Question
Q66
Section
Numerical Ability
Sub-topic
Number Puzzles
Type
Factual single
Difficulty
Hard
Source hint
Cryptarithmetic / Digit puzzles
Same sub-topic — other years
Number Puzzles has appeared in multiple CSAT papers:
Q10
2022
Arranging digits in rows based on multiplication conditions
Q54
2022
Finding properties of the sum of all permutations of 3 distinct digits
Q66
2022
Solving a digit reversal multiplication puzzle to find difference
Q78
2022
Finding sets of consecutive integers whose sum equals their product
See all questions on Number Puzzles
Browse every tagged question across all years