Evaluating properties of digits and their divisibility
Question
A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?
Options
3
4
5
6
Explanation
The problem requires the bottle capacity to be a common integer factor of both 399 and 532 to ensure completely clean bottling without mixing[cite: 1253, 1254].
Find the common factors by analyzing the difference between the numbers: 532 - 399 = 133. Verify if 133 divides both numbers: 399 = 133 × 3 and 532 = 133 × 4. Yes, 133 is the Highest Common Factor (HCF).
The number of valid uniform bottle sizes equals the total count of factors belonging to their HCF (133). Find the factors of 133. Testing small primes shows 133 = 7 × 19. Since 7 and 19 are both prime, the factors are explicitly: 1, 7, 19, and 133. There are exactly 4 possible bottle capacities.
Answer: (b).
Question details
Year
2024
Paper
CSAT
Question
Q19
Section
Numerical Ability
Sub-topic
Number Properties
Type
Statement-based
Difficulty
Medium
Source hint
General number system property evaluation
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