# Q. A can X contains 399 liters of petrol and a can Y contains 532 liters of diesel. They are to be bottled in bottles of equal size so that the whole of petrol and diesel would be separately bottled. The bottle capacity in terms of liters is an integer. How many different bottle sizes are possible?

a) 3

b) 4

c) 5

d) 6

Correct answer: b) 4

#### Question from UPSC Prelims 2024 CSAT

**Explanation : **

## A can X contains 399 liters of petrol

Let’s approach this step-by-step:

1) To find the possible bottle sizes, we need to find the common factors of 399 and 532.

2) First, let’s find the factors of 399:

399 = 3 × 7 × 19

3) Now, let’s find the factors of 532:

532 = 2² × 7 × 19

4) The common factors will be those that appear in both factorizations:

Common factors: 1, 7, 19, and 7 × 19 = 133

5) Therefore, the possible bottle sizes are:

1 liter

7 liters

19 liters

133 liters

6) Count the number of possible bottle sizes:

There are 4 different possible bottle sizes.

Therefore, the correct answer is b) 4.

** **