I have two containers with different capacities. Initially, the larger one is full of water and the smaller one is empty. I pour water from the larger container into the smaller container until they contain the same volume of water. The volume of water in the large container is now p times its capacity and the volume of water in the small container is q times its capacity. Which one of the following statements about p and q must be true?

Answer:

4) C

Since the big container is full of water, it represents 1 (whole). The water from the big container is emptied into the smaller container in such a way that both contain the same amount. This is only possible when half of the water in the big container is emptied into the smaller container.

So, the big container has 0.5 times is capacity. Hence, p = 0.5. This rules out A, D and E.

Now, the smaller container has equal amount of water as the big container i.e. 0.5.
However, q is the volume of water times its OWN capacity. Try visualising the situation. Half of the water from a big container is emptied into a smaller container.

Let’s say that the big container had 10 units of water, which is its full capacity. Let us say the smaller container had a capacity of 7 units of water. Half of the volume of water from the big container, i.e. 5 units is emptied into the smaller one. Therefore, q would be 5/7 full. This is more than 0.5 times its capacity as 0.5 times is capacity would be 3.5 units. Hence, q > 0.5.