A classic hip-hop radio station can play up to 12 songs per hour.

This is an easy question on interpretation of ratios.

In this question, you are required to check whether the total number of songs, a maximum of 12, can be broken into two parts, such that both the parts are integers and not greater than 12. After all, you can’t split up 12 songs into 3.5 rap songs and 8.5 R&B songs, right?

Now that we know what we are looking for, let’s see how we can find it.

Can we break up 12 in the ratio of 2:1 such that both parts are integers? Well, yes, we will have 8 rap songs and 4 R&B songs. So, option A 2:1, CAN represent the ratio of rap songs and R&B songs.

The reason behind this is, when we total the two terms of the ratio 2:1, we get 3. 3 is a factor of 12. If 3 parts represent 12, 1 part represents 4 and 2 parts represents 8. Had 3 not been a factor of 12, we would have got 1 part as a decimal value, which is obviously not acceptable in this case. So, the trick is to see which ratios, whose terms when added up, will give a factor of 12 and hence give a total not more than 12.

Sum of ratio terms in option B = 5+1 =6. Hence, this is also a possible ratio. Similarly, option C and option D also represent possible ratios of the rap songs to R&B songs.

The only option left is E. This HAS to be the answer. Sum of ratio terms in this option = 7 + 6 = 13. 13 is greater than 12 and hence not a factor. Since we require integer number of songs and maximum 12 songs, this cannot represent the split up of rap to R&B songs.

Remember that, when you come across such simple problems, you have to make sure that you solve them in the least possible time and move on quickly.

Hope this helps!

If the ratio were 7 : 6, at a minimum 7 + 6 = 13 songs would have played between 1 p.m. and 2 p.m.,, and since the maximum number of songs is 12, 13 songs is not possible.

Answer: E

ScottTargetTestPrep KarishmaB

How can option C, 3:2 be correct, are we assuming 7.2 rap songs and 4.8 R&B songs were played as 2.4 * 3 and 2.4*2 will have to be considered for total of 12 songs in the ratio 3:2

If any of you can throw light, thanks

It's because the question says "up to 12 songs", so it's possible the station plays less than 12 -- it might only play 5 songs in the hour, 3 rap and 2 R&B (or ten songs, with 6 and 4 respectively).

Ohh yeah missed that bit, thanks IanStewart

If we were told that the radio station played exactly 12 songs each hour, then you would be absolutely correct. In that case, 3 : 2 would be another ratio which could not represent the ratio of rap songs to R & B songs played by the station. However, it is possible that the radio station plays less than 12 songs in one hour. If they play 6 rap songs and 4 R & B songs, then the ratio of rap songs to R & B songs is 3 : 2.