The numbers of marbles of each of four different colors in a box are

RATIO: 3N+4N+6N+8N=21N

SO, 21*3=63
21*4=84
21*6=126
21*8=168 Therefore, Answer :D

The total number of marbles can be represented as 3x + 4x + 6x + 8x = 21x. Since 144 is not a multiple of 21, 144 cannot be the total number of marbles in the box.

Answer: D

Video Explanation

This is a very easy question on Ratios.

In this question, instead of trying to compare 24 with each of the ratio terms and establishing the 4 values, the easier approach would be to find the total of the ratio terms and look at which option is not a multiple of this total.

The ratio given to us is 3:4:6:8. Since this ratio represents the number of marbles, each of the ratio terms will represent a positive integer.
The total of the ratio terms is 21; this means that the total number of marbles in the box should be a multiple of 21. This will help us eliminate all options which are not multiples of 21.

Clearly, there is only one option like that and that is 144. So, the correct answer option is D.

If you have made a habit of looking at the options after reading the question statement, this question would just be a piece of cake for you because you’d be able to figure out that the common thread that binds options A, B, C and E is the fact that they are all multiples of 21 and so is the total of the ratio terms. This is actually a huge clue that the options are giving you.

Unfortunately, the 24 given in the question statement is actually redundant in my opinion. Had it not been given also, we could have answered the question without much difficulty.

Hope that helps!