Answer is D.

You just substitute 30 for each of the four cases. For each case get the factor by which you need to multiply the rest of the ratios.

Case 1: A:B:C:D = 2:3:5:6
Assume A = 30 , the value you need to multiply 2 to get to 30 is 15.
Now multiply 15 with each of the ratio values to preserve the ratios.
Here it will be 30(2*15): 45(3 * 15) : 75 (5 * 15) : 90 (6 *15)

The addition will give you 30 + 45 + 75 + 90 = 240

Similarly you will get 80, 96 and 160.

The only value you don't get is 192.

Is there a faster method to solve this problem?

ddm wrote:Is there a faster method to solve this problem?

Well there is one

2:3:5:6

2+3+5+6 = 16

80/16 = 5, 5*6 = 30. Eliminate.

96/16 = 6, 6*5 = 30. Eliminate.

160/16 = 10, 3*10 = 30. Eliminate.

240/16 = 15, 15*2 = 30. Eliminate.

192/16 = 12, 12*2 = 24, 12*3 = 36, 12*5= 60, 12*6 = 72.

We dont get a single value 30, therefore this is the answer.

Hope this helps.

parallel

that is somewhat close to what i did.

i laid out each fraction first,

2/16 (i.e. 1/8), 3/16, 5/16, 6/16 (i.e. 3/8)

then i worked with each answer choice and eliminated those which resulted in a fraction that i didn't have in the list above.

for e.g. 30/240 = 1/8 - so eliminate this answer choice

and so on.

Little different approach(but close to others though)

30 can be wither 2x,3x,5x,6x

Case 1: 2x= 30 x=15

2x = 30
3x = 45
5x = 75
6x = 90

240

Case 2: 3x= 30
Case3: 5x=30
Case4: 6x=30

The only value you wont get is 192.

I think parallel chase's solution would be slighlty faster than the others though since we dont spend that extra time to check if we get to the total in 4 of the 5 cases