Ratio and Proportion

[knight247]

Five glasses of same capacity are partly filled with water. The quantities of water in each of the glasses are in the ratio 2:3:4:5:6. The total quantity of water in the glasses is 2/5 of the total capacity of the five glasses. How many glasses are at least half full?
(A)1
(B)3
(C)2
(D)4
(E)5


No OA...Sorry

[GMATGuruNY]

Five glasses of same capacity are partly filled with water. The quantities of water in each of the glasses are in the ratio 2:3:4:5:6. The total quantity of water in the glasses is 2/5 of the total capacity of the five glasses. How many glasses are at least half full?
(A)1
(B)2
(C)3
(D)4
(E)5


No OA...Sorry

We can plug in values.
Since 2+3+4+5+6 = 20, the total amount of water should be a multiple of 20.
Let the capacity of each glass = 20 ounces.
Then the total capacity of the 5 glasses = 5*20 = 100 ounces.
The total quantity of water = (2/5)100 = 40 ounces.
Since 2:3:4:5:6 = 4:6:8:10:12, the amounts of water in the 5 glasses are 4 ounces, 6 ounces, 8 ounces, 10 ounces, and 12 ounces, for a total of 4+6+8+10+12 = 40 ounces.
Since each glass can hold 20 ounces, the first glass is 4/20 full, the second 6/20 full, the third 8/20 full, the fourth 10/20 full, and the last 12/20 full.
Only the last two glasses (10/20 and 12/20) are at least half full.

The correct answer is B.

Please note that I rearranged the answer choices in ascending order, as they would likely be listed on the GMAT.

[LeoBen]

ratio = 2:3:4:5:6

lets consider the multiple as 1 -- bcz the answer needs ratio itself.

total quantity = 2+3+4+5+6 = 20.

capacity = 5/2 (quantity) = 5/2 x 20 = 50.

capacity per glass = 50/5 (as each of the 5 glasses has equal capacity) = 10

question hence = no. of glasses >= half of 10 full i.e. >=5. only two as per our ratio 5 & 6. (note: our multiple was 1)

[tomada]

I have a knack for pointing out the trivial, so I'll just mention that, in the problem as initially posed, choices (B) and ( C) are the reverse of what GMATGuru used.