ps 500 test21 #18

4 gallons can be written as :

1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2


Only this combination gives you 3 parts of white and
5 parts of black


When you expand any other choice in terms of 1 or 1/2 gallon,
you do not get 3 parts of white and 5 parts of black.
Hence E

Can someone please elaborate on how to solve such problems?
I am not convinced with the explanation for 4 gallons as breaking up using the explanation gives 4 gallons of the mixture and not 2 as asked in the question.
Suppose there should be some way to solve this...thankx in advance

Paints are in the ratio 3:5

Suppose there is a common factor x in both

So, 3x+5x = 2 => x = 1/4

White paint needed = 3/4 gallon => least amount of paint needed is 1 Gallon

Black Paint needed = 5/4 gallon => least amount of paint needed is 1.5 gallon

So, IMO ans should be B

What's the OA

I agree with kajcha. Answer should be 2.5 gallons

Me 2... I think the answer should be B i.e 2.5

I think the key here is "that must be purchased in order to measure out the portions needed for the mixture"

Though B gives the minimum amount required,(1 gallon White and 1.5 gallon Black), it also requires the extraction of 3/4 gallon white paint from the 1 gallon white paint and 1.25 gallon black paint from 1.5 gallon black paint.

E does not have this requirement.

Makes sense... answer would be E.. now i understand the reason why question says "1 gallon"and "1/2 gallon" cans...

From my earlier explanation

least amount of white paint needed = 3/4 gallon.. but 3/4 gallon cannot be measured from 1 and 1/2 gallon cans.. we can measure 3/2 gallon of paints.. means 2*3/4 = 3/2

similarly for black paints 2*5/4 = 5/2 (2 one gallon paints and 1 half gallon paints)n

3/2+5/2 = 4 gallon..

Thanks shymab

Sorry Kajcha & Shyamb! I can not be agree with u. According to me, the problem does not have so much complex interpretation. To me still B stand for the answer. And in support, the OA is also - B. Kajcha & Shyamb I just expressed my thoughts and request you not to take it in other sense!

I would agree with Amitava here , now in a limited time frame of 2-3 mins one can think of anything.

Now the stmt "that must be purchased in order to measure out the portions needed for the mixture"

does not explicity say that there is no measuring device etc available for measuring the reqd quantity.

and one will always tend to consider the most efficient combination/answer which here is 2.5 gallons, whereas 4 will involve the maximun wastage.

So IMO this question involves some anomaly.

samir and amitava, I would have gone for 2.5 gallons as my first answer.. If we assume the answer is reliable then this is wrong answer... and only way 4 can be the answer is if we interpret "measuring out" as one of the key points here...