asmit123 wrote:

Hi Friends,

I am new to gmatclub.

I would like to put across the below question so that you can help me out in solving.

Each of 435 bags contains at least one of the following three items: raisins, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item?

256

260

316

320

It cannot be determined from the given information.

Let A, R and P denote the bags with only Almond, Raisin and Peanuts

Let AR, RP and AP denote bags containing any two of them

Let ARP denote bags containing all three.

We know \(A+R+P+AR+RP+AP+ARP = 435\) ..(1)

Also, \(R=10P\),

\(A=20RP\),

\(P=1/5*A\)

Also given that \(A+AR+AP+ARP = 210\) ...(2)

Put 2 in 1 and bring everything in form of A to solve for A and get A = 100, so P = 20 and R = 200

So, A+P+R = 320