Mixture, Series,and Combination Problems

1. 25
The ratio of concentrate to water is 1:3. The total amount of orange juice is 6 x 200 = 1200 ounces. So if you divide this total amount into four parts, it is one part concentrate and three parts water which means you need 300 ounces of concentrate. If one can is 12 ounces then 25 cans are needed to get a total of 300 ounces.

Agree with fiercepoint on #1.

#2. Note that 77 = 11 * 7, and you know 350 = 50 * 7

So, you would need 50 - 11 = 39 "7's", and 1 77, which is a total of n = 39 + 1 = 40. Choice C.

Check: 39 * 7 + 77 = 273 + 77 = 350. Works.

#3. Choice B. I did it the longer way to verify, however, not doing all the math, I've identified a quick way to solve this.

The way I thought about this was as follows: You have 10 partners total, and you need to choose 3, so 10C3 = 120. Now, you know that you have additional constraints, therefore, the total number of combinations must be less than 120. Eliminate C,D,E.

Now, I just did the first set of combinations by myself (choose 1 senior member, and 2 juniors).

Your combinations for the first senior partner is as follows: {S1,J1,J2},{S1,J1,J3},{S1,J1,J4},{S1,J1,J5},{S1,J1,J6},{S1,J2,J3},{S1,J2,J4},{S1,J2,J5},{S1,J2,J6},{S1,J3,J4},{S1,J3,J5},{S1,J3,J6},{S1,J4,J5},{S1,J4,J6},{S1,J5,J6}, a total of 15 combinations for 1 senior partner.

There are 4 senior partners, so there are 4 * 15 = 60 possible combinations JUST by using 1 senior partner and 2 juniors.

That means you can eliminate A, and you're left with choice B.

For problem 3 I have a simpler solution

Whenever the question asks for atleast 1,I always use the probability rule of
Atleast 1 = 1 - none
In our case 1 would be choosing 3 members from a group of 10 people without any restriction

10C3 = 120

Now choosing 3 such that none is a Senior partner is equivalent to choosing 3 from the 6 junior members
6C3 = 20

Therefore required number = 120-20 = 100

Hope this helps.

sanjana wrote:For problem 3 I have a simpler solution

Whenever the question asks for atleast 1,I always use the probability rule of
Atleast 1 = 1 - none
In our case 1 would be choosing 3 members from a group of 10 people without any restriction

10C3 = 120

Now choosing 3 such that none is a Senior partner is equivalent to choosing 3 from the 6 junior members
6C3 = 20

Therefore required number = 120-20 = 100

Hope this helps.

I love you style, It's so simple and straight forward