Tickbox Quiz 6 Question 13

GRE Quant Problem Solving
1

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As the mixture is in the ratio A:B, I assumed A should be the larger one and, as the second solution had the highest alcohol content, I assumed that the second solution will be A

How can we conclusively infer that A is the first solution and B is the second solution?

The correct answer is 2.

2

Try the case you mentioned - what answer do you get?

3

I get A:B = 2:1
=> A = 2*B
=> B = 1/2*A

4

Suppose she mixed 2 L of solution A and 1 L of solution B. Then,

  • Amount of alcohol in A = 0.16 \times 2 = 320 ml
  • Amount of alcohol in B = 0.25 \times 1 = 250 ml
  • Amount of alcohol in the combined solution: 570 ml
  • Amount of (A + B) = 3L
  • Proposal of alcohol in the solution: 19%

So that can’t work.

5

Your solution makes sense. I guess better to check by plugging in numbers whenever in doubt

Btw, for such questions, was my interpretation correct?

  • Is it logical to assume that “A” will be the one with larger amount?
  • or is it logical to assume that the first solution will always be the one that will be mixed first and will be referred to as “A”? [Nothing about the order in which the solution was mixed has been given in the question]
6

Not quite. The reason I showed you an example is to hopefully show intuitively why your reasoning wasn’t correct.

One way to think about it is this:

  • 22% alcohol is more than the average of 16% and 25%, so it is not the case that she mixed equal volumes of both solutions
  • So if she filled more A than B, the combined alcohol content should tend towards the amount of alcohol in A → it should reduce from the mean (20.5%)
  • Hence she must have filled more B than A (and think about how that’s intuitive)

Getting the intuition right is a very useful sanity check.

7

I understand what you’re saying, but how do we decide which solution is A and which solution is B based on the question stem?
I assumed that the second solution containing 25% alcohol will be A and the first solution containing 16% alcohol will be B. As the mixture contains 22% alcohol, it has more A than B. So the ratio would be A:B = 2:1; B = 1/2 A.

The reason I considered the second solution containing 25% alcohol to be A is that the mixture contains more of that solution than the other.
I hope I am able clarify my confusion.

8

I think I see where you are coming from. Check the question now.

9

It’s clear now. Thanks :+1: