Question: Combining Solutions W and X

Comment on Combining Solutions W and X

I solved using the same method and got the answer. My question again here regarding mixture problems is, will we have time to solve by sketching the solutions? because when I sketch using a timer for the question, it is taking me more than 2 minutes to solve. Please suggest.
greenlight-admin's picture

Perhaps you're being too artistic :-)

For me, the sketches add perhaps 10 seconds to the solution.


Too fast wow! For the moment I'm just going through your videos and trying to understand the questions and solve. But I need to increase my speed and start solving with timer. The moment I pause thinking or get stuck at some point, time runs. Does this mean I have lack of practice? I have been practicing maths since May month. Thanks again for the prompt replies and solutions from you. On a lighter note- How do you respond to all our questions so fast? :)
greenlight-admin's picture

Getting faster at solving questions can take a while. Be sure to master the content BEFORE trying to get faster. For more on this, read these two articles:



That said, one way to increase your speed is to take the time to review the responses from the experts on the questions I have linked to. These experts often model the steps one should take to answer questions quickly.

Question: "How do you respond to all our questions so fast?"
Answer: Magic!! :-)

I did exactly the same way, but didn't need the help of those drawings.
I don't know if I'm starting to make sense of these things in my mind. But, these sketching method helps to visualize things so easily. Your method is excellent, Dear Brent.
greenlight-admin's picture

You're absolutely right; we don't necessarily need the sketches to answer these kinds of questions. However, as you've noted, the visual representations make the problems easier to manage for many students.

Kudos to you!


A faster approach is testing the answer choices! (I have come to LOVE this method hehe)

So what I did was I figured out Solution W is 50 mL salt and 200 mL water = 250 mL total

I started with answer C:
100 mL solution X means --> 80 mL salt + 20 mL water
TOTAL solution volume = 250 mL + 100 mL = 350 mL

So the concentration of salt in the new solution = (80+50)/(350) = (130)/(350) = 37% --- But we need it to be 40% so we need more of solution X so Eliminate C as well as A and B

Then test D:
125 mL solution X means --> 100 mL salt + 25 mL water
TOTAL solution volume = 250 mL + 125 mL = 375 mL

So the concentration of salt in the new solution = (50+100)/(375) = (150)/(375) = 40%

Therefore, the answer is D
greenlight-admin's picture

That's a perfect approach - nice work!!!

Have a question about this video?

Post your question in the Comment section below, and a GRE expert will answer it as fast as humanly possible.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Let me Know

Have a suggestion to make the course even better? Email us today!

Free “Question of the Day” emails!