Doubt from Thursdays with RON - Nov 3, 2011 session

[shankhamala28]

Hi Ron,

The following question was given as part of homework on the 3rd Nov, 2011 session:

There are 6 consecutive positive integers in the set S. What is the value of the positive integer n?
1. When each integer in S is divided by n, the sum of the remainders is 11.
2. When each integer in S is divided by n, the remainders include five different values.

The answer is B.

Though I solved the above problem (couldn't solve it in 3 mins - It took me far beyond 3 mins to get the answer), I faced great difficulty in figuring out the following:
1. I had to try in-numerous options to find the remainders that would sum to 11 (considering the integers in S are consecutive).
After cracking my head for quite some time I figured out that remainders 3 2 1 0 3 2 would sum up to 11 and the integers will be consecutive.
2.After this, I checked for some random values of n to see if st. 1 is satisfied or not. I agree that once I figured out the above thing, it was easier to test different integers for n and solving st. 2.

Now, as stated by you in the video to try some variations such as 12, 13, 14 etc. in st.1 and figure out the answer.
When I tried solving with the other variations, I was once again cracking my head to get the combination of remainders which would sum to 12, 13 etc. and would be consecutive. As usual, I again could not solve it in 3 mins.

Is there any other approach to these problems or it can only be solved by randomly trying out various combinations that would sum to a particular no. ,i.e., the sum of the remainders = 11 or 12 or 13 etc.

[RonPurewal]

Is there any other approach to these problems or it can only be solved by randomly trying out various combinations that would sum to a particular no. ,i.e., the sum of the remainders = 11 or 12 or 13 etc.

Trying out various combinations? Yes.
Randomly? No.

What's interesting about your analysis here is that you haven't mentioned n, the number by which you're dividing -- which is the focus of the whole problem!
If you have a super-hard time with this problem, the most likely cause is that you've forgotten (or never really were thinking about) the GOAL of the problem.

Here, the goal of the problem is to find n. So, your thoughts should center on different values of n.

If n = 3, the remainders are 0, 1, 2, 0, 1, 2, ...
If n = 4, the remainders are 0, 1, 2, 3, 0, 1, 2, 3, ...
If n = 5, the remainders are 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, ...
If n = 6, the remainders are 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, ...

If you have these lists in front of you, then it's not that hard to come up with two possibilities for a sum of 11:
From the n = 4 list: 2, 3, 0, 1, 2, 3
From the n = 5 list: 1, 2, 3, 4, 0, 1
If you're focused on the thing you actually need to find in the problem, you'll notice that you don't even have to find the integers themselves. Just n and the string of remainders.

As for statement 2, the values of n below 5 don't even have five different values to offer in the first place, and a quick glance at the lists for n > 5 shows that you'll get six different remainders every time. So, statement 2 implies n = 5.

Focus!

[shankhamala28]

What's interesting about your analysis here is that you haven't mentioned n, the number by which you're dividing -- which is the focus of the whole problem!

You 're so right. All this while when I was solving the question, my only objective was to look for integers which when divided by n, the sum of the remainders will be 11.
I didn't even think to consider values of n and see the pattern formed with the remainders. Though I had noted this pattern while solving this question, I simply ignored it because I was so into the fact that the sum of the remainders should be 11.

Thanks a ton. Now when you mentioned that what I need to focus, I suddenly find this problem to be far less complex.
Thanks once again Ron!!!! All your videos have been so helpful to me. Though you have always stressed on the fact that "what's the question asking", yet I somehow seem to ignore it while solving this question(may be for some more).
It's a big lesson for me!!!!!!

[RonPurewal]

Thanks a ton. Now when you mentioned that what I need to focus, I suddenly find this problem to be far less complex.

Yep, that's the point.

In fact, this is the only reason why DS problems even exist in the first place -- to test focus and goal-oriented thinking.

The math is basically never the issue on these problems. This problem, for instance, involves literally nothing beyond fourth- or fifth-grade math (basic remainders).
That's actually why the DS problems are there -- because they don't test mathematics. They're there to test (a) your ability to see the goal of a problem, and (b) your ability to ignore distractions and stay focused on that goal.

[arnabgangully]

This is not the first time i am reading your posts or details or your session!!! I admit it whole heartedly that GMAT is a exam of focus , serious thinking , endurance and unconventional thinking .

Ron You are the Best.

[jnelson0612]

This is not the first time i am reading your posts or details or your session!!! I admit it whole heartedly that GMAT is a exam of focus , serious thinking , endurance and unconventional thinking .

Ron You are the Best.

:-)

[RonPurewal]

This is not the first time i am reading your posts or details or your session!!! I admit it whole heartedly that GMAT is a exam of focus , serious thinking , endurance and unconventional thinking .

Ron You are the Best.

Thanks.

Keep in mind what the problems are testing, and you'll find the test much easier. In many cases, you'll even be able to see what the problem writers are trying to do with the problems.

Just remember, math isn't the point. Basically, math is like a common language -- everyone applying to U.S. business school has reasonably studied math up to algebra and geometry, so it's not unfair to anyone. So, they use that level of math (and everything up to it) as a "language" in which to write problems about focus, following directions, reading carefully, solving for specific goals, etc.

As an analogy -- If you're taking a biology test written in English, then it's not an English test. It's a biology test, which just happens to be written in English.
This is a test of focus, due diligence, attention, and goal-oriented thinking, which just happens to be written in the "language" of mathematics.

[arnabgangully]

Thanks ron will remember it.

[jnelson0612]

Great!