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Can you explain how this makes sense?

Problem Solving — algebra and arithmetic
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by yumi2012 » Fri Nov 08, 2013 2:02 pm
Totally clueless with this chart-involved IR question.. Thanks in advance.
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by Mike@Magoosh » Fri Nov 08, 2013 4:27 pm
yumi2012 wrote:Totally clueless with this chart-involved IR question.. Thanks in advance.
Dear Yumi,
I'm happy to help. :-)

You may find this blog informative:
https://magoosh.com/gmat/2013/gmat-ir-nu ... -problems/

Let's just follow this through, step-by-step. We have to keep track of three variables: T, a, and b. I just suggest a notation of (T, a, b), so that at each step we are aware of all three values.

I'll just point out --- any "process" with an equation in it, such as b = b/2 --- the value on the left is the new value of that variable, and the values on the right are the old values. The process b = b/2 means: the new value of b is the old value of b divided by 2, or, more simply, "divide b by 2."


First problem
START
T = 0, then we enter a = 24 and b = 35, so we are have (0, 24, 35).
Question: Is b odd? Yes, 35 is odd, so we follow the "yes" arrow up. Still at (0, 24, 35).
The box with the equation T = T + a means --- the new value of T equals the old value of T plus the value of a. Thus, T = 0 + 24 = 24. Now, are values are (24, 24, 35).
OK, we have reached our first non-zero value of T, which is T = 24, so we are done with the first question.

Second problem
START
T = 0, then we enter a = 35 and b = 27, so we are have (0, 35, 27).
Question: Is b odd? Yes, 27 is odd, so follow the "yes" arrow up. Still at (0, 35, 27).
Then, T = T + a, so T = 0 + 35 = 35. Now, we are at (35, 35, 27).
Then, b = b - 1, so b = 27 - 1 = 26. Now, we are at (35, 35, 26).
Then, a = 2a, so a = 2*35 = 70. Now, we are at (35, 70, 26).
Then, b = b/2, so b = 26/2 = 13. Now, we are at (35, 70, 13). (This is FIRST time we pass through this process)
Question: Is b = 1? No, b = 13. Follow the long "no" arrow. We are still at (35, 70, 13).
Question: Is b odd? Yes, 13 is odd, so follow the "yes" arrow up. Still at (35, 70, 13).
Then, T = T + a, so T = 35 + 70 = 105. Now, we are at (105, 70, 13).
Then, b = b - 1, so b = 13 - 1 = 12. Now, we are at (105, 70, 12).
Then, a = 2a, so a = 2*70 = 140. Now, we are at (105, 140, 12).
Then, b = b/2, so b = 12/2 = 6. Now, we are at (105, 140, 6). (This is SECOND time we pass through this process)
After the second time of passing through the b = b/2 process, b = 6.

Does all this make sense?
Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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by marshelle.slayton » Wed Nov 27, 2013 1:45 pm
The easiest way I am able to do these problems is by recording how the numbers change. If you write down the solution of each block with an arrow to the next equation it helps.

Also, keeping a grid of what all variables are at each block helps. Maybe try numbering the blocks and then you can use that in your grid. Have block # and varliables as the two defining properties. If you are looped back to a block make it vs by doing this, 1st time, Block 1.0, second time, Block 1.1. That will help you keep track of how many times you have been at that block. I would fill out the variables before you start and number the blocks. Fill in the block #'s in the chart as you go so as to not confuse yourself.

Let me know if you have any questions and I can send an example!
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by Poisson » Mon Aug 29, 2016 1:59 pm
Mike@Magoosh wrote:
yumi2012 wrote:Totally clueless with this chart-involved IR question.. Thanks in advance.
Dear Yumi,
I'm happy to help. :-)

You may find this blog informative:
https://magoosh.com/gmat/2013/gmat-ir-nu ... -problems/

Let's just follow this through, step-by-step. We have to keep track of three variables: T, a, and b. I just suggest a notation of (T, a, b), so that at each step we are aware of all three values.

I'll just point out --- any "process" with an equation in it, such as b = b/2 --- the value on the left is the new value of that variable, and the values on the right are the old values. The process b = b/2 means: the new value of b is the old value of b divided by 2, or, more simply, "divide b by 2."


First problem
START
T = 0, then we enter a = 24 and b = 35, so we are have (0, 24, 35).
Question: Is b odd? Yes, 35 is odd, so we follow the "yes" arrow up. Still at (0, 24, 35).
The box with the equation T = T + a means --- the new value of T equals the old value of T plus the value of a. Thus, T = 0 + 24 = 24. Now, are values are (24, 24, 35).
OK, we have reached our first non-zero value of T, which is T = 24, so we are done with the first question.

Second problem
START
T = 0, then we enter a = 35 and b = 27, so we are have (0, 35, 27).
Question: Is b odd? Yes, 27 is odd, so follow the "yes" arrow up. Still at (0, 35, 27).
Then, T = T + a, so T = 0 + 35 = 35. Now, we are at (35, 35, 27).
Then, b = b - 1, so b = 27 - 1 = 26. Now, we are at (35, 35, 26).
Then, a = 2a, so a = 2*35 = 70. Now, we are at (35, 70, 26).
Then, b = b/2, so b = 26/2 = 13. Now, we are at (35, 70, 13). (This is FIRST time we pass through this process)
Question: Is b = 1? No, b = 13. Follow the long "no" arrow. We are still at (35, 70, 13).
Question: Is b odd? Yes, 13 is odd, so follow the "yes" arrow up. Still at (35, 70, 13).
Then, T = T + a, so T = 35 + 70 = 105. Now, we are at (105, 70, 13).
Then, b = b - 1, so b = 13 - 1 = 12. Now, we are at (105, 70, 12).
Then, a = 2a, so a = 2*70 = 140. Now, we are at (105, 140, 12).
Then, b = b/2, so b = 12/2 = 6. Now, we are at (105, 140, 6). (This is SECOND time we pass through this process)
After the second time of passing through the b = b/2 process, b = 6.

Does all this make sense?
Mike :-)
Thank you so much. This really wasn't that bad after I took it step by step. Could you please recommend the best way to organize this data on a the notepad? Would you recommend certain column headers?
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by Matt@VeritasPrep » Thu Sep 01, 2016 4:05 pm
Poisson wrote: Thank you so much. This really wasn't that bad after I took it step by step. Could you please recommend the best way to organize this data on a the notepad? Would you recommend certain column headers?
That's way too much writing, especially under test conditions!

I'd start at the first box in the flowchart, then recompute A and/or B after each step. You only really need to write down the value at each step, not how you got it or what the step is asking you to do. (Luckily, all that stuff is already printed on the flowchart.)
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