CP #5

Question #2 from Kaplan Problem Solving challenge.

The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b.  For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 

The positive integer y is less than 20 and the connection between y and 6 is equal to . How many possible values of y are there?

	7
	8
	9
	10
	11

Answer Explantion:

If the connection between y and 6 is , then the least common multiple of y and 6 must equal the product 6y. The least common multiple of two numbers equals the product of the two numbers only when there are no common factors (other than 1). Since y is a positive integer less than 20, check all the integers from 1 to 19 to see which ones have no factors greater than 1 in common with 6:  1, 5, 7, 11, 13, 17, and 19. So there are 7 possible values for y.

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In my own words (which I can actually understand!),

for the ratio to be 1:1, the LCM should be =6y (so that it cancels out with the product).

For this to be possible, y should NOT be a multiple of 6, and should not include 2,3 or any multiples of 2,3. The only numbers that are not multiples of 2,3 and 6 are 1,5,7,11,13,17,19, a total of 7 numbers!

Why I got it wrong:
I actually randomly guessed on this one cos I knew it would take me more thinking to get the right answer, and so I tried applying the pacing advice I read on a MGMAT forum today.

CP #4

This is a Kaplan Problem Solving Challenge question. It's a 25 minute quiz with 16 questions. I finished it just in time, but I got 2/16 wrong. Here's the first one:


In the diagram above, the line y = 4 is the perpendicular bisector of segment JK (not shown).  What is the distance from the origin to point K ?

	4
	8

Answer Explantion:

Don't try to keep all the information in your head - add to the diagram so you can refer to it as you solve. Horizontal line y = 4 is the perpendicular bisector of JK, so JK must be vertical and parallel to the y-axis. Draw in segment JK, dropping straight down from point J through the x-axis. Before you can find the distance from the origin to point K, you need to know its coordinates. K is directly below J so both points are the same distance from the y-axis and their x-coordinates must be the same. So the x-coordinate of K is 6. Since the line y = 4 bisects JK, the vertical distance from J to the line must be the same as the vertical distance from the line to K. Vertical distance is the difference between the y-coordinates, so the vertical distance from J to line y = 4 is 10 - 4, or 6. Therefore the difference between the y-coordinates of line y = 4 and point K is also 6, so the y-coordinate of K = 4 - 6, making -2 the y-coordinate of point K. So the coordinates of point K are (6, -2). You will notice that K, the origin O, and the point where JK crosses the x-axis is a right triangle, with its hypotenuse being the distance from the origin to point K. Use the Pythagorean theorem to find the length of the hypotenuse. Hypotenuse² = (length of leg lying on the x-axis)² + (length of the leg parallel to the y-axis)² = 6² + 2² = 40. So the distance from the origin to K =  = . 

 

What I did wrong 

1. Didn't remember distance formula

2. Made a mistake in considering K (6,0) since I didn't realise that my K to line y=4 was only 4 points away, not 6.

Wow, this is a first! Didn't remember the formula, AND made a silly mistake!

CP #3

Another good question. They haven't posted the answer yet.

MGMAT Challenge Problem of the Week

10/26/09

Machines A, B, and C

Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?

(A)	12 minutes
(B)	15 minutes
(C)	18 minutes
(D)	36 minutes
(E)	54 minutes

I think the answer is C. I don't think my method is long, but I do think I took a little extra time to think up of the process (again, cos I doubted my concept clarity a little, and so didn't quickly start to solve it the way I was thinking...tried applying formula first, but what good is that if I don't know the concept extremely well?). I'll wait till tomm for them to give the right answer, as well as their explanation. Then I'll compare my answer with theirs.

Much Ado about Nothing...

So, no. Nothing has been happening. Haven't been able to go through GMATPrep questions. Which sucks. And no studying has been happening. Too much other stuff to do.
Anyway, hopefully by tomm I will post something substantial about my studying.
For today, here's a very, very useful link!
The GMAT Club Guide to The-Official Guide-for GMAT Review, 12th Edition

CP #2

Wicked question by MGMAT this week! Check it out...


MGMAT Challenge Problem of the Week

10/19/09

Question

If a, b, and c are positive integers, with a < b < c, are a, b, and c consecutive integers?

(1) 1/a – 1/b = 1/c

(2) a + c = b² – 1

(A)	Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B)	Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C)	BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D)	EACH statement ALONE is sufficient.
(E)	Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Answer

The question can be rephrased "Is b = a + 1 and is c = a + 2?"

One way to approach the statements is to substitute these expressions involving a and solve for a. Since this could involve a lot of algebra at the start, we can just substitute a + 1 for b and test whether c = a + 2, given that both are integers.

Statement 1: SUFFICIENT.
Following the latter method, we have
1/a – 1/(a + 1) = 1/c
(a + 1)/[a(a + 1)] – a/[a(a + 1)] = 1/c
1//[a(a + 1)] = 1/c
a² + a = c

Now we substitute a + 2 for c and examine the results:
a² + a = a + 2
a² = 2
a is the square root of 2. However, since a is supposed to be an integer, we know that our assumptions were false, and a, b, and c cannot be consecutive integers.

We can now answer the question with a definitive "No," making this statement sufficient.

We could also test numbers. Making a and b consecutive positive integers, we can solve the original equation (1/a – 1/b = 1/c). The first 4 possibilities are as follows:
1/1 – 1/2 = 1/2
1/2 – 1/3 = 1/6
1/3 – 1/4 = 1/12
1/4 – 1/5 = 1/20

Examining the denominators, we can see that c = ab. None of these triples so far are consecutive, and as a and b get larger, c will become more and more distant, leading us to conclude that a, b, and c are not consecutive.

Statement 2: SUFFICIENT
Let's try substituting (a + 1) for b and (a + 2) for c.

a + a + 2 = (a + 1)² – 1
2a + 2 = a² + 2a
2 = a²

Again, we get that a must be the square root of 2. However, we know that a is an integer, so the assumptions must be false. We can answer the question with a definitive "No," and so the statement is sufficient.

The answer is D: Each statement is sufficient.
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The first option required just a little more calculation that the second.
I did get the answer on my first try, but I still wanted to post it here because the logic that struck me while trying to solve it may not have struck me at another point of time. I know I've opened my mind to newer ways of solving questions. Earlier, even if the idea would've struck me, just knowing it was a little bit more complicated than what I'm extremely comfortable with, I would've confused myself. Now, I take a deep breath, try to understand why I'm thinking that way, and the answer comes. Even if it doesn't, atleast I'm aware of the logic I used! I should be thanking the people at T.I.M.E classes for this. The Math teacher in Delhi (Kailash Colony) as well as Bombay (Charni Road) were pretty damn good. And they have helped me think of Math in a simpler, clearer manner, and I think I'm getting over my fear now, and beginning to not underestimate myself.
I think I've left my notepad at home. I should write my thought process here.

Plan of Action

Math - IMS BRMs, that CAT Math book for Number Systems, Time,Speed&Dist - TIME. Probability,P&C-tuition notes and class XI qs. Note: Make notebook of qs. u found challenging, and make FCs of new concepts. (1 week)
Once this is done, do PR Math Bin 4 under timed conditions. Then, do questions you got wrong from PR Bin 3. Note: Keep error log (different from book of tough qs from above) (3 days)
Now, give math diagnostic from ...GMATClub maybe? (1 day)
Proceed to DS qs. from TIME Material first (randomly select qs. from appropriate topics-arnd 50-60 qs) (3 days). Then, do PS qs. from OG11 - all questions (yes, you HAVE to do OG now)

Verbal.
CR:
Analyse what went wrong in GMATPrep, do all PR CR qs (2 days), then do MGMAT CR guide (3 days), and then do LSAT qs. (2 days) Finally, do OG11 CR qs -all of them.

SC:
Again, see what sort of problems I had on GMATPrep. Go through MGMAT SC. Do a few PR Bin 3&4 SC questions after each chapter, keep error log on qs I don't get. Do MGMAT FCs (1 week). Finally, get to OG11 SC qs. - all qs.

RC:
Do PR Bin 3&4 qs. (2 days) Then do OG11 qs. - all qs

I didn't do anything GMAT related yesterday. Updated my CV, and rearranged its format, which took about 1.5 hours! Totally worth it though. It's so much better now! Will go through wrong ans. on gmatprep today.

GMATPrep 1

 Two things I'm very proud of completing:
1. Finished CR review from PR yesterday. Finally! :)
2. Gave GMATPrep 1 a couple of hours back.
Also went through Math review from GMATPrep software and no, there was nothing new on it, which was disappointing.
Anyway, so got a 620. Which I guess isn't that bad with this amount of prep.

Verbal - 31.
Was kind of expecting more here, cos I'm usually good at verbal. And while I was doing this section, I actually felt like I was doing well. Which is why the score surprised me even more. I was afraid I won't get to finish the section, but I actually had almost 7 minutes for the last 3 questions.
Incorrect questions:
CR: 6/11...really, really bad.
RC: 3/13...but I consider it pretty damn good. 2 reasons: firstly, I'm usually scared of RC cos of my slow reading speed. But I guess it isn't that slow, and what I read from PR really helped me. Secondly, the 3 questions I got wrong were from the same RC - cos I didn't GET it! Was a science passage, but got a lil too complicated to get while trying to speed read I guess.
SC: 5/17. That's over 70% accuracy. I think it's alright.

Quant - 44.
Man, this section really sucked. I was go bloody slow. I actually ended up randomly clicking options from question number 26, all the way to question number 32. I think in about a minute or so. Seriously, I was so slow. Even out of the 25 I did answer, I got only 15 right. That's terrible. I ended up guessing on some of those 25 too! Sheesh. I need to study so much more here. Need to do lots of practice questions. Do some of my CAT stuff from last year. Some topics I def need to cover - Geometry (co-ordinate plane!), AP/GP, number properties (can try doing it from that CAT aptitude book I have, or my sister's IMS BRM, or TIME material), time,speed&distance, averages! Once I'm thorough with different types of questions, I'll have to do OG and Kaplan questions under timed conditions. Tenaday.com might help in this. I got pretty confused in DS questions. Wow, basically, a lot to work on.

Tomorrow morning I'm not waking up early to study. And I'm meeting a friend for dinner to help him with his CAT verbal. Hopefully I can be of some real help!

Happy studying!

PS. Just posted on PagalGuy.com's thread...gives a short recap of what I've done till now, and about my areas of concern wrt first GMATPrep test. Find it here. ankurgupt was very sweet to post a quick reply to my queries, and you can find his post here. I'm definitely going to use his advice. Trying to get a hold on MGMAT CR Guide.


Day 14: MGMAT's Geometry Guide - Chapter 1 (Polygons)
Day 15: PR CR theory
Day 16: Revise RC notes from PR & give GMATPrep #1