CP#17

Question (from MGMAT Practice Test #1)
For positive integer k, is the expression (k + 2)(k² + 4k + 3) divisible by 4?

(1) k is divisible by 8.

(2)

k + 1 3

is an odd integer.

Solution
The quadratic expression k² + 4k + 3 can be factored to yield (k + 1)(k + 3). Thus, the expression in the question stem can be restated as (k + 1)(k + 2)(k + 3), or the product of three consecutive integers. This product will be divisible by 4 if one of two conditions are met:

If k is odd, both k + 1 and k + 3 must be even, and the product (k + 1)(k + 2)(k + 3) would be divisible by 2 twice. Therefore, if k is odd, our product must be divisible by 4.

If k is even, both k + 1 and k + 3 must be odd, and the product (k + 1)(k + 2)(k + 3) would be divisible by 4 only if k + 2, the only even integer among the three, were itself divisible by 4.

The question might therefore be rephrased “Is k odd, OR is k + 2 divisible by 4?” Note that a ‘yes’ to either of the conditions would suffice, but to answer 'no' to the question would require a ‘no’ to both conditions.

(1) SUFFICIENT: If k is divisible by 8, it must be both even and divisible by 4. If k is divisible by 4, k + 2 cannot be divisible by 4. Therefore, statement (1) yields a definitive ‘no’ to both conditions in our rephrased question; k is not odd, and k + 2 is not divisible by 4.

(2) INSUFFICIENT: If k + 1 is divisible by 3, k + 1 must be an odd integer, and k an even integer. However, we do not have sufficient information to determine whether k or k + 2 is divisible by 4.

The correct answer is A.


Query
I think the answer is D. In Statement (2), for (k+1)/3 to be an odd INTEGER, k+1 has to be divisible by 3. Also, k must be even. Therefore, k could be 2,8,... And if k is an even integer, (k + 1)(k + 2)(k + 3) will not be divisible by 4 for any of these values of k. Therefore, Statement (2) also gives us the answer. Please tell me where I'm going wrong.

CP #16 - have not understood why not my way?

Question (from MGMAT Practice Test #1)
In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?

Solution
We are told that 4 people have exactly 1 sibling. This would account for 2 sibling relationships (e.g. AB and CD). We are also told that 3 people have exactly 2 siblings. This would account for another 3 sibling relationships (e.g. EF, EG, and FG). Thus, there are 5 total sibling relationships in the group.

Additionally, there are (7 x 6)/2 = 21 different ways to chose two people from the room.

Therefore, the probability that any 2 individuals in the group are siblings is 5/21. The probability that any 2 individuals in the group are NOT siblings = 1 – 5/21 = 16/21.

The correct answer is E. 

OG 12 Diagnostic - Quant

Scored Excellent in both PS and DS (got 20/24 right in each). Put in my answers in the Error Log. Had to combine an error log and a guide to OG12 to make my error log make sense (will post this on GMATClub once I'm done with OG12 I guess). Apparently, my accuracy in Geometry pulled down my score. And that could be because I studied Geo a couple of weeks before the test, and managed to just put in 2-3 hours of going through my FCs on the night before the test. Still, Geo's my strong point, so not glad to see this.

Will now try the questions I got wrong once again, without looking at the actual answer (although my previous answer choice will be POEd beforehand). Once I'm done, will go through explanations of all the questions I had issues with, and fill in whatever's remaining in the error log.

Absolutely Not So Simple

Tried going through GMATClub's chapter on Absolute Value, 'tried' being the key word here.
I thought it was going to simple restate that the absolute value is the distance between two points. However, it took me back to my Class XI days of trying to solve absolute value questions. Damn my sister, she's lost my theory notebook from my tuition days, and now I need to redo all the thinking for this chapter.
It's not as simple as it sounds, need to try my luck again. In other words, bhai samajh mein hi nahi aaya. Probably needs a fresh mind. If it still doesn't work, Aman Chawla to the rescue I guess.

CP #12

Another one from GMATClub Math Book's Probability chapter.
Given that there are 5 married couples. If we select only 3 people out of 10, what is the probability that none of them are married to each other?

They have given 3 different ways to solve it. All have gone over my head. Help!

CP #11

This one's from the Probability chatper in GMATClub's Math Book.

If the probability of raining on any given day in Atlanta is 40%, what is the probability of raining on exactly 2 days in a 7-day period?

The way I look at it is this:
7 days, out of which on 2 it rains.
2 rain, 2 without rain = 0.4*0.4*0.6*0.6*0.6*0.6*0.6
= (0.4)^2 * (0.6)^5

However, the actual answer is
7C2 * (0.4)^2 * (0.6)^5

I don't understand why the 7C2 is required.

--

Went through the explanation in the chapter itself. It says that, it could rain on Day 1 and 2, or on Day 3 and 7. The sequence changes, although the number of days on which it rained remains the same. This must be factored in to get the correct answer. So other than the probability of it raining on those 2 and 5 days, we must also factor in the possibilites of different days on which it must rain.
At a preliminary level, I get it. But, I'll probably need a few more questions of the type or a different explanation to understand this thoroughly. Thoughts anyone?

1 hr to go to office 20 kms away, 1 hr 15 mins to come back. On an avg, how much time do I waste everyday?

Finished Distance, Speed & Time from a GMATClub post. The tabular representation method is brilliant. It saved me a lot of time, since I don't have to keep writing the different forms of the formula S=D/T for every component of the question. Am definitely using the table form from now on! :-)

Also went through the post on Work problems. Didn't require much effort since my concepts are pretty clear. The only issue I have here is the time I take to solve a question, if I only rely on my concept. I will need to practice a lot of Work problems, and probably revisit my TIME notes for shortcuts. Buit I will get back to this post my diagnostic test, as the diagnostic test is untimed. Plus, there is only a limit to how much I can do in every topic over the next 2 days. Yup, probably giving the test on Saturday. Should revise everything on Friday. Phew...

Update on P&C: went through most of the solved examples in RS Aggarwal, need to wrap up Combinations with the last few questions from the book. Once this is done, need to go back to the GMATClub Math book chapter on Probability and try solving those examples I was having trouble with.

As for Remainders, still need to speak to that friend regarding the questions from the link I did not understand.

The Remainder of the previous post.

Before I forget, I also went through a post on Remainders. The formulae are easy, but when I tried solving the last question, I couldn't understand the reasoning. Also, there was a link to other questions - I had a problem grasping the reasoning there too. Need to sit down with my friend and understand all these concepts, before I can consider remainder theory finished.

What's your excuse? (Number Theory & Percents)

Project is almost done. Have not been able to study properly for 3 weeks I think. But I'll just put in extra effort this week and wrap it up...I hope I'll be able to!

Done with:
1. Number Theory
2. Percents
from GMATClub's Math Book.

Phew.

Also, revised Mutliplying with 2 Reference Nos. Had forgotten how to do it. Need to revise Addition Chapter.
I must repeat myself - I LOVE Bill Handley's book! :-)

And it's a wrap.

Done with Geometry Theory. Got 38/42 correct in Kaplan book's practice sets. 3 questions - very silly mistakes. 1 question - although easy, it had a particular method to solve it. It's definitely a CP. Will post it soon.

Now starting off with Standard Deviation.

CP #10

GMAT Blue Quiz - Kaplan

UNDERSTAND EXPLANATION!!!

Question

Is a – b > 0?

(1)    a > 2b

(2)    b > a + 3

Solution

The inequality in the question stem can be manipulated so that the question reads "is a > b?"

At first glance, Statement (1) would seem to be sufficient. If a and b are both positive, and then a is certainly greater than b. But what if a and b are negative? If a = -3 and b = -2? Since -3 > -4, a would be greater than 2b; but since -2 > -3, b would be greater than a. Since Statement (1) can lead to either a yes or no answer, it is insufficient.

Manipulating the inequality in Statement (2) is more fruitful. Subtracting b and 3 from both sides gives you -3 > a-b. If that's true, then a – b is certainly less than zero. Statement (2) leads to a single, definite answer (which happens to be "no") and so is sufficient.

Kaplan Permier: Blue Quiz

Completed Kaplan Premier's Blue Quiz today. Scored an 87% overall. Got 26/30 right. Wrong - 2 CR (DOUBT IN #20 - ASK A KAPLAN INSTRUCTOR), 1 SC (idiom - as many...as) and 1 DS (ASK FRIEND!).

Speed Math: Multiplying Decimals

Went through the chapter on Multiplying Decimals. The concept is the same as any other multiplication, but one use of it is super-cool.

If you need to multiply 8 x 88, make it 8.0 x 88. Essentially, you're multiplying 80 x 88 and can just add a decimal point at the end of your answer. Super-awesome!

To Do

Hopefully will get to go through the next chapter (Multiplying Using Two Reference Numbers) today itself.

Tables upto 20!

Kaplan Diagnostic Quiz & Speed Math

Hi...

Work has kept me quite busy, so had left GMAT studies for sometime. It's time now.

Recap

Took the GMAT Diagnositc Quiz on Kaplan Premier's online companion. Scored 89% - 34 / 38 were correct answers. Got 1 wrong each in DS, PS, RC and CR. It was untimed.

To Do

While reviewing, there is 1 DS question I could not understand - will ask a friend - also, need to put it as a CP.

Another DS question took too long - must review that.

RC Strategy

In RC, writing what the para is talking about as short notes helps me. It's a PR method, but it seems to be working. It doesn't work in those passages where I have literally been unable to comprehend the meaning. To reduce the probability of that happening, I need to start taking out time to read (I used to be a voracious reader till time constrains brought my reading time down to near negligible). I also need to work on my vocab - I have Word Power Made Easy (WPME) by Norman Lewis. Maybe I should revisit it.

Speed Math

Have also been learning calculation shortcuts from Bill Handley's Speed Mathematics. It's actually quite fun and I've done a few chapters.

To Do

Do the chapter on decimal multiplication. Practise calculations.

Day 29-30

Day 29:
Qs. 1-19 from PR VB3. Timed: 1.8 min/qs.

Day 30:
Qs. 20-26 from PR VB3. Timed. Done now.

Review & error log entry coming soon...

Day 28

Here is the PR Assessment Summary:

QUANT

Category	R	W	U	% Correct
Problem Solving	19	3	0	86%
PS Math Definitions	1	0	0	100%
PS Frac/Dec/Percent	3	0	0	100%
PS Exponents/Roots	1	0	0	100%
PS Ratios/Proprtns	2	0	0	100%
PS Avgs/Rates/Stats	2	0	0	100%
PS Probablility	0	1	0	0%
PS Plugging In	5	1	0	83%
PS PITA	2	1	0	67%
PS Estimation	1	0	0	100%
PS Geometry	2	0	0	100%
Data Sufficiency	12	3	0	80%
DS Math Definitions	2	1	0	67%
DS Frac/Dec/Percent	1	0	0	100%
DS Ratios/Proprtns	1	1	0	50%
DS Avgs/Rates/Stats	1	0	0	100%
DS Eqtns/Inequals	2	1	0	67%
DS Simul Eqtns	1	0	0	100%
DS Geometry	1	0	0	100%
DS Yes/No	3	0	0	100%

Most of my Math errors were caused by not reading the question/statements/answer choices carefully! I used the wrong formula in one place (silly!!! I knew the right formula but blanked out during the exam), and there was one concept error. I didn't realise that if you try to put a cylinder in a cuboid, the maximum diameter of the cylinder can NEVER be equivalent to the longest side of the cuboid. This is because even the floor of the cuboid would have one side which is NOT the longest side. And therefore, the diameter of that cylinder can only be equal to the second longest side of the cuboid, and not more than that (ADD THIS TO FCs!).
There is one Math question I couldn't solve even on my second try, and when I checked the answer, I still didn't get it! I don't understand the solution, and am probably understanding the question wrong. I'll add it here later. I've asked a friend to look into it and let me know.

VERBAL

Category	R	W	U	% Correct
Sentence Corr.	13	2	0	87%
Red Pencil Fever	1	0	0	100%
Idiom	3	1	0	75%
Verb Tense	2	0	0	100%
Subject/Verb Agreement	1	0	0	100%
Pronouns	1	0	0	100%
Parallel Construction	4	0	0	100%
Quantity Words	1	0	0	100%
Misc	0	1	0	0%
Arguments	11	1	0	92%
Weaken	3	1	0	75%
Assumption	5	0	0	100%
Resolve/Explain	1	0	0	100%
Strengthen	2	0	0	100%
Reading Comp.	9	5	0	64%
RC General	2	1	0	67%
RC Specific	5	4	0	56%
RC Reasoning	2	0	0	100%

I started reviewing the Verbal part here in office, but got stuck with the solution of the first wrong answer itself! It's an SC question, and my God! What solutions! I may be good at Verbal and may assume I write grammatically correct sentences, but I am completely unaware of technical explanations for why one answer is better than another! I've always been dependent on what sounds right to my ear, because I thought my extensive reading would be of help. Apparently, not on the GMAT! Hmmm...thinking of picking up MGMAT SC book. Anyway, I'll add to this when I get back home.