This post is a just a saved .doc file which I had, and I am merely reproducing it in its original form, I am not sure of its original author/source but I am grateful to him/her/them for the same.
256! is expanded and expressed in base 576 . how many zeroes will this expression have on its right end?
Such questions are same as finding maximum power of 576 in 256!
576 = 2^6 x 3^2
to get six 2s i have to travel eight places...1x2x3x4x5x6x7x8 has seven 2s. but to two 3s i have to travel only six places...1x2x3...6 has two 3s...hence 2 will be the constrain.
total 2s in 256! = 255
hence, no. of zeroes = 256/6 = 42.
just to check...3s = 126, 126/2 = 63>42
ans-42
300! is divisible by (24!)^n. what is the max. possible integral value of n?
such questions are tricky...when u expand 24!...u get 1x2x3...24.
in this range the highest prime no. is 23...so maximum power of 23 in 300! will decide the max value of x...
when v expand 300!...v get a 23 in 23, 46,69,92....
total no of multiples of 23 in 300! will be 300/23 = 13,
forget the fractional part. so the maximum possible answer is 13. hope am clear...else, feel free to revert.
500! is divisible by 99^n...what is the max. integral value of n?
now every 99 is made of two 3s and one 11. obviously 11 will be the deciding factor. so count no. of 11s for the answer
500/11 = 45
45/11 = 4
ans will be 49.
so in such questions, just check which prime no. will be the deciding factor and count the no. of times it occurs. but please understand that highest prime no. is not necessarily always the deciding factor. see this example:
100! is divisible by 160^n...what is the max. integral value of n?
now 160 = 2^5 * 5^1. now although 5 is the biggest prime no. that 160 is made of, the deciding factor wud be 2. because five 2s occur less often than one 5 does. so we'll count the no. of 2s and divide by 5.
100/2 = 50
50/2 = 25
25/2 =12
12/2 = 6
6 /2 = 3
3/2 = 1
add 'em all...97.
97/5 = 19.
so the answer wud be 19
had we taken 5 as the deciding factor, the answer wud have been 100/5 + 100/25 = 24 which is more than 19...hence a wrong answer...
Showing posts with label MOCK. Show all posts
Showing posts with label MOCK. Show all posts
Saturday, November 14, 2009
Fact Inference & Judgment ....
One of the most dreaded question type in Management Entrance Exam, this section has questions which compel even the best of minds to ponder.
Here is a little help in how to identify them and differentiate among them.
FACTS:
• They can be verified or discovered
• Applicable to all – Universal truths.
• Anything that is seen, heard or read is a fact.
• Anyone else’s opinion stated by the author is a fact. (The personal opinion will become a judgement)
• Figures, Statistics or other data without an opinion attached to it is a fact. ( with an opinion attached becomes an inference).
INFERENCES:
• A logical conclusion based on a set of facts. (Logical conclusion meaning, anyone seeing those set of facts should be able to arrive at that.)
• Change the facts and the conclusion will no longer be valid.
• Inferences are self-explanatory. It tells you “why”. (If you have a statement which looks like an inference and you form a “why” question on it, you should be able to get an answer. If you don’t, it will become a Judgement.)
• An inference is an opinion that doesn’t change according to perspective.
• If the set of sentences given to you are connected, you can only do UPLINKING to decide that a statement as an inference. Meaning – You should have the facts preceeding this statement. If the facts are provided as the next statements it cannot be an inference. It will be a judgement.
Ex:
•
o X is a good student when it comes to attendance.
o X attends college regularly.
In this example, statement A is a judgement, statement B is a fact.
If you change the order like below –
•
o X attends college regularly.
o X is a good student when it comes to attendance.
In this case A is a fact and B is an inference.
• One fact can lead to multiple inferences.
• Inference will have verbal bridges with facts ( words like leads to, points to, indicates, shows, explains, expresses)
• A cause and effect relation ship can be termed as an inference.
• A statement backed up by an example in the same sentence will be an inference.
JUDGMENT:
1.Any statement that could lead to an approval or disapproval.
2.It is the author’s personal opinion.
3.It is open to challenge.
4.It doesn’t tell you why. ( see point 3 of inference for clarity)
5.It changes according to perspective.
P.S. -> because of my project work, industrial training, aimcat and above all my laziness, I haven't been posting for past 2 days, but let me assure you that it will be taken care of.
P.P.S -> I have got quite a few suggestions to discuss the smart methods (aka option rejection, value putting etc) and some others regarding maximization/minimization using venn dig / set theory. I will definitely try to write about the same in my future posts.
Here is a little help in how to identify them and differentiate among them.
FACTS:
• They can be verified or discovered
• Applicable to all – Universal truths.
• Anything that is seen, heard or read is a fact.
• Anyone else’s opinion stated by the author is a fact. (The personal opinion will become a judgement)
• Figures, Statistics or other data without an opinion attached to it is a fact. ( with an opinion attached becomes an inference).
INFERENCES:
• A logical conclusion based on a set of facts. (Logical conclusion meaning, anyone seeing those set of facts should be able to arrive at that.)
• Change the facts and the conclusion will no longer be valid.
• Inferences are self-explanatory. It tells you “why”. (If you have a statement which looks like an inference and you form a “why” question on it, you should be able to get an answer. If you don’t, it will become a Judgement.)
• An inference is an opinion that doesn’t change according to perspective.
• If the set of sentences given to you are connected, you can only do UPLINKING to decide that a statement as an inference. Meaning – You should have the facts preceeding this statement. If the facts are provided as the next statements it cannot be an inference. It will be a judgement.
Ex:
•
o X is a good student when it comes to attendance.
o X attends college regularly.
In this example, statement A is a judgement, statement B is a fact.
If you change the order like below –
•
o X attends college regularly.
o X is a good student when it comes to attendance.
In this case A is a fact and B is an inference.
• One fact can lead to multiple inferences.
• Inference will have verbal bridges with facts ( words like leads to, points to, indicates, shows, explains, expresses)
• A cause and effect relation ship can be termed as an inference.
• A statement backed up by an example in the same sentence will be an inference.
JUDGMENT:
1.Any statement that could lead to an approval or disapproval.
2.It is the author’s personal opinion.
3.It is open to challenge.
4.It doesn’t tell you why. ( see point 3 of inference for clarity)
5.It changes according to perspective.
P.S. -> because of my project work, industrial training, aimcat and above all my laziness, I haven't been posting for past 2 days, but let me assure you that it will be taken care of.
P.P.S -> I have got quite a few suggestions to discuss the smart methods (aka option rejection, value putting etc) and some others regarding maximization/minimization using venn dig / set theory. I will definitely try to write about the same in my future posts.
Monday, November 9, 2009
Tournament Based Sets in DI .
There are 16 teams and they are divided into 2 pools of 8 each. Each team in a group plays against one another on a round-robin basis. Draws in the competition are not allowed. The top four teams from each group will qualify for the next round i.e round 2. In case of teams having the same number of wins, the team with better run-rate would be ranked ahead.
1. Minimum number of wins required to qualify for the next round _____?
2. Minimum number of wins required to guarantee qualification in the next round _____?
Now, I don't know how many of you are aware of the following method. But 1 thing I mention in advance that this should take only 30 seconds to solve
1.
1 group is consisting of 8 teams. So each team will play 7 match each. Suppose each of the 8 teams were seeded and we consider the case where a higher seeded team will always win.
So the number of wins for the 8 teams would be 7,6,5,4,3,2,1,0 with highest seeded team winning all and lowest seeded team losing all.
For minimum number of wins we allow 3 teams to win maximum number of matches. Of the remaining 5 teams just find out the mean of their number of wins.
In this case it would be (4+3+2+1+0)/5=2.
So 5 teams can end up with 2 wins each and a team with better run rate will qualify with 2 wins.
2.
In this case consider the mean of first 5 higher seeded teams
(7+6+5+4+3)/5=5
So it may be the case that 5 teams can end up having 5 wins each. And hence 1 team will miss the second round birth. So minimum number of wins to guarantee a place would be 6.
Note 1: The author Vipul Tyagi is a CAT '09 aspirant, member of Pagal Guy Dream team '09 has scored 16/20 times a percentile greater than 99.49 in AIMCATs with AIRs of 1,7,8,9,10 ... From past three aimcats he has achieved AIR 1 with a comfortable margin in DI.
Note 2: Visit : The original post on pg
1. Minimum number of wins required to qualify for the next round _____?
2. Minimum number of wins required to guarantee qualification in the next round _____?
Now, I don't know how many of you are aware of the following method. But 1 thing I mention in advance that this should take only 30 seconds to solve
1.
1 group is consisting of 8 teams. So each team will play 7 match each. Suppose each of the 8 teams were seeded and we consider the case where a higher seeded team will always win.
So the number of wins for the 8 teams would be 7,6,5,4,3,2,1,0 with highest seeded team winning all and lowest seeded team losing all.
For minimum number of wins we allow 3 teams to win maximum number of matches. Of the remaining 5 teams just find out the mean of their number of wins.
In this case it would be (4+3+2+1+0)/5=2.
So 5 teams can end up with 2 wins each and a team with better run rate will qualify with 2 wins.
2.
In this case consider the mean of first 5 higher seeded teams
(7+6+5+4+3)/5=5
So it may be the case that 5 teams can end up having 5 wins each. And hence 1 team will miss the second round birth. So minimum number of wins to guarantee a place would be 6.
Note 1: The author Vipul Tyagi is a CAT '09 aspirant, member of Pagal Guy Dream team '09 has scored 16/20 times a percentile greater than 99.49 in AIMCATs with AIRs of 1,7,8,9,10 ... From past three aimcats he has achieved AIR 1 with a comfortable margin in DI.
Note 2: Visit : The original post on pg
Sunday, November 8, 2009
How To Identify Incorrect Sentences .
In this post I will be writing about some of the common mistakes in sentences (as in selecting the correct/wrong/most-appropriate/least-appropriate sentence from the given options.)
Mistake 1.) Using misplaced modifiers.
Funda : When a word modifies another word, the two should be next to each other.
Mistake 2.) Using improper pronouns.
funda : Each pronoun must agree with the pronoun it replaces.
Each pronoun must refer directly and unambiguously to the noun it replaces.
Mistake 3.) Changing the verb tense unnecessarily.
funda : The verb tense of a sentence should remain consistent. If the tense is established somewhere in the sentence, there is rarely a need to change it. // I don't have any example of when this ' rarely ' happens.
Mistake 4.) Constructing sentences that lack parallelism.
funda : Just as in previous funda, the structure of the sentence must remain consistent.
Mistke 5.) Comparing Apples and Oranges . // How catchy isn't it ???
funda : When-ever you compare two or more things in a sentence, you have to make sure that all of them are in fact comparable + there must not be any ambiguity as to the validity of the comparison.
Mistake 6.) Improper subject-verb agreement.
funda : The subject and the verb of a sentence must be in agreement.
Mistake 7.) Using incorrect idioms.
Funda : Idioms are idioms and whether or not they sound correct to you, they can't be changed or modified.
Courtesy : GMAT preparatory resources.
P.S. -> I am not very good in verbal, and probably not the right person to give insights into it, kindly ensure that the mentioned rules are correct before applying them in any entrance exam.
Mistake 1.) Using misplaced modifiers.
Funda : When a word modifies another word, the two should be next to each other.
Mistake 2.) Using improper pronouns.
funda : Each pronoun must agree with the pronoun it replaces.
Each pronoun must refer directly and unambiguously to the noun it replaces.
Mistake 3.) Changing the verb tense unnecessarily.
funda : The verb tense of a sentence should remain consistent. If the tense is established somewhere in the sentence, there is rarely a need to change it. // I don't have any example of when this ' rarely ' happens.
Mistake 4.) Constructing sentences that lack parallelism.
funda : Just as in previous funda, the structure of the sentence must remain consistent.
Mistke 5.) Comparing Apples and Oranges . // How catchy isn't it ???
funda : When-ever you compare two or more things in a sentence, you have to make sure that all of them are in fact comparable + there must not be any ambiguity as to the validity of the comparison.
Mistake 6.) Improper subject-verb agreement.
funda : The subject and the verb of a sentence must be in agreement.
Mistake 7.) Using incorrect idioms.
Funda : Idioms are idioms and whether or not they sound correct to you, they can't be changed or modified.
Courtesy : GMAT preparatory resources.
P.S. -> I am not very good in verbal, and probably not the right person to give insights into it, kindly ensure that the mentioned rules are correct before applying them in any entrance exam.
Saturday, November 7, 2009
Finding out smallest number which leaves specific remainders when divided with specific divisors.
Type 1: Find smallest number other than k, that leaves remainder k when divided by x, y, z.
How to Solve: take L.C.M of x, y, z and add k to it.
Type 2: Find smallest number which leaves the remainders x-r, y-r, z-r when divided by x, y, z.
How to Solve: take L.C.M of x, y, z and subtract r from it.
Type 3: Find the smallest number which when successively divided by x, y, z leaves remainders a, b, c respectively.
How to Solve: Start from the last divisor, here the last divisor is z which leaves remainder c, smallest number satisfying this condition will be ‘c’.
Now this ‘c’ must have came after the number was divided by y, so the number must have been c*y + b.
Continue in the same manner.
Variations Of The Basic Types Discussed.
(1) Smallest number that leaves remainders x, y, z when divided by a, b, c and leaves remainder X when divided by Y.
This and similar variations are based upon a simple fact.
To a number if we add the l.c.m. of its divisors, the corresponding remainders don’t change.
What this effectively means is we will first find out a no. which leaves remainders x, y, z when divided by a, b, c respectively and then keep adding the L.C.M of a, b, c to it until the other condition(s) are not satisfied.
Courtesy : Varied sources on Internet.
P.S-> For those of you, who haven't been using these methods, please try them on at-least 5 problems of each type before relying on them for the D-day.
How to Solve: take L.C.M of x, y, z and add k to it.
Type 2: Find smallest number which leaves the remainders x-r, y-r, z-r when divided by x, y, z.
How to Solve: take L.C.M of x, y, z and subtract r from it.
Type 3: Find the smallest number which when successively divided by x, y, z leaves remainders a, b, c respectively.
How to Solve: Start from the last divisor, here the last divisor is z which leaves remainder c, smallest number satisfying this condition will be ‘c’.
Now this ‘c’ must have came after the number was divided by y, so the number must have been c*y + b.
Continue in the same manner.
Variations Of The Basic Types Discussed.
(1) Smallest number that leaves remainders x, y, z when divided by a, b, c and leaves remainder X when divided by Y.
This and similar variations are based upon a simple fact.
To a number if we add the l.c.m. of its divisors, the corresponding remainders don’t change.
What this effectively means is we will first find out a no. which leaves remainders x, y, z when divided by a, b, c respectively and then keep adding the L.C.M of a, b, c to it until the other condition(s) are not satisfied.
Courtesy : Varied sources on Internet.
P.S-> For those of you, who haven't been using these methods, please try them on at-least 5 problems of each type before relying on them for the D-day.
Friday, November 6, 2009
How to attempt DI : part 1
Please read Introduction post first.
The first few minutes we spend on any section have a huge bearing on how we are going to perform in that section. So u should have complete familiarity with the set that u attempt first. Never venture into unknown waters initially. Now it can't be that u are not having any idea about all the sets asked in exam. In that case, the paper is really testing or u should be prepared to give the test next year ( sorry if this sounds harsh, but it's true).
So the best option would be select a DI set first. The chances of cracking a DI set are always more than cracking an obscure LR set. Again if a set based on tournament is asked and u hv the confidence to crack any tournament set, u may start with tht as well.
But to all those who are weak in DI, i'll suggest u to start with a DI set. So my suggestion to all of you is to start working on speed maths a little bit. The time u save while doing DI can be allotted to a tough LR set. Develop good calculation speed and try to attempt all DI sets, and may be 1 LR set and this should be enough to secure a 97-98%ile. ( I'm assuming tht there would be atleast 2 DI sets).
Now those who want 99.5+ in DI, start loving DI and LR. If u can't enjoy doing DI/LR it would be tough to get 99.5+. I know it's all about marks and we not giving CAT for fun, but i personally believe tht unnecessary pressure doesn't help in this section.
You see what kind of a person u are, also determines how u'll fare in this section. If u are by nature a bundle of nerves and allow even small occasions to get to u, chances are tht u'll find going tough in this section.
The reason is that compared to other sections the stakes are very high in this section. Other sections do have single questions but DI section generally has questions in sets. At a time 4-5 questions are at stake. That translates into around 15-20 marks which will be the difference between a 94%ile and a 99%ile. So at the back of the mind there is always this thought that if I'm not able to crack the set, then those 15-20 mins tht i'hv invested in the set would become a liability. This pressure does not help ur cause really. The best way to avoid this mental trap is to start loving those sets. Just don't think abt cut-off and %iles and other things while attempting DI and specially LR. I know what i'm saying is tough to follow but trust me the day u clear these demons from ur mind, u'll start doing exceedingly well.
Note : The author Vipul Tyagi is a CAT '09 aspirant, member of Pagal Guy Dream team '09 has scored 16/20 times a percentile greater than 99.49 in AIMCATs with AIRs of 1,7,8,9,10 ... From past three aimcats he has achieved AIR 1 with a comfortable margin in DI.
The first few minutes we spend on any section have a huge bearing on how we are going to perform in that section. So u should have complete familiarity with the set that u attempt first. Never venture into unknown waters initially. Now it can't be that u are not having any idea about all the sets asked in exam. In that case, the paper is really testing or u should be prepared to give the test next year ( sorry if this sounds harsh, but it's true).
So the best option would be select a DI set first. The chances of cracking a DI set are always more than cracking an obscure LR set. Again if a set based on tournament is asked and u hv the confidence to crack any tournament set, u may start with tht as well.
But to all those who are weak in DI, i'll suggest u to start with a DI set. So my suggestion to all of you is to start working on speed maths a little bit. The time u save while doing DI can be allotted to a tough LR set. Develop good calculation speed and try to attempt all DI sets, and may be 1 LR set and this should be enough to secure a 97-98%ile. ( I'm assuming tht there would be atleast 2 DI sets).
Now those who want 99.5+ in DI, start loving DI and LR. If u can't enjoy doing DI/LR it would be tough to get 99.5+. I know it's all about marks and we not giving CAT for fun, but i personally believe tht unnecessary pressure doesn't help in this section.
You see what kind of a person u are, also determines how u'll fare in this section. If u are by nature a bundle of nerves and allow even small occasions to get to u, chances are tht u'll find going tough in this section.
The reason is that compared to other sections the stakes are very high in this section. Other sections do have single questions but DI section generally has questions in sets. At a time 4-5 questions are at stake. That translates into around 15-20 marks which will be the difference between a 94%ile and a 99%ile. So at the back of the mind there is always this thought that if I'm not able to crack the set, then those 15-20 mins tht i'hv invested in the set would become a liability. This pressure does not help ur cause really. The best way to avoid this mental trap is to start loving those sets. Just don't think abt cut-off and %iles and other things while attempting DI and specially LR. I know what i'm saying is tough to follow but trust me the day u clear these demons from ur mind, u'll start doing exceedingly well.
Note : The author Vipul Tyagi is a CAT '09 aspirant, member of Pagal Guy Dream team '09 has scored 16/20 times a percentile greater than 99.49 in AIMCATs with AIRs of 1,7,8,9,10 ... From past three aimcats he has achieved AIR 1 with a comfortable margin in DI.
Friday, October 2, 2009
Strategy For attempting mock-CATs and CAT .
Disclaimer : Every-one has different strengths and weaknesses, so the strategy and approach of one may not work that well for some-one else.
The author has tried to do post the strategies in the most generic way and they are based upon the common methodologies adopted by him, his friends who are scoring consistently in the higher 99s and those who have belled the CAT in previous years and are in the IIMs, FMS, XLRI.
Assumption : i.) As explained in the previous posts, there are some topics which are repeatedly found as the major areas tested in CAT, so the reader must have gained some proficiency in them till now.
ii.) CAT is a paper of 2:15 hours, is online and provides facility to bookmark a question / skip the question / come back to previous question.
_____________________________________________________________________
QA : Start from the very first question, if it is from a topic you r good at, read it, see if you can solve it under 3 minutes, if yes solve it, if no bookmark it. If it is from a topic you aren't good at, read it, if it looks too easy solve it, see if you can do some value putting etc, if you can't leave it.
Once you have seen all the questions and hopefully solved some of them, you can be sure that you haven't missed any sitter from the sections you are comfortable.
Depending on the time left with you, you can either solve the bookmarked questions right away or go to the next section and come back if you have time left.
DI : ever leave a set untouched. // work on a set for 3-4 minutes and see if u r heading some-where, if u feel u can crack it under 10 minutes, do it. If u feel u can crack it but it will take time, bookmark it, if u feel it can't be done in exam conditions forget about it.
If u have wasted 6-7 minutes on a question aren't able to get a definite direction but have a feel that u will be able to crack it . DONT BELIEVE ON UR FEEL book-mark it and leave it, u can always come back if time permits.
Always look for the individual questions like Data Sufficiency etc. which are usually (but not always) easier.
Even if u aren't able to crack a set, have a look at the questions, at times there are some questions in a set which are pretty doable and some which are time-taking, this isn't that significant in Aimcats but in actual CAT papers, u will almost always have some of these kind of sets.
VA : Okie, I am not really good in VA, so I won't say much , though I would like to make two suggestion to those who have good reading speed but aren't too sure of VA.
Trust on RC, reading comprehension are high-investment high return questions, though u need more time to do them w.r.t. VA questions, but u have higher accuracy in them.
Don't do RC questions with-out first reading the passage, I know that a lot of coaching institutes say that one should read the questions first before reading the passage, but I would suggest to at-least try reading passages first and then attempting the questions and see which one has higher accuracy.
The author has tried to do post the strategies in the most generic way and they are based upon the common methodologies adopted by him, his friends who are scoring consistently in the higher 99s and those who have belled the CAT in previous years and are in the IIMs, FMS, XLRI.
Assumption : i.) As explained in the previous posts, there are some topics which are repeatedly found as the major areas tested in CAT, so the reader must have gained some proficiency in them till now.
ii.) CAT is a paper of 2:15 hours, is online and provides facility to bookmark a question / skip the question / come back to previous question.
_____________________________________________________________________
QA : Start from the very first question, if it is from a topic you r good at, read it, see if you can solve it under 3 minutes, if yes solve it, if no bookmark it. If it is from a topic you aren't good at, read it, if it looks too easy solve it, see if you can do some value putting etc, if you can't leave it.
Once you have seen all the questions and hopefully solved some of them, you can be sure that you haven't missed any sitter from the sections you are comfortable.
Depending on the time left with you, you can either solve the bookmarked questions right away or go to the next section and come back if you have time left.
DI : ever leave a set untouched. // work on a set for 3-4 minutes and see if u r heading some-where, if u feel u can crack it under 10 minutes, do it. If u feel u can crack it but it will take time, bookmark it, if u feel it can't be done in exam conditions forget about it.
If u have wasted 6-7 minutes on a question aren't able to get a definite direction but have a feel that u will be able to crack it . DONT BELIEVE ON UR FEEL book-mark it and leave it, u can always come back if time permits.
Always look for the individual questions like Data Sufficiency etc. which are usually (but not always) easier.
Even if u aren't able to crack a set, have a look at the questions, at times there are some questions in a set which are pretty doable and some which are time-taking, this isn't that significant in Aimcats but in actual CAT papers, u will almost always have some of these kind of sets.
VA : Okie, I am not really good in VA, so I won't say much , though I would like to make two suggestion to those who have good reading speed but aren't too sure of VA.
Trust on RC, reading comprehension are high-investment high return questions, though u need more time to do them w.r.t. VA questions, but u have higher accuracy in them.
Don't do RC questions with-out first reading the passage, I know that a lot of coaching institutes say that one should read the questions first before reading the passage, but I would suggest to at-least try reading passages first and then attempting the questions and see which one has higher accuracy.
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