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Mock 15 can be attempted in unproctored mode right? It's not showing up in my online mocks, anyone else facing the same problem?

  • 4Comments
  • @ferlonso sir results of mock 15 are out? I mean solution.... 25m.
  • @ani6 No, the window is not yet over. 23s.
ferlonso
Valar Morghulis @ferlonso 492

Yup it can be. When I took it on Monday, it was showing

ani6
ano ii @ani6 30

@ferlonso sir results of mock 15 are out? I mean solutions. I have taken non proctored mode and there are no solutions and analysis activated

51s ago 14.4k CAT Quant CAT

Official Quant Thread for CAT 2014!!

This is the Official CAT 2014 Quantitative preparation group. Solve questions & discuss answers/solutions shortcuts &...

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What are the last two digits of 25 times the LCM of 31^22 – 11 and 31^22 + 14?

22 people answered this question.
1 Comments
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Many young children in India have started taking up sports as a profession for various reasons- parental pressure, lure of fame and fortune, competitive spirit or a sheer passion for the game and the dwerst of winning.


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5m ago 685 CAT

[OFFICIAL] IMS SIMCAT scores and Discussion for the entire 2014-15 season !!!

Dear Puys & Pirls, Use this thread for scores and discussion for all the IMS SIMCATs!! It will serve as a repository ...

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guys is there any challenge test going on ?

i am not able to book the slots

24m ago 291 CAT

The PaGaLGuY UnderDogs Team 2014

Do you love taking up the challenge where you are considered as a person who cannot achieve the pinnacle easily but t...

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Missed RoH by 2 marks. But it doesn't matter. This is the boost I need for the final month of my preparation.

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A dream doesn't become reality through magic; it takes sweat, determination and hard work.

29m ago 661 CAT

Logical Reasoning

The question is followed by two statements X and Y. Answer using the following instructions: Choose 1 if the question...

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from the choices, choose a pair in which the first statement implies the second statement and the two are logically consistent with the main statement-

Q- teachers can teach, only if students are well mannered.

A) teachers can teach.
B) students are not well mannered.
C) teachers cannot teach.
D) students are well mannered.

1)AB 2)BC 3)DA 4)CD

  • 2. 29m.
"Aut inveniam viam aut faciam"- Hannibal
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How to find number of solutions of equation involving difference of perfect squares?

Before solving questions based on this concept, let us understand the absolute basics from where we build upon.

Equations involving difference and addition of two numbers, say x and y, will give solution over the set of integers only when either both x and y are odd or both are even. Let us understand this in 3 cases:

1. If x - y =Odd and x + y = Even
Then adding these two equations,
We will get 2 x = odd
(We all know: 2 X any number= even, odd+even=odd)
Which implies x cannot be an integer.
Similarly y cannot be integer.

2. If x - y =Even and x + y = Even
Then adding we will get 2 x = even
which implies x will be an integer.
Similarly y will be an integer.

3. If x - y =Odd and x + y = Odd
Then adding we will get 2 x = even
which implies x will be an integer.
Similarly y will be an integer.

NOTE: Thus while solving these questions given below we will keep in mind such equations will have solutions over the set of integers only when either both x and y are odd or both are even.

We will categorize such problems into 4 parts

CASE 1. Odd Number written as difference of two perfect squares

Example : Find the number of positive integer solutions of equation x2 - y2 = 85 ?

Sol : We can write given equation as

(x- y)(x +y )= 85
Now we want x and y both to be integers and we are given odd number on the right hand side of equation .So clearly both factors will be odd
For finding factors of any number we decompose that number into prime factors
Since 85 = 5. 17
Factors of 5 are 50, 51 (2 in number)
Factors of 17 are 170, 171 (2 in number)
Thus total factors of 85 are obtained by multiplying the factors of 5 and 17 respectively
(i.e. 50170=1 , 50171= 17, 51170=5 , 51171= 85)
Thus total no of factors of 85 are 4 .

But our aim is that we have to write 85 as a product of two factors and Obviously difference of two positive integers is less than their sum i.e. x-y < x+y.So clearly there are two ways we can write 85 as a product of two factors i.e.

85 = 1 x 85 and 85 = 5 x 17

Thus the two possibilities are :
Either (x- y)= 1 and (x +y )= 85
Or (x- y)= 5 and (x +y )= 17.

So in above example answer is
(No of factors of 85)/2
i.e. 4/2 = 2

Answer : 2

NOTE:
Infact we can find the numbers also by solving the above equations x =43 ,y =42 and x=11 ,y = 6.But we are generally asked to find number of solutions only in such questions

GENERALIZATION
So in such cases we can generalize no of ways in which we can write a given number as a product of two factors is : (No of factors on the right hand side of given)/2

Questions for Practice:

1. Find the number of positive integer solutions of equation x2 - y2 = 105 ?
Answer : 4

2. Find the number of positive integer solutions of equation x2 - y2 = 1815 ?
Answer : 6

3. Find the number of positive integer solutions of equation x2 - y2 = 1547 ?
Answer : 3

4. Find the number of positive integer solutions of equation x2 - y2 = 845 ?
Answer : 3

5. Find the number of positive integer solutions of equation x2 - y2 = 1215 ?
Answer : 10

CASE 2. Even Number which is not a multiple of 4 written as difference of two perfect squares

Example : Find the number of positive integer solutions of equation x2 - y2 = 66?

Sol : We can write given equation as
(x- y)(x +y )= 66
Now we want x and y both to be integers and we are given an even number on the right hand side of equation which is not a multiple of 4.We know such equations will have solutions over the set of integers only when either both x and y are odd or both are even.
But none of the above case is possible

Case 1 : If both x and y are odd then (x- y) is also even and (x +y ) is also even i.e. both are multiple of 2
Which implies that Left Hand Side is a multiple of 4 but right hand side is not .Hence no solution is possible in case both are odd.
So clearly both factors on the Left Hand Side cannot be odd

Case 2 : If both x and y are even then (x- y) is also even and (x +y ) is also even i.e. both are multiple of 2
Which implies that Left Hand Side is a multiple of 4 but right hand side is not .Hence no solution is possible in case both are even.
So clearly both factors on the Left Hand Side cannot be even

Answer: Zero

Generalisation: Thus every number of the form 4k + 2 (where k is any integer ) can never be written as difference of perfect squares.

Questions for Practice:

1. Find the number of positive integer solutions of equation x2 - y2 = 1098 ?
Answer : Zero

2. Find the number of positive integer solutions of equation x2 - y2 = 3462 ?
Answer : Zero

3. Find the number of positive integer solutions of equation x2 - y2 = 3782 ?
Answer : Zero

4. Find the number of positive integer solutions of equation x2 - y2 = 84546 ?
Answer : Zero

5. Find the number of positive integer solutions of equation x2 - y2 = 1213514 ?
Answer : Zero

CASE 3. Even Number which is a multiple of 4 written as difference of two perfect squares

Example : Find the number of positive integer solutions of equation x2 - y2 = 56?
Sol : We can write given equation as

(x- y)(x +y )= 56 (1)

Now we want x and y both to be integers and we are given an even number which is a multiple of 4 on the right hand side of equation .We know such equations will have solutions over the set of integers only when either both x and y are odd or both are even.
So clearly both factors will be even

Let us take (x- y) =2p
(x + y)= 2q

So finally putting these in (1) we get
4 p q = 56
p q = 14

So our question reduces to writing 14 as a product of two factors

For finding factors of any number we decompose that number into prime factors
14 = 21. 71
Factors of 2 are 20, 21 (2 in number)
Factors of 7 are 70, 71 (2 in number)

Thus total factors of 14 are obtained by multiplying the factors of 2 and 7 respectively

(i.e. 2070=1 , 2071= 7, 2170=2 , 2171= 14)
Thus total no of factors of 14 are 4 .
So clearly there are 4 ways we can write 36 as a product of two factors

14 = 1 x 14
14 = 2 x 7
Answer: 2

GENERALIZATION
So in such cases we can generalize no of ways in which we can write a given number as a product of two factors is : (No of factors on the right hand side of given after dividing by 4) /2.

Questions for Practise

1. Find the number of positive integer solutions of equation x2 - y2 = 67500 ?
Answer : 10

2. Find the number of positive integer solutions of equation x2 - y2 = 588 ?
Answer : 3

3. Find the number of positive integer solutions of equation x2 - y2 =10780 ?
Answer : 6

4. Find the number of positive integer solutions of equation x2 - y2 = 168 ?
Answer : 4

5. Find the number of positive integer solutions of equation x2 - y2 =720 ?
Answer : 9

CASE 4. Perfect square written as difference of perfect squares

Example : Find the number of positive integer solutions of equation x2 - y2 = 144?
Sol : We can write given equation as

(x- y)(x +y )= 144 (1)

Now we want x and y both to be integers and we are given an even number which is a multiple of 4 on the right hand side of equation .We know such equations will have solutions over the set of integers only when either both x and y are odd or both are even.

So clearly both factors will be even

Let us take (x- y) =2p
(x + y)= 2q
So finally putting these in (1) we get
4 p q = 144
p q = 36

So our question reduces to writing 36 as a product of two factors

For finding factors of any number we decompose that number into prime factors
36 = 22. 32
Factors of 22 are 20, 21 , 22 (3 in number)
Factors of 32 are 30, 31, 32 (3 in number)

Thus total factors of 36 are obtained by multiplying the factors of 22 and 32 respectively

(i.e. 2030=1 , 2031=3, 2032=9 , 2130=2, 2131=6 , 2132=18, 2230=4 , 2231=12, 2232=36)

Thus total no of factors of 36 are 3 X 3 =9 .(Also note factors of perfect square are always odd )

Note : Both the factors cannot be 6 because if both (x- y)= 6 and (x +y )=6 Then x = 6 and y= 0 which is not possible as we are talking of positive integers. Since we cannot take both the factors 6 therefore remaining 8 factors can be written in 8/2 = 4 ways as a product of two factors.

So clearly there are 4 ways we can write 36 as a product of two factors
36 = 1 x 36
36 = 2 x 18
36 = 3 x 6
36 = 4 x 9

GENERALIZATION:
So in such cases we can generalize no of ways in which we can write a given number as a product of two factors is:

{(No of factors on the right hand side of given after dividing by 4) - 1 }/2.

Questions for Practice

1. Find the number of positive integer solutions of equation x2 - y2 = 900 ?
Answer : 4

2. Find the number of positive integer solutions of equation x2 - y2 = 225 ?
Answer : 4

3. Find the number of positive integer solutions of equation x2 - y2 =324 ?
Answer : 2

4. Find the number of positive integer solutions of equation x2 - y2 = 122500?
Answer :7

5. Find the number of positive integer solutions of equation x2 - y2 =19600 ?
Answer : 13

-Wordpandit

  • 5 Likes   5Comments
  • @amanbharti. 7d.
  • @psycho.munna @harshcat91 how u are getting 10 for x^2.... 41m.
Happy Diwali! 
  5 Comments
micflic23
@micflic23 8

@harshcat91 how r u getting 10 for x^2-y^2 =1215 as 10

anuhbti
Pagal AJ @anuhbti 19
@harshcat91

bhai how to approach

 x2 - y2 = 225 

with the formula

(No of factors on the right hand side of given after dividing by 4) - 1 }/2


(as 225 is not divisible by 4) ?

dazzysen
sonal kanchan @dazzysen 79

@psycho.munna @harshcat91  how u are getting  10 for  x^2-y^2= 1215?                                  factors will be 6*2/2   =6( 3^5* 5). can u tell me where m making the mistake?

50m ago 938 CAT Quant CAT

Permutations & Combinations - Questions & Discussions

.Can someone help me out with the following problems with some clear and simple approcah to these qustions 4 balls ar...

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1) IxI+IyI+IzI=15- Total no. of integral solutions?

2) xyz=10^6- Total no. of natural no. solutions?

Can someone explain the approach to such questions please?

  • 5Comments
  • #. 13h.
  • 1) 902. Ans = 4k^2 +2.where k =15 2) Take x, y, z as 2^.... 50m.

57m ago 38 CAT

Official Thread for Maharashtra MBA/MMS CET-2015

LET US ADD MORE PEOPLE TO IT. Let's start discussing questions on MHCET -Verbal Reasoning, Visual Reasoning, Quant, P...

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kisi ke pass cet mock test papers hai kya pdf?..ims,cetking,cl,testfunda..if yes then plz share..

i have time papers last yr..if you want then mail me

  • 3 Likes   11Comments
  • can you please mail me... suyashsshinde@gmail.com. 57m.
  11 Comments
extremist1
yash shinde @extremist1

can you please mail me... suyashsshinde@gmail.com

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Register for the exam on Day 1 of the booking period and get a centre 350 kms from my place!!! i.e. second preference city!! What logic is used in this random allocation, yaar!! Seems like a broken logic :I

  • 4Comments
  • #. 1d.
  • @sunilsabapathy no buddy. I dont think you can request a .... 58m.
sunilsabapathy
sunil sabapathy @sunilsabapathy

Even I got a center 500 km away :). Is there any way to request for a change of test center ?

Sunilbaffna
Nobody is anybody without some(buddies) @Sunilbaffna 60

@sunilsabapathy no buddy. I dont think you can request a change in CAT test centre for yourself. It is given only in extreme cases like medical constraints etc. .

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8 people answered this question.
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1h ago 331 CAT

CAT 2014 Preparation

Hello all, I am starting the preparation for CAT 2014, which is less than an year for now. I am a BE graduate with 2....

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Hi guys, can you please suggest me the best mock test series for CAT 2014.. 

  • 7Comments
  • Mera mobile keyboard bhuka tha. Option word khaa gaya sor.... 4d.
  • I find time somewhat easier compared to CL mocks. Will it.... 1h.
  7 Comments
abd7
barfi . @abd7 287

Mera mobile keyboard bhuka tha. Option word khaa gaya sorry ^

Mudhabir
Mudhabir Ahmed @Mudhabir 1

I find time somewhat easier compared to CL mocks. Will it be good for me to enroll for an IMS test series?? 

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Hi Puys.... QADI 41

                 VALR 34

                  Total  75

 I know it's pretty low score but what would be my percentile???

  • maybe around 85....not sure. 9h.
  • I checked on CL percentile predictor. It was 90... 1h.
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Hi All,

  I  have enrolled for AIMCATs .In the new format my percentile is ranging from 35 to 70. Not able to attempt more number of questions .On an average 20 to 25 questions overall I could able to solve in mocks.Most of the time DI & LR questions .I have skipped RCs every time.

 Please suggest me some tips and strategies to improve the number of attempts .

 My CAT is on 22nd Nov.

Thanks

CAT '13 : 80.82 

3h ago 64 CAT

cat notification 2014....out!!!!!

check it outhttp://handakafunda.com/cat-2014-exam-dates-notification-important-details/

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6h ago 7 CAT

[2015-17] K J Somaiya aka SIMSR, Mumbai Admission related queries

*Qualifying Exam -** *CAT 2014, XAT 2015, CMAT 2014 (Sept), CMAT 2015 (Feb), GMAT(last 2 years) for NRI *This is the...

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For the year 2014, What was the cutoff  ??

  • CAT cutoff was around 90 percentile and the CMAT cutoff w.... 15h.
  • CAT Cutoff for 2014 admissions was 88.17% and CMAT cutoff.... 6h.
postbox77
Postbox 77 @postbox77 15

CAT cutoff was around 90 percentile and the CMAT cutoff was less than 3000 rank

venkat89
Venkat Akella @venkat89 2.8 k

CAT Cutoff for 2014 admissions was 88.17% and CMAT cutoff was less than 3000 rank.

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Business Article Writing Challenge | Facebook
The competition provides an opportunity to write on one of the finest business blogs in India. In addition to this, selected articles will also be featured in the third edition of Sparks! Magazine, the monthly business magazine of the website. Prizes: pkart Voucher First Prize: Rs. 2500 Flipkart Voucher Second Prize: Rs.

Facebook

  • sir,my dob is 15/12/1989 nd i failed in 7 std,completed m.... 7h.
pratikumar15
Pratik Kumar @pratikumar15

sir,my dob is 15/12/1989 nd i failed in 7 std,completed my engg frm pune university in 5 years.will i'll b selected for cat evenif i score good percentile in cat and 1 year gap for prep. of cat.will iims will accept me or not.if not tell me the other alternative.please.should i focus cat or other management exams.tell me the path.even my engg aggregate is 53.33% bt degree % is 60.66% which one will be accepted degree% or aggregate% by any management institute. 

9h ago 2.7k CAT Verbal CAT

Sentence Correction, Fill in the blanks, Vocabulary

Choose the option in which the usage of the word is incorrect or inappropriate.In each question, the word at the top ...

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Q.  Arrange the sentences A,  B, C and      D to form a logical sequence  &              to construct a coherent paragraph.

A. It must be viewed, as some new epidemic would be viewed, as a common peril to be met by concerted action.

B. If we are to think wisely about the new problems raised by nuclear weapons, we must learn to  view the whole matter in a quite different way.

C. These conflicts are so virulent and so passionate that they produce a wide spread inability to understand even very obvious matters.

. D. It is a profound misfortune that the whole question of nuclear warfare has become entangled in the  age-old conflicts of power politics.

https://www.youtube.com/channel/UCwA7FhAHLqqmjlVjhiwG8GQ

  • DCBA. 11h.
  • Dcba. 9h.
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Took this today..Weirdest QA section ever..VA was Okaiish

OA - 128 (56/46/10) QA-54 (22/19/3) VA-74(34/27/7)..Expected %ile...?

  • 99.47. 9h.
Don't watch the clock. Do what it does. keep goin'