This is the Official CAT 2014 Quantitative preparation group. Solve questions & discuss answers/solutions shortcuts &...
The owner of a shop increases the price of an article by x% and then decreases it by x%. As a result, the price of the article is decreased by Rs 625. After this, he again increased the price of the article by y% and then decreased it by y% and the price of the article became Rs 3500. If the original price of the article is Rs 4225, then
8m ago CAT
AIMCAT 1505-New: Scores And Discussion ~ (Non-Invigilated: Oct 21-24, 2014)TIME's mock CAT
QA - 60 (21C/24A)
VA - 45 ( 15C/15A)
Overall - 105 (36C/39A)
This is what happens when you get stuck in the quant (pathetic no. of attempts)and end up attempting the LR's only...
10m ago 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 ...
Simcat 12 unproctored qa 75 va 105 oa 180.
@Darknight123 - hw many LR sets did u do in this? were u able to do the University LR?
Just 1 set of lr.agar woh easy aaye toh it was a 140+ va paper.
Well let just say my marks were not bad, they were depressing.
29m ago CAT Verbal CAT
Official verbal ability thread for CAT 2014Amidst IIFT,NMAT and other exams preparation we have come so far and near to CAT 2014. Not so many Days (Literally) f...
'I can crack CAT'
1h ago CAT
[2014] CL Mock CAT 15 Scores and Discussion (DON'T OPEN UNLESS ATTEMPTED)Discussion related to CL Mock CAT 15.
could anyone tell me how many ppl gave mock 16 on an average and why doesnt cl give the number of ppl registered fr the test?
They don't give that info for unproctered mocks.
They don't give the number because it'll be so low, it'll be fucking embarrassing.
hahhaha.. have you given mock 16? was it easier than cat or actual level?
1h ago CAT
The PaGaLGuY UnderDogs Team 2014Do you love taking up the challenge where you are considered as a person who cannot achieve the pinnacle easily but t...
Happy Diwali to All Puys + UDTians + DTians
UDT'14
It ain't over till I say it is over.
http://www.pagalguy.com/discussions/2014-mock-score-repository-25116679/20106521
ironically we won't have time to celebrate, so here's to not celebrating diwali next year.
1h ago CAT
AIMCAT 1513-New: Scores And Discussion ~ ( Invigilated: Aug 31-Sept 7, 2014 )Slot booking started ATB
Hi Puys.... QADI 41
VALR 34
Total 75
I know it's pretty low score but what would be my percentile???
I checked on CL percentile predictor. It was 90..
lol why would you check aimcat's percentile on CL predictor ?
I think you hav not enrolled for any test series in CL... On checking our percentile for CL mocks, it asks us to enter our AIMCAT scores( for particular test mentioning the test name).
1h ago CAT
CAT 2014 Exam day and slot discussionDiscuss about your date of exam, slot and centre in this thread.
Nov 22, evening slot.. In a remote, largely unknown village near by a unknown town 60 kms from Trichy.... ( I have lived in Trichy for some time, but still the place seems new
So the exact place is some ^@$%@# college, Thollupatti, Thottiyam...
Anybody with me for CAT and the road trip... :P
.Can someone help me out with the following problems with some clear and simple approcah to these qustions 4 balls ar...
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?
1h ago CAT
CAT test taking strategiesIf you are going out shopping do you make plan or list of things to do? Girls if you are planning to do dieting you m...
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
#following - btw i guess u shd post this in a more active thread like udt
2h ago CAT
AIMCAT 1519-New: Scores And Discussion ~ (Non-Invigilated: Oct 20-23, 2014)TIME's mock CAT
Total: 58C/85A = 147
OK this was tougher than expected. Although a totally new mock for me, not having attempted any of its old ones, 147 is way less
DT '14
Be the change you wish to see in the world
http://www.pagalguy.com/discussions/2014-mock-score-repository-25116679/20090363
this would give you your lowest percentile score of the season
@shashwatdgr8 chill bhai!! i know
aise hi bola. I know you are a champ
2h ago CAT
CAREER LAUNCHER PROCTORED,UNPROCTORED MOCK 2014Hey puys n pirls, This forum is meant for detailed discussion of the CL mocks 2014. One can feel free to ask anything...
can I postpone a booked test?
3h ago CAT
Logical ReasoningThe question is followed by two statements X and Y. Answer using the following instructions: Choose 1 if the question...
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
Hey puys, As we all are geared up to prepare ALL NEW CAT 2014, let us refresh our quant concepts bit by bit. All we n...
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
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) ?
@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?
3h ago CAT
Official Thread for Maharashtra MBA/MMS CET-2015LET US ADD MORE PEOPLE TO IT. Let's start discussing questions on MHCET -Verbal Reasoning, Visual Reasoning, Quant, P...
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Hi guys, can you please suggest me the best mock test series for CAT 2014..
Mera mobile keyboard bhuka tha. Option word khaa gaya sorry
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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cat notification 2014....out!!!!!check it outhttp://handakafunda.com/cat-2014-exam-dates-notification-important-details/
Which gud colleges to apply before CAT /which have deadline before CAT?
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CAT Cutoff for 2014 admissions was 88.17% and CMAT cutoff was less than 3000 rank.
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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.
12h ago CAT Verbal CAT
Sentence Correction, Fill in the blanks, VocabularyChoose the option in which the usage of the word is incorrect or inappropriate.In each question, the word at the top ...
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.
Read more at www.englishgrammarlesson.blogspot.in
https://www.youtube.com/channel/UCwA7FhAHLqqmjlVjhiwG8GQhttps://www.youtube.com/channel/UCwA7FhAHLqqmjlVjhiwG8GQ
lol all correct lrs ? nice
Last aimcat I attempted 21 and got 13 wrong in VA itself...imagine..just hope 22nd isn't that kind of day...