Official Quant thread for CAT 2013

@pyashraj said:
@mohitjainShl be Option E: 7, 12 N 17..Let the Amt of Vessels be x-5 kg, x kg n x+5 kg receptively..n let c% be the conc in each Vessel..Given, c/100*(x-5 + x + x + 5)= 5.4, or, cx = 180...(i)Again, c -(x-5) = 8, or, c-x=3, or, c = x+3...(ii)Thus, x^2 + 3x - 180 = 0=>(x+15)(x-12) = 0Thus, x will be 12 kg..Thus, V1= 7 kg, V2= 12 kg n V3= 17 kg..
yes its e..
@mohitjain said:
@saurav205@mailtoankit@joyjitpalThe quantities of a sugar solution in three different vessels form an arithmetic progression with a common difference of 5 kg. All the three sugar solutions have the same concentration. The difference between the numerical values of the concentration of sugar in the sugar solution and the quantity of sugar solution in the vessel having the least quantity is 8. The total quantity of sugar in the three vessels is 5.4 kg. What are the quantities of sugar solution in the three vessels? a 5 kg, 10 kg and 15 kg b 6 kg, 11 kg and 16 kg c 7 kg, 11 kg and 18 kg d 8 kg, 13 kg and 18 kg e 7 kg, 12 kg and 17 kg
did it by options.
e.
see.. if C% is the conc .
then c/100*(7+12+17)=5.4
c=15
c-7 (the least quantity)=8.
15-7= 8only.

for other options..
a. C=18 and 18-5 = 13..not 8
b. C=180/11 and (180/11)-6 is not 8.
c. C=15 ...and 15-6=9 again wrong
d C= 180/13 ...(180/13)-8 cannot be 8.
only e fits.

@ChirpiBird said:
did it by options. e.see.. if C% is the conc .then c/100*(7+12+17)=5.4c=15c-7 (the least quantity)=8.15-7= 8only.for other options..a. C=18 and 18-5 = 13..not 8b. C=180/11 and (180/11)-6 is not 8.c. C=15 ...and 15-6=9 again wrongd C= 180/13 ...(180/13)-8 cannot be 8.only e fits.
i guess doin by options wud hav been a bettr choice rather den solvin equations..i did it by equations nd it took me a lot of tym..
@Logrhythm said:
Chalo mein hi question daal deta hun...If x^4*y^2 = 400 and x and y are positive, then the least value of 5x + 8y isA)40 B)30 c)25 D)None of these
(x^4)(y^2) = 400 => y = 20/(x^2)

Now 5x+8y = 5x + 8[ 20/(x^2)]
= 5x + 160 /(x^2)

To find min, diff and equate to 0
=> 5 + (-2) (160) (x^-3) = 0
=> x = 4
=> y = 5

=> 5x + 8y = 20 + 10
=30
How many integer values of x & y satisfy the expression 4x+7y=3 where lxl
@mailtoankit said:
323 ?323 = 17*1920^2004 + 16^2004 - 3^2004 - 1 mod 17 = 020^2004 + 16^2004 - 3^2004 - 1 mod 19 = 0
bhai last two expressions explain karna
seven boxes numbered 1 to 7 are arranged in a row . each is to be filled by either by black or blue ball such that no two adjacent boxes contain blue ball. in how many ways these boxes be filled ?23
33
34
32
seven boxes numbered 1 to 7 are arranged in a row . each is to be filled by either by black or blue ball such that no two adjacent boxes contain blue ball. in how many ways these boxes be filled ?23
33
34
32
@MANJULNEOGI said:
How many integer values of x & y satisfy the expression 4x+7y=3 where lxl
392
@MANJULNEOGI said:
How many integer values of x & y satisfy the expression 4x+7y=3 where lxl
is 285 the answer bro?
@raopradeep said:
seven boxes numbered 1 to 7 are arranged in a row . each is to be filled by either by black or blue ball such that no two adjacent boxes contain blue ball. in how many ways these boxes be filled ?23333432
CASE 1 : 1st box is black
then arrangement can be
B __ B __ B__B
each box can now be filled in 2 ways: black or blue
total ways possible = 2.2.2 = 8

CASE 2: 2nd box black
then arrangement can be
__ B __ B __ B __
possible ways = 2.2.2.2 = 16
total ways = 8 +16 = 24

Now note that there will be an arrangement wer all are black in both cases so effectively we have counted it twice and so must subtract 1
thus answer is 24 -1
=23
@surajmenonv no answer is 34 iam posting soln in a minute

@raopradeep said:
seven boxes numbered 1 to 7 are arranged in a row . each is to be filled by either by black or blue ball such that no two adjacent boxes contain blue ball. in how many ways these boxes be filled ?23333432
@mailtoankit , @saurav205 @ChirpiBird @catahead @Logrhythm @surajmenonv @abhishekhenry

take cases

black blue cases
7 0 8c0 = 1
6 1 7c1 = 7
5 2 6c2 = 15
4 3 5c3 =10
3 4 4c4 =1
total =34 ways
suppose 4 black 3 blue balls this is the way to obtain
_ bk _bk_bk_bk_ ,where _ indicates blue ball and "bk" as black ball
so we get 5c3 ways to arrange 3 blue balls similarly all others
hope it helps
How many words can be formed of the letters in the word RAINBOW, so that the vowels may occupy only even positions?

I solved it in this way: R_N_B_W_
These four positions are even positions which can be occupied by 3 vowels.
So Ans is 4P3 * 4!

But the solution given in the book is:
_A_I_O_
4! * 3!

While I have no beef with the solution given in the book, I don't understand why my approach is incorrect !
@Shrutim90 said:
How many words can be formed of the letters in the word RAINBOW, so that the vowels may occupy only even positions?I solved it in this way: R_N_B_W_These four positions are even positions which can be occupied by 3 vowels.So Ans is 4P3 * 4!But the solution given in the book is:_A_I_O_4! * 3!While I have no beef with the solution given in the book, I don't understand why my approach is incorrect !
R_N_B_W These three positions are even positions which can be occupied by 3 vowels.So Ans is 3!* 4!

Is n^2+3n+5 divisible by 121?....plz share the approach

@maroof10 said:
Is n^2+3n+5 divisible by 121?....plz share the approach
wats the whole question?
Because clearly it is not for n = 1, 2,3,4,5, etc...
@surajmenonv said:
is 285 the answer bro?
approach?
@maroof10

I thnk it will never be divisible by 12..

Here, n^2 + 3n + 5 => (n^2 + 2^2 + 2*2*n) - (n-1)

=>(n+2)^2 - (n-1)

Now, when n is odd...(n+2)^2 is odd and (n-1) is even..Thus, there difference will always give odd..

Again, when n is even..(n+2)^2 is even and (n-1) is odd..Thus, there difference will always give odd..

Since, in both the cases its odd..It wnt be divisible by 12..Hwever..I thnk n is always a +ve Integers..That's an assumption i am taking..
@pyashraj said:
@maroof10I thnk it will never be divisible by 12..Here, n^2 + 3n + 5 => (n^2 + 2^2 + 2*2*n) - (n-1)=>(n+2)^2 - (n-1)Now, when n is odd...(n+2)^2 is odd and (n-1) is even..Thus, there difference will always give odd..Again, when n is even..(n+2)^2 is even and (n-1) is odd..Thus, there difference will always give odd..Since, in both the cases its odd..It wnt be divisible by 12..Hwever..I thnk n is always a +ve Integers..That's an assumption i am taking..
i think the question says divisible by 121