link to previous thread :-
http://www.pagalguy.com/forum/quantitative-questions-and-answers/71846-official-quant-thread-cat-2011-a.html
Please use the posts for discussions as judiciously as you can.
Try to stick ...
31
31
Official Quant Thread for CAT 2011 [Part 7]
Quantitative
Add more users
Please continue here with all the quant queries and their discussions.
link to previous thread :-
http://www.pagalguy.com/forum/quantitative-questions-and-answers/71846-official-quant-thread-cat-2011-a.html
Please use the posts for discussions as judiciously as you can.
Try to stick ...
link to previous thread :-
http://www.pagalguy.com/forum/quantitative-questions-and-answers/71846-official-quant-thread-cat-2011-a.html
Please use the posts for discussions as judiciously as you can.
Try to stick ...
E(17)=16
How?????
How?????
At the end of the year 2000, Karan started a business with 50 horses. After that, every year he increased his stock (horses) by x% at the beginning of the year and sold y% of the horses at the end of the year, where x > 0 and y > 0. If Karan had 50 horses at the end of the year 2005, after ma...
4.Let P = {2, 3, 4,- - - - -, 100} and Q = {101, 102, 103, - - - -, 200}. How many elements of Q are there such that they do not have any element of P as a factor?
u r a genius bro!!
IIM A is waiting for u..
Thanks^infinity..
IIM A is waiting for u..
Thanks^infinity..
repeating decimal with cyclicity of 6 i gues..
Option b ??
@vikas bhai : Aap apne break mein bhi coffee peete huye cup ka volume aur milk ka conc. nikaalte hoge .. Sab pata hai mujhe .. :D
@vikas bhai : Aap apne break mein bhi coffee peete huye cup ka volume aur milk ka conc. nikaalte hoge .. Sab pata hai mujhe .. :D
2
bakar.............abe yaar aaj kal so bahut raha hoon ..10 ghante sota hoon 10 ghante ofc..
122. A, B and C run around a circular track of length 750m at speeds of 3
m/sec, 6 m/sec and 18 m/sec respectively. If all three start from the same
point, simultaneously and run in the same direc...
122. A, B and C run around a circular track of length 750m at speeds of 3
m/sec, 6 m/sec and 18 m/sec respectively. If all three start from the same
point, simultaneously and run in the same direc...
Q. 22/7 is a
a) Non-terminating, non-repeating decimal.
b) Non-terminating, repeating decimal.
c) Terminating decimal.
d) Not a rational number.
@PK bhai: Kal se break par hi tha. Abhi just aya hoon.
a) Non-terminating, non-repeating decimal.
b) Non-terminating, repeating decimal.
c) Terminating decimal.
d) Not a rational number.
@PK bhai: Kal se break par hi tha. Abhi just aya hoon.
Padhne ka mood nahi hai yaar.. timepass kar rahe hain bas..
Aap bhi jaao .. thoda break-sheak lo padhai se ..
Aap bhi jaao .. thoda break-sheak lo padhai se ..
1
One more simpler way to do this.. rather than differentiation..
y = 1-(9/(x2+6x+16))
to minimize y gotto maximize the term after the '-' sign or gotto minimize the term (x2+6x+16) = (x+3)^2 + 7.. so minimum value of 7 at x=-3
subsitue in the main eqn to get 1-(9/7) = -2/7
@Chin2 bhai ...
y = 1-(9/(x2+6x+16))
to minimize y gotto maximize the term after the '-' sign or gotto minimize the term (x2+6x+16) = (x+3)^2 + 7.. so minimum value of 7 at x=-3
subsitue in the main eqn to get 1-(9/7) = -2/7
@Chin2 bhai ...
6
?
Assuming the term on the RHS is 2^(log16(x) +2)
log81(x)=log3(x)/log3(81)=log3(x)/4
243^log81(x)=243^log3(x)/4=3^5/4.log3(x)=3^log3(x)^5/4=x^5/4
similarly,
log16(x)=log2(x)/4
2^log(16)x=2^log(x^1/4)=x^1/4
Solving,
x^5/4-2x=4.x^1/4-8
let x^1/4=t
t^5-2t^4=4t-8
t^5-2t...
log81(x)=log3(x)/log3(81)=log3(x)/4
243^log81(x)=243^log3(x)/4=3^5/4.log3(x)=3^log3(x)^5/4=x^5/4
similarly,
log16(x)=log2(x)/4
2^log(16)x=2^log(x^1/4)=x^1/4
Solving,
x^5/4-2x=4.x^1/4-8
let x^1/4=t
t^5-2t^4=4t-8
t^5-2t...
6
a/2+a/2+2b/3+2b/3+2b/3+3c/4+3c/4+3c/4+3c/4+(4d/7+4d/7..7 times)=48
Since all the terms now are interchangeable, put all of them as equal to k.
k+k+k.. 16 times=48
16k=48,k=3
a/2=3,a=6
2b/3=3, b=9/2
3c/4=3,c=4
4d/7=3,d=21/4
Value of the expression is 36.729/8.256.(21/4)^7.
Since all the terms now are interchangeable, put all of them as equal to k.
k+k+k.. 16 times=48
16k=48,k=3
a/2=3,a=6
2b/3=3, b=9/2
3c/4=3,c=4
4d/7=3,d=21/4
Value of the expression is 36.729/8.256.(21/4)^7.
2
use the concept if hcf(a,b)=1
the hcf (a-b,b)=1
on successively doing this
you will get hcf(3n,3n+1)=1
which is always true for consecutive no.
hence it will satisfy for all n.
the hcf (a-b,b)=1
on successively doing this
you will get hcf(3n,3n+1)=1
which is always true for consecutive no.
hence it will satisfy for all n.
1
querry:
Find the attachment and plz exp how 10 will be left after first removal.... and how it is calculated 2^11, ie.. 11 removal steps would be needed..
![]()
Find the attachment and plz exp how 10 will be left after first removal.... and how it is calculated 2^11, ie.. 11 removal steps would be needed..
If a, b, c and d are positive real numbers such that a + 2b + 3c + 4d = 48, then the maximum value of a^2*b^3*c^4*d^7 is?????
Same question and solution posted by quantphobic about 10-15 pages back..
1
if a number divides 6n+1 and 15n+2, it also divides 15n+2 - 6n+1 i.e. 9n+1.
It also divides 9n+1 - 6n+1 i.e. 3n. Since 6n+1 itself is 3n+1, so the number has to divide 3n and 3n+1, which is not possible. Hence no such number exists.
So, for all 99 natural numbers from 1 to 99, 6n+1 and 15...
It also divides 9n+1 - 6n+1 i.e. 3n. Since 6n+1 itself is 3n+1, so the number has to divide 3n and 3n+1, which is not possible. Hence no such number exists.
So, for all 99 natural numbers from 1 to 99, 6n+1 and 15...
Find the sum of all the real values of 'x' that satisfy the equation
Please solve the prob...in detail
Please solve the prob...in detail
for how many values of n<100 does (6n+1) & (15n+2) are relatively prime??
xane bhai pi/3 hai kya??
(x-4)(x+2)(X+3)(X-1)<0 so either 3 negative or 1 negative,
But for integers on no. line Only 1 negative is possible and it is at X=2 and X=3 so 2 values.
But for integers on no. line Only 1 negative is possible and it is at X=2 and X=3 so 2 values.
From a circular sheet of paper of radius a, a sector with a central angle is cut out and folded in to the shape of a conical funnel. The volume of this funnel is max when the angle of the sector equals x. Find x (in radians) ?
is it 1/2??
Overcouting hi5blast bhai..
When you pick 8 chocolates, say, leaving out chocolate a9 and give it to one who has a1.
In one more case, you leave out a1 and give it one who has a9. So, a repeat case here..
Check this..
http://www.pagalguy.com/forum/quantitative-questions-and-answers/72...
When you pick 8 chocolates, say, leaving out chocolate a9 and give it to one who has a1.
In one more case, you leave out a1 and give it one who has a9. So, a repeat case here..
Check this..
http://www.pagalguy.com/forum/quantitative-questions-and-answers/72...
3
in case of n=24, at least 2 combinations would be possible..ie 24*24 and 16*36..but we want unique combo..
that is possible by a prime number..so 23 is ans..
aur 'n' diamonds nahi diya hai..only n necklaces bola hain..
that is possible by a prime number..so 23 is ans..
aur 'n' diamonds nahi diya hai..only n necklaces bola hain..
1
2 solutions
my ans is -2/7..when x = -3
is it -2/7????????
@grm_bh
but we have been told that there are n neckles and each has n diamonds so it has to be n^2. ye distinct wala samja nahi. Can u plz elaborate??
@grm_bh
but we have been told that there are n neckles and each has n diamonds so it has to be n^2. ye distinct wala samja nahi. Can u plz elaborate??
1
agar 24 liya toh..
24*24=576=16*36=....so on...
distinct nahi ho paayega..
24*24=576=16*36=....so on...
distinct nahi ho paayega..
2
first select 1 choclate each for 8 ppl
9C8*8!..
remaing one choclacte can be gicen to any of 8 bacche..
so
72*8!
9C8*8!..
remaing one choclacte can be gicen to any of 8 bacche..
so
72*8!
1
Find the number of integral values of x, that satisfy the inequality (x^2-2x-(x^2+2x-3)<0
0
1
2
3
0
1
2
3
make a triangle,angle A=30 B=60,c=90
ac=250 sq rt 3, ab=500
time taken frm b to c=250/50=5 hrs
rahim shd reach b4 8:00+5hrs-15min=12:45 pm
thus shd leave b4 12:45-6:11=6:34
hence B
ac=250 sq rt 3, ab=500
time taken frm b to c=250/50=5 hrs
rahim shd reach b4 8:00+5hrs-15min=12:45 pm
thus shd leave b4 12:45-6:11=6:34
hence B
1
let speed of a be a,
b.....b
c..........c
now
in total b has covered 32 meter to over take C in 224 meter..
since at one pont they were at same point..
that means..
12/b-c=12/a-b=24/a-c
2b-2c=2a-2b=a-c
OR
a=k+2
b=k+1
C=k
noW
so they must have travelled fo...
b.....b
c..........c
now
in total b has covered 32 meter to over take C in 224 meter..
since at one pont they were at same point..
that means..
12/b-c=12/a-b=24/a-c
2b-2c=2a-2b=a-c
OR
a=k+2
b=k+1
C=k
noW
so they must have travelled fo...
1
Vikas bhai Prime no. hi kyoun???
24 kyo nahi????
24 kyo nahi????
People, could you please help me with the solutions for the below mentioned questions. Thanks in advance
Q1) Find the volume of the largest right circular cone that can be inscribed in a cube of edge length 1.
a) (2*pi)/9 b) (2*pi)/(9*(3^0.5)) c) pi/9 d) pi/3
Ans: b
Q2) For how many numbers, all their factors add up to 48?
a) 0 b) 1 c) 2 d) 3
Q3) P = {1, 3, 5, 7, 9, 11, 13, , 99, 111, } is a set of all natural numbers containing odd digits only. S is the sum of reciprocals of all the numbers in set P. Which of the following is definitely false?
a) S is greater than 4
b) S is less than 5
c) S is greater than 7
d) S is less than 8
Ans: c
Q4) A pan-digital sum is the sum which uses all the digits from 1-9 exactly once. For example: 128 + 439 = 567 is one such case.
If AB + CD + EF = GHI represents a pan-digital sum where each letter represents a different digit from 1-9, then what is the minimum value of G + H + I?
a) 9 b) 18 c) 27 d) None of these
Ans: a)
Q5) In triangle ABC, P lies on AC and Q lies on BC. A circle with center M is inscribed in APQB and another circle with center N is inscribed in PQC. Find the measure of PMQ + PNQ.
a) 90 b) 180 c) 270 d) data insufficient
Ans: c
More Questions Coming Soon
Q1) Find the volume of the largest right circular cone that can be inscribed in a cube of edge length 1.
a) (2*pi)/9 b) (2*pi)/(9*(3^0.5)) c) pi/9 d) pi/3
Ans: b
Q2) For how many numbers, all their factors add up to 48?
a) 0 b) 1 c) 2 d) 3
Q3) P = {1, 3, 5, 7, 9, 11, 13, , 99, 111, } is a set of all natural numbers containing odd digits only. S is the sum of reciprocals of all the numbers in set P. Which of the following is definitely false?
a) S is greater than 4
b) S is less than 5
c) S is greater than 7
d) S is less than 8
Ans: c
Q4) A pan-digital sum is the sum which uses all the digits from 1-9 exactly once. For example: 128 + 439 = 567 is one such case.
If AB + CD + EF = GHI represents a pan-digital sum where each letter represents a different digit from 1-9, then what is the minimum value of G + H + I?
a) 9 b) 18 c) 27 d) None of these
Ans: a)
Q5) In triangle ABC, P lies on AC and Q lies on BC. A circle with center M is inscribed in APQB and another circle with center N is inscribed in PQC. Find the measure of PMQ + PNQ.
a) 90 b) 180 c) 270 d) data insufficient
Ans: c
More Questions Coming Soon
My take is 1/2.
Equation (2) - equation (1)
=> 2x+y+z = 10
And putting a=1 and r=5 in equation (3)
=> x+by+cz = 5
=> 2x+2by+2cz = 10
We will get infinite solutions if 2b=1 and 2c=1
This is because, to solve 3 variable problem; we need 3 distinct equations.
But, with b = 1/...
Equation (2) - equation (1)
=> 2x+y+z = 10
And putting a=1 and r=5 in equation (3)
=> x+by+cz = 5
=> 2x+2by+2cz = 10
We will get infinite solutions if 2b=1 and 2c=1
This is because, to solve 3 variable problem; we need 3 distinct equations.
But, with b = 1/...
3
What is the minimum value of ?
koi ye bhi kardo.....
:banghead::banghead::banghead:
:banghead::banghead::banghead:
If we have to consider sum of digits, then no such number exists.
All two digit numbers divisible by 11 have same digits i.e. they are 11, 22, 33, ..
Say, number is aa.
So, number = 10a + a = 11a
But it is given number = 11*(a+a) = 22a
=> 11a = 22a => a = 0
=> Not possible.
I...
All two digit numbers divisible by 11 have same digits i.e. they are 11, 22, 33, ..
Say, number is aa.
So, number = 10a + a = 11a
But it is given number = 11*(a+a) = 22a
=> 11a = 22a => a = 0
=> Not possible.
I...
1
Find the volume in cu cm of the largest right cone that can be cut out of a cuboid of dimensions 9cm,7cm and 4 cm
189p
108p
49/6p
49/3p
P.S P stands for Pie
can somebiody pl explain the approach a bit
189p
108p
49/6p
49/3p
P.S P stands for Pie
can somebiody pl explain the approach a bit
the question never states its a positive two digit number so the negative aspect doesnt matters.
reposting the question
consider the system of linear equations
2x+3y+4z=16
4x+4y+5z=26
ax+by+cz=r
for r=5 and a=1 then the system of linear equation will have infinite solution if c=?
3/2
1
1/2
0
need help with this question.plz explain the approach as well
consider the system of linear equations
2x+3y+4z=16
4x+4y+5z=26
ax+by+cz=r
for r=5 and a=1 then the system of linear equation will have infinite solution if c=?
3/2
1
1/2
0
need help with this question.plz explain the approach as well
answer is 200 and solution is already given by ishant in above thread.
this is exactly how i tried it, but acc to the result, the number comes out to be negative...:O
Three people A, B and C start moving around a circular track of 100 m simultaneously with speeds of 2 m/s, x m/s and y m/s respectively in clock wise direction. They meet for the first time after t seconds and they meet for the first time at their common starting point after 3t seconds. Which of ...
Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is kno...
My take is 5.
We need to mizimize the 'maximum number of boxes with same number of items'
So, we should try to as much distinct number of items as possible.
So, we will go on placing 130, 131, ..., 155, 130, 131, ... so on.
So, we have 26 distinct numbers from 130 to 155.
We can fi...
We need to mizimize the 'maximum number of boxes with same number of items'
So, we should try to as much distinct number of items as possible.
So, we will go on placing 130, 131, ..., 155, 130, 131, ... so on.
So, we have 26 distinct numbers from 130 to 155.
We can fi...
1
is the ans 5 boxes?
1
We need to select a prime p, such that , 500<600.
So, p is 23.
So, p is 23.
1
Unless means 'if not'. So, in plain English, the statement is 'If A is not selected, B or C is selected'.
i.e. ~A->(B or C)
and of course, it's contrapositive, as you wrote
~(B or C)=>A
i.e. ~A->(B or C)
and of course, it's contrapositive, as you wrote
~(B or C)=>A
2
as far as i think ,
structure =>unless a , b.
this means either of them is happening i.e. a and b aren't happening together. i.e. either a or b. or we can say
Not A => (B or C)
=> ~(B or C) => A
structure =>unless a , b.
this means either of them is happening i.e. a and b aren't happening together. i.e. either a or b. or we can say
Not A => (B or C)
=> ~(B or C) => A
1
as the data is sufficient & we can uniquely determine it ,it has to be a square of prime no
here 23*23=569
hence 23
here 23*23=569
hence 23
1
when AB=BC = sqrt50, then max value is obtained as 200..
.There are 120 boxes, each of which can contain any number of tennis balls which are at least 130 and at most 155. The maximum number of boxes containing the same number of tennis balls is at least
My take is 36*8!
Chocolates will be given as 2, 1, 1, ... 8 times 1.
So, pair of 2 chocolates can be made in 9C2 ways. With this pair and 7 other chocolates, we will have 8 things to distribute to 8 people, which can be done in 8! ways.
So, 9C2*8! ways = 36*8! ways
Chocolates will be given as 2, 1, 1, ... 8 times 1.
So, pair of 2 chocolates can be made in 9C2 ways. With this pair and 7 other chocolates, we will have 8 things to distribute to 8 people, which can be done in 8! ways.
So, 9C2*8! ways = 36*8! ways
3
the problem is in the bold part it shud only be 12*2 as far as i believe via the wordings f questions.
m getting 100 by using cauchy schwarz
THough its silly doubt but doesn't matter if its before 14 Nov
In LR in selections a statement "unless A is selected ,B or C is selected "
Isme logical connectives wala funda lagta hei kya means does dis statement implies
=> Not A => (B or C)
=> ~(B or C) => A
Watsay guys?
In LR in selections a statement "unless A is selected ,B or C is selected "
Isme logical connectives wala funda lagta hei kya means does dis statement implies
=> Not A => (B or C)
=> ~(B or C) => A
Watsay guys?