p^q is a perfect square as well as a perfect cube, (p&q; are natural nos.), then q must b a multiple of
a.2 b.3 c.6 d.9 e.can't be determined

Waise to 6 hona chahiye par agar p 1 hua to q kuch bhi ho skta hai..
so wl go with cbd

p^q is a perfect square as well as a perfect cube, (p&q; are natural nos.), then q must b a multiple of
a.2 b.3 c.6 d.9 e.can't be determined

Cant be determined,
Check the case of 8^2, it both a square as well as a cube(of 4)
Also check 729 which is 9^3, its both cube and square(of 27)

p^q is a perfect square as well as a perfect cube, (p&q; are natural nos.), then q must b a multiple of
a.2 b.3 c.6 d.9 e.can't be determined

Wonder if it simply means, max value eof x+y and min value of x-y, if so then,

max value of x+y putting x=4&y;=3 is 7 & min value is for x=2&y;=1, ratio 7/1=7

Is that the answer?

minimum value of x-y = -1 and not 1... Please correct me if worng..

A test has 50 qstns....1 mark for correct answer , -1/3 for wrong answer and -1/6 for every unattempted qstn.A student scored 32,Atleast how many qstns can he mark wrong?
a)9 b)12 c)6 d)3

Conceptually samjha do yaar and how to solve these kind of qstns algebraically???

Q55)If 2<4 and 1<3,then find ratio of the upper limit for x+y and lower limit of x-y?
a)6 b)7 c)8 d)4 e)none
What is meaning of upper & lower limit?

in 2 < x < 4
upper limit of x it 4 and lower limit is 2

come to question

upper limit of x+y = upper limit of x + upper limit of y = 4+3 = 7

lower limit of x-y = lower limit of x - upper limit of y = 2-3 = -1

so ratio will be 7 : -1 = 7/-1 = -7

1*1!+2*2!+....+12*12! = 1!*(2-1) + 2!(3-1) + 3!(4-1) + ... + 12!(13-1)

= 2! - 1! + 3*2! - 2! + 4*3! - 3! + ... + 13*12! - 12!

Every term will be cancelled except 13! - 1!

=> 13! - 1! mod 13 = -1 or 12

Hi

How did u find the remainder of 13!-1! mod 13?

Q55)If 2<4 and 1<3,then find ratio of the upper limit for x+y and lower limit of x-y?
a)6 b)7 c)8 d)4 e)none
What is meaning of upper & lower limit?

Upper limit is max value
lower limit is min value
so m getting ans as 7...

Q55)If 2<4 and 1<3,then find ratio of the upper limit for x+y and lower limit of x-y?
a)6 b)7 c)8 d)4 e)none
What is meaning of upper & lower limit?

Wonder if it simply means, max value eof x+y and min value of x-y, if so then,

max value of x+y putting x=4&y;=3 is 7 & min value is for x=2&y;=1, ratio 7/1=7

Is that the answer?

Q55)If 2<4 and 1<3,then find ratio of the upper limit for x+y and lower limit of x-y?
a)6 b)7 c)8 d)4 e)none
What is meaning of upper & lower limit?

Q4)The sum of two numbers is 15 and their geometric mean is 20% lower than their A.M.Find the number
a)11,4 b)12,3 c)13,2 d)10,5 e)9,6

a+b = 15
or a = 15-b

AM = 15/2 = 7.5
GM = 7.5*80/100 = 6

GM = rt(ab) = 6
ab = 36

putting a = 15-b

b(15-b) = 36
15b-b^2 = 36
b^2-15b+36 = 0
(b-12)(b-3) = 0
b = 12, 3

so b = 12, a = 3 or vice versa

so 2 numbers are 3 and 12

why couplw is aa and bb?? if we assume m1 w1 as one couple and m2 w2 as 2nd couple then u r nt taking sm arrangement lyk
m1 w1 m2 w2 x..... 1 arrngement
w1 m1 m2 w2 x... 2 arrangement
bt u r tking both arrangement as 1 .. why so?????

Bhai it means the same... If i take them different... Then total arrangements = 12 * 21 * 2! = 48..

And total = 5! = 120..

Probability = 2/5... I had taken them same to had divided 5! by 2!*2!.

Hope you got it:grin:

1)Find the number of consecutive zeroes immediately after the decimal in 1/(20^37)
(log 2 = 0.3010)
(a) 46 (b) 47 (c) 48 (d) 49

question-take log 20^-37=-37log20=-37(log2+log10)=-37(1.3010)=-48.137

concept - The characteristic (in the logarithm of a number) is one more than the number of zeroes to the right of the decimal in a positive number less than 1

now the decimal should be positive therefore -49 + .693

so the no of zeroes will be 1 less than characteristic no..so ans is 48..

Q4)The sum of two numbers is 15 and their geometric mean is 20% lower than their A.M.Find the number
a)11,4 b)12,3 c)13,2 d)10,5 e)9,6

The nos are 12&3 because the AM of 2 nos whose sum is 15 is 7.5 and 20% lower than 7.5 is 6. Is it not sufficient to just check the answers and see which one gives 6?

couples = aa and bb...

Possibilitites in our favour = abcab, abcba, bacba, bacab, acbab, bcaba, abacb, babca, cbaba, cabab, babac,ababc

Total = 5!/2!2! = 30...
Pobability = 12/30 = 2/5

Bhailog __________________//\\_________________

why couplw is aa and bb?? if we assume m1 w1 as one couple and m2 w2 as 2nd couple then u r nt taking sm arrangement lyk
m1 w1 m2 w2 x..... 1 arrngement
w1 m1 m2 w2 x... 2 arrangement
bt u r tking both arrangement as 1 .. why so?????

Q32)Four bells ring at regular intervals of 6,8,12,18 sec.They start ringing together at 12clock.How many times they will ring together during next 12 min?(including 12 min marks)
a)9 b)10 c)11 d)12 e)none of above

LCM of 6 8 12 and 18 is 72
total time duration is 12 mins = 720 seconds
thus number of times they ll ring together including 12: 00 and 12:!2
= 720/72 + 1 = 11 times

LCM = 72 sec...

Total time they ring together = 12*60 / 72 + 1 (for the 1st time)= 10 + 1 = 11

acc to soln key,correct ans is b

Q4)The sum of two numbers is 15 and their geometric mean is 20% lower than their A.M.Find the number
a)11,4 b)12,3 c)13,2 d)10,5 e)9,6

Sum = 15
so AM = 7.5
GM is 20% lower than AM
So GM = 6
check with options where a and b when multiplied gives 36 and hence a GM of 6

else solve it as
a+b = 15
ab = 36
a = 12 and b = 3

Datta Bhai, I think you didnt get the question... I may be wrong...

I think you took it that the 2 coupens should not be together.. But the question is that the people of a couple should not be together...

if aa is a couple, then a and a should be be besides each other...

you took aa =1.. Measn in all your cases, the pair is always together..

Hope you got it.:grin:

Eisa???? I totally mis-interpreted

Q4)The sum of two numbers is 15 and their geometric mean is 20% lower than their A.M.Find the number
a)11,4 b)12,3 c)13,2 d)10,5 e)9,6

This is easier with options

Answer = 12,3...

Bs bhai, Varun, Chill sir and other bhailog.. Iska koi method hai kya?

Q4)The sum of two numbers is 15 and their geometric mean is 20% lower than their A.M.Find the number
a)11,4 b)12,3 c)13,2 d)10,5 e)9,6

answer is b...just check for which value ab is a perfect square u will get your answer.

Q32)Four bells ring at regular intervals of 6,8,12,18 sec.They start ringing together at 12clock.How many times they will ring together during next 12 min?(including 12 min marks)
a)9 b)10 c)11 d)12 e)none of above

LCM = 72 sec...

Total time they ring together = 12*60 / 72 + 1 (for the 1st time)= 10 + 1 = 11

Q32)Four bells ring at regular intervals of 6,8,12,18 sec.They start ringing together at 12clock.How many times they will ring together during next 12 min?(including 12 min marks)
a)9 b)10 c)11 d)12 e)none of above

1)Find the number of consecutive zeroes immediately after the decimal in 1/(20^37)
(log 2 = 0.3010)
(a) 46 (b) 47 (c) 48 (d) 49

log x = -37 * 1.3010 = -48.137 = -49 + 0.863...

So there are 48 zero?

Q4)The sum of two numbers is 15 and their geometric mean is 20% lower than their A.M.Find the number
a)11,4 b)12,3 c)13,2 d)10,5 e)9,6

dont u think it should be...

couples aa-1 bb-2 single c-3

total ways
123 132 213 231 321 312
favourable when 3 in middle
so 2/6....just asking :)

bcoz condition is just couples shoudnt sit together....Are we concerned with how the couples arrange themselves when they sit????

Datta Bhai, I think you didnt get the question... I may be wrong...

I think you took it that the 2 coupens should not be together.. But the question is that the people of a couple should not be together...

if aa is a couple, then a and a should be be besides each other...

you took aa =1.. Measn in all your cases, the pair is always together..

Hope you got it.:grin:

1)Find the number of consecutive zeroes immediately after the decimal in 1/(20^37)
(log 2 = 0.3010)
(a) 46 (b) 47 (c) 48 (d) 49

Foster87 Says

what are the last two digits of (1/5^903)??(approach please)

is it 05?????

2 couples and a single person is to be seated in 5 chairs.What is the probability that no couple is to be seated together?
Answer 2/5 kaise hai...

1 way is when single person sits in the middle chair??? what is the 2nd arrangement....

couples = aa and bb...

Possibilitites in our favour = abcab, abcba, bacba, bacab, acbab, bcaba, abacb, babca, cbaba, cabab, babac,ababc

Total = 5!/2!2! = 30...
Pobability = 12/30 = 2/5

Bhailog __________________//\\_________________

E(153) = 96

thus, 128^960/153 = 1

we r left with 128^40/153

splitting denominator to find the remainder now ,

153 = 9 x 17

where, 9 gives us a remainder of 7 where 17 gives 1

hence, 9k+7 = 17p +1

therefore, remainder is 52

========================================

bhai logo chinese remainder theoram kaise lagatey hain ??

2 couples and a single person is to be seated in 5 chairs.What is the probability that no couple is to be seated together?
Answer 2/5 kaise hai...

1 way is when single person sits in the middle chair??? what is the 2nd arrangement....

Anand and Bala started from towns P and Q simultaneously towards Q and P respectively. After 6 hours, they crossed each other at town R. After that, Anand took 5 hours more to reach Q than Bala took to reach P. Find the sum of the times taken by them to reach their destinations from R ( in hours).
(A) 15 (B) 11 (C) 13 (D) 17

Total Distance --> 6a+6b
Time taken by B to travel 6a is t
=> 6a/b = t
Time taken by A to travel 6b is (t+5)
=> 6b/a = t+5

So add --> 13

if a four digit number N has 15 factors?
then N^2 has how many factors?

a- 29
b- 30
c- 45
d- none
plz help........!!

N = p^14 or (p^4 * p^2)

Now p^14 > 4 digit number hence not possible

So N = (p^4 * p^2) = 9*5 = 45

So option (c)

if a four digit number N has 15 factors?
then N^2 has how many factors?

a- 29
b- 30
c- 45
d- none
plz help........!!

A no. "N" with 15 factors can be of the form,
(2^14)
(2^4)*(3^2)

But (2^14) is a a no. more than 4 digits.
Thus,we take (2^4)*(3^2)
Now,N^2= {(2^4)*(3^2)}^2
(2^8 )*(3^4)

Thus,no. of factors=(8+1)*(4+1)=45(option c)

Foster87 Says

what are the last two digits of (1/5^903)??(approach please)

getting ans as 08
rewrite.it as 2^903/10^903
now 2^903= (1024)^90*8
so last 2 digits wl b.. 76*8 = 08

if a four digit number N has 15 factors?
then N^2 has how many factors?

a- 29
b- 30
c- 45
d- none
plz help........!!

I got 45


15 can be written as 5X3
There the powers will be 5-1,3-1 =4,2
Squaring powers will become 8,4
The no of factors will be 9X5=45

If the number has only one prime number then
Power will be 15-1=14
Squaring 14X2=28
No of factors=28+1=29

Due to 4 digit restriction will be 45 only.

Anand and Bala started from towns P and Q simultaneously towards Q and P respectively. After 6 hours, they crossed each other at town R. After that, Anand took 5 hours more to reach Q than Bala took to reach P. Find the sum of the times taken by them to reach their destinations from R ( in hours).
(A) 15 (B) 11 (C) 13 (D) 17

Bheja fry ho gaya yeh karte karte...

Jara method bhi bata dena...

form 2 eqn..
6a = bx .... 1
6b = a(x+5) ... 2
so put value of a in terms of b from eq 1
u get.. x^2+5x-36 =0
so x is 4 and x+5 is 9
sum = 13

if a four digit number N has 15 factors?
then N^2 has how many factors?

a- 29
b- 30
c- 45
d- none
plz help........!!

If a+b+c=24,then the maximum value of (a)^2*(b)^3*(c) is

A) (2^3)*(3^10)
B) (6^3*2^10)
C) (6^3*2^8 )
D) (2^14*3^3)

here the expression is a^2*b^3*c....
hence we will write a+b+c=24 as
a/2+a/2+b/3+b/3+b/3+c=24.

to have maximum value,each f the no's should be 4...i.e..a/2=4=>a=8,b/3=4=>b=12,c=4
hence the maxm value is 2^14*3^3:)

If a+b+c=24,then the maximum value of (a)^2*(b)^3*(c) is

A) (2^3)*(3^10)
B) (6^3*2^10)
C) (6^3*2^8 )
D) (2^14*3^3)

Better to use Ratio Method:

a/2 = b/3 =c/1 =k

So, a=2k ;b=3k ;c=k

So, 6k =24
=>k=4

So a=8;b=12;c=4

So (a)^2*(b)^3*(c)

=8^2*12^3*4

=2^6*2^6*3^3*2^2

=2^14*3^3

just_nishu4u Says

It's right but how?? Solution please.......

Split terms like a/2 a/2 b/3 b/3 b/3 and c ..
a.m of 6 terms is a+b+c/6 is 4
g.m of 6 terms is
(a^2*b^3*c)^1/6
now use a.m > g.m ... u wl get ans


p.s sorry bhai mob se type krna hard hai

what are the last two digits of (1/5^903)??(approach please)

i wl go wth opt D
used A.M > G.M

It's right but how?? Solution please.......

Anand and Bala started from towns P and Q simultaneously towards Q and P respectively. After 6 hours, they crossed each other at town R. After that, Anand took 5 hours more to reach Q than Bala took to reach P. Find the sum of the times taken by them to reach their destinations from R ( in hours).
(A) 15 (B) 11 (C) 13 (D) 17

Bheja fry ho gaya yeh karte karte...

Jara method bhi bata dena...

If a+b+c=24,then the maximum value of (a)^2*(b)^3*(c) is

A) (2^3)*(3^10)
B) (6^3*2^10)
C) (6^3*2^8 )
D) (2^14*3^3)

i wl go wth opt D
used A.M > G.M

If a+b+c=24,then the maximum value of (a)^2*(b)^3*(c) is

A) (2^3)*(3^10)
B) (6^3*2^10)
C) (6^3*2^8 )
D) (2^14*3^3)

bs0409 Says

Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe B fills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow?

40 1/3 minute

A=40l/min
B=30l/min
C=20l/min
In 3 minutes 50l is filled.
In 13 cycles 650l will be filled.
Time will be 39 min.
50l is left so A will fill 40l in 1 minute.
10l left which will be filled in 1/3 minutes.
Time = 39 +1 + 1/3 = 40 1/3 minute

bs0409 Says

Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe B fills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow?

I am gettin as as 40min
20 sec

p.s .. bhai logo iss thread ki speed kam karo .. pichala cover krte krte aur 10 20 pages aa jate hai

Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe B fills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow?

Q)
n! has 23 zeroes.What is max possible value of n?

q)how to solve below mentioned types of question in quickly
Find max value of n such that
42x57x92x91x52x62x63x64x65x66x67 is perfectly divisible by 42^n.

100! ---> 24 zeros
99! --->22 zeros

So In this case I don't think any value will satisfy.
---------------------------------------------------------------

42^n =7^n*3^n*2^n
Highest power of 7 and 3 is 3.

So It must be divisible by 42^3

in a colony of cells, each cell multplies into 2 every hour. if there is single cell in the beginning and the process continue for 9 hours, how many cells woudl be there at the end of 9 hours? its known that life of indivdual cell is 20 hour?

i think the ans shud be 2^9 but the OA mentioned (2^10)-1
anyone can help me with this???

Q)
n! has 23 zeroes.What is max possible value of n?

q)how to solve below mentioned types of question in quickly
Find max value of n such that
42x57x92x91x52x62x63x64x65x66x67 is perfectly divisible by 42^n.

find complete 42

42


which is 6*7

u can visualise that 7 is less so find out that
which in turn is 3hence 42^3 is the answer

Q)
n! has 23 zeroes.What is max possible value of n?

q)how to solve below mentioned types of question in quickly
Find max value of n such that
42x57x92x91x52x62x63x64x65x66x67 is perfectly divisible by 42^n.

1)n=0..
n 2)1..??

A ---> a hrs more than AB combined
B ---> b hrs more than AB combined

Then AB -->sqrt(ab)
Proof:
A --->(x+a)
B--->(x+b)
AB --->x

So (x+a)*(x+b)/(x+a+x+b) = x

Solve for x

x=_/(ab)

bhai trick sirf etni hai u can remember few values:)

1/20+1/30=1/12
1/20+1/60=1/15
1/10+1/10=1/5
1/12+1/8==1/4.8

like that

Q)
n! has 23 zeroes.What is max possible value of n?

q)how to solve below mentioned types of question in quickly
Find max value of n such that
42x57x92x91x52x62x63x64x65x66x67 is perfectly divisible by 42^n.

question 1:

answer is0

it will be either 22 or 24


beech ka kuch nahi hota

Q)
n! has 23 zeroes.What is max possible value of n?

q)how to solve below mentioned types of question in quickly
Find max value of n such that
42x57x92x91x52x62x63x64x65x66x67 is perfectly divisible by 42^n.

bs0409 Says

There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?

7 pipes 'll be filling

Originally Posted by bs0409
Sam and Aizen working together can finish a job in T days. If Sam works alone and completes the job, he will take T + 5 days. If Aizen works alone and completes the same job, he will take T + 45 days. What is T?

Directly find GM of excess:

=_/(T+5-T)(T+45-T)

=_/(45*5)

=_/225

=15 days

i know.. that's why i asked if there was some trick way...



is this some established rule or universally applicable formula (in similar ques ofcourse) ??

A ---> a hrs more than AB combined
B ---> b hrs more than AB combined

Then AB -->sqrt(ab)
Proof:
A --->(x+a)
B--->(x+b)
AB --->x

So (x+a)*(x+b)/(x+a+x+b) = x

Solve for x

x=_/(ab)

bs0409 Says

There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?

7 filling and 5 drain :)


no of filling tanks in 24 hour by 1 pipe =3
no of draining in 24 hour by 1 pipe =4

also

3x-4y=1
x+y=12

:)

7 is the Answer