Quant by Arun Sharma

Q)
Find the number of numbers between 100 to 400 which are divisible by either 2,3,5,7....

Plz check my answer..i am getting 294...


i think its not correct data, this 2,3,5,7.....continue or end with 2,3,5,7

can u check plz

its written divisible by either 2,3,5 and 7...

Abhinav90 Says
its written divisible by either 2,3,5 and 7...


2,3,5,7..... means data says 2,3,5,7,11,13,17,19,23..... or its 2,3,5,7

or u have posted u r data is perfect as per hard copy?

HI PGS I AM A NEW PG JUST JOINED YESTER NIGHT. IHAVE A PROB PLS HELP

IF N=a^3 and N=b^4 then find the smallest possible value of N.here a,b,N are all natural nos

HI PGS I AM A NEW PG JUST JOINED YESTER NIGHT. IHAVE A PROB PLS HELP

IF N=a^3 and N=b^4 then find the smallest possible value of N.here a,b,N are all natural nos

The LCM of 3 and 4 is 12...so the number should have a power of 12...since number has to be smallest, we choose 2 as the base ...so the number will be 2^12 . :cheerio:
HI PGS I AM A NEW PG JUST JOINED YESTER NIGHT. IHAVE A PROB PLS HELP

IF N=a^3 and N=b^4 then find the smallest possible value of N.here a,b,N are all natural nos


ans is 8 because , 8=1^4*2^3
jigar_p_civil Says
ans is 8 because , 8=1^4*2^3

incorrect, because a and b should be able to represent N by themselves...1 to any power cannot represent 8
r11gupta Says
incorrect, because a and b should be able to represent N by themselves...1 to any power cannot represent 8



yes dear u totally correct , drunk too much
2,3,5,7..... means data says 2,3,5,7,11,13,17,19,23..... or its 2,3,5,7

or u have posted u r data is perfect as per hard copy?


Sir,I have posted the Question as per hard copy...

Find the number of numbers between 100 to 400 which are divisible by either 2,3,5 and 7....

I thinnk it is asking for those numbers b/w 100 to 400 which are only divisible by 2,3,5 and 7...like 300,301,302,303,304,305,306,308....
HI PGS I AM A NEW PG JUST JOINED YESTER NIGHT. IHAVE A PROB PLS HELP

IF N=a^3 and N=b^4 then find the smallest possible value of N.here a,b,N are all natural nos


The Answer is 4096...
Though did with a layman method...

u got the answer right 2^12 but what is the logic behind it.pls explain

dindosaha1 Says
u got the answer right 2^12 but what is the logic behind it.pls explain

as i wrote in my reply to your question, the LCM of 3 and 4 is 12..this makes 12 the least power which can be expressed as a cube as well as a fourth power of any number...and since the minimum value is needed, i chose the smallest number possible i.e. 2...choosing 1 is not correct because 1 will not change, irrespective of the power it is raised to...2 is the first [ and smallest] number that has different values for the third and fourth powers... hope this helps.

Hi Shashank,

Thanks a lot for the guidance.

Here my doubt...
Q)Which of the following is not a perfect square?
100856,325137,945729,All of these,None of these....

So,the query is that traditional way says to find their prime factors and then conclude..But that process is very tedious..N I seek some short method....

Do Anyone know any shortcut?..

Here my doubt...
Q)Which of the following is not a perfect square?
100856,325137,945729,All of these,None of these....

So,the query is that traditional way says to find their prime factors and then conclude..But that process is very tedious..N I seek some short method....

Do Anyone know any shortcut?..


squares of numbers that are not multiples of 3 are of the form 3n+1.
If you are looking for a single number that is not a perfect square , then it is 100856.

It is not a multiple of 3 and it is not of the form 3n+1.

Please correct me if I am wrong.

Why are u checkin it with 3?
well the answer is :All of these..

Why are u checkin it with 3?
well the answer is :All of these..


As I have already told, if you were looking for a single non perfect number out of the three, then you could have used that method.

I am just using the property that the square of all numbers that are not the multiples of 3 are of the form 3n+1.

Ex: 7^2= 49 can be written as 3n+1
whereas 9^2 =81 cannot be written as 3n+1.

But anyways this cannot determine if the other 2 are perfect squares or not.
Here my doubt...
Q)Which of the following is not a perfect square?
100856,325137,945729,All of these,None of these....

So,the query is that traditional way says to find their prime factors and then conclude..But that process is very tedious..N I seek some short method....

Do Anyone know any shortcut?..


Every square is of the form 3n or 3n+1, but vice versa need not be true.

did we miss out 3m+8...correct me if i am wrong!!

manisphere Says
did we miss out 3m+8...correct me if i am wrong!!


where does 3m+8 come in the picture??

see,any number is of the format 3n,3n+1 or 3n+2

now,

(3n)^2=9n^2=3x

(3n+1)^2=9n^2+6n+1=3y+1

(3n+2)^2=9n^2+12n+4=9n^2+12n+3+1=3z+1

so,any square can be written as 9k if its divisible by 3 or 3k+1 if it is not.