A six digit number has the maximum number of possibilities of perfect square as given below 1) Firs

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22 Jan 2015 Six digit number

A six digit number has the maximum number of possibilities of perfect square as given below
1) First digit is a perfect square
2) Second digit is a perfect square
3) Third digit is a perfect square
4) Number formed by first and second digit in order is perfect square.
5) Number formed by third and fourth digit in order is a perfect square.
6) Number formed by fifth and sixth digit in order is a perfect square.
7) Number formed by last 3 digit in order is a perfect square.
Here sixth digit means the units place.
All the digits in the number are different and non-zero.
The product of all the six digit will be

OPtion

1) 720
2) 5040
3) 20160
4) 1080
5) 1344
6) 4032
7) 1890
8) 3360
9) 2160
10)3780

Solution

Perfect square single digits are 1, 4, 9
Two digit no by using 1, 4, 9 is only 49
So first three no will be 491 now third and fourth digit number is perfect square so it will be 16 and last two digit set will only be 25 because no integer can be revised so no is 491625

Correct Option: 9 Best Solution (52)

Mahesh   9 years AGO

The only possible single digit numbers which are squares are
1, 4, 9
The first three digits should be from these three only
But the number formed by first two digits should be a perfect square
First two digits should be 49
Third digit should be 1
Third and fourth digits should be a perfect square
The only square starting with 1 is 16
Fourth digit is 6
First four digits are 4916
Last three digits form a perfect square
The only squares in six hundreds are 625 and 676
But 7 or 6 cannot be used again
Last three digits are 625
The whole number is 491625
Product of the digits is 2160

491625 is the number
2160 is the answer
Option (9) is the answer

Like? Yes (4) | No (1)  

Swathy Murugan   9 years AGO

1 digit possible perfect square is 1,9,4
first two digit possible square from the above combination is 49(7^2)
then third digit is perfect square so it should be 1
third and fourth digit is perfect square so the fourth digit must be 6
last two digit is perfect square so we can place 25
last 3 digit is perfect square so it is 625
Thus the 6 digit number is 491625
the product of this is 2160

Like? Yes (3) | No   

Ankit Pandey   9 years AGO

First digit=4
Second digit=9
third digit=1
fourth digit=6
fifth digit=2
sixth digit=5
Hence,
Six digit no. is = 491625 which fulfill all the conditions
and hence the product of all digits = 4*9*1*6*2*5=2160

Like? Yes (3) | No   

Ankit   9 years AGO

The number will be 491625 as according to the given Condition so the product of the digits will be 2160.

Like? Yes (3) | No   

ganesh babu   9 years AGO

The number is 491625
4x9x1x6x2x5=2160

Like? Yes (4) | No (1)  

pradeep   9 years AGO

first two digits-49
3 rd and 4 th are-16
5 th and 6th -25

Like? Yes (3) | No   

apurva katyayni   9 years AGO

six digit no. will be 491625

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b.subbarao   9 years AGO

There are 3 digits which are perfect squares. those are 1,4,9. so first 3 digits of number is formed by using these three. but another condition is number formed with first and second digits should be perfect square so first digits of number is 491.
next condition number formed with third and fourth digit should be perfect square so suitable digit is 6 in fourth place.
first four digits of number is 4916.
number formed with fifth and sixth digits is 25.
finally 6 digits number is 491625.
product of digits is 2160.

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MD SOHAIL AKHTER   9 years AGO

no. is 491625

Like? Yes (3) | No (1)  

Sravanthi   9 years AGO

491625 is number
product is 2160

Like? Yes (3) | No (1)  

Supriya Mondal   9 years AGO

From the given condition we get that,
The number will be 491625
i)4 is a perfect square
ii)9 is a perfect square
iii)1 is a perfect square
iv)49 is a perfect square
v)16 is a perfect square
vi)25 is a perfect square
vii)625 is a perfect square
All the digits in the number are different and non-zero.
Here, all the 8 conditions are satisfied
So the number is 491625.
Products of all its digit is=4*9*1*6*2*5=2160
so, option 9)2160 is the right answer

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llamar   9 years AGO

simply the numbers are
in order 4,9,1,6,2,5

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Satya B   9 years AGO

the six digit number is 491625

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anup   9 years AGO

491625 .....

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MRITUNJAY KUMAR   9 years AGO

Options9)

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Niraj Agarwal   9 years AGO

The number formed is: 491625

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pravallika nathi   9 years AGO

six digit number is 491625 peoduct of digits gives 2160

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Abhik Das   9 years AGO

According to the given condition
1st,2nd,3rd digit should be either 4/9/1
as number formed by 1st and 2nd no is perfect square so it should be 49
Then number formed by 3rd & 4th digit is also perfect square so it should be 16
and the number formed by the 4th,5th and 6th digit is also perfect square and the number formed by 5th and 6th digit is also perfect square so the three digit number would be 625.
The number is=491625
and the product is=(4*9*1*6*2*5)=2160

Like? Yes (2) | No   

Anshul Garg   9 years AGO

According to 5h and 6th Statement 625 is three digit number which is a perfect square and 25 is a perfect square.

According to 4th statement 3rd digit is 1 (Because it follows statement 3 also).

According to 1, 2 and 4 statement 49 is the number at First Two digits.

Hence, the product of 6 digits is 4*9*1*6*2*5 = 2160

Like? Yes (2) | No   

nithin kumar   9 years AGO

all possible first 3 digits are 1,4,9 (only these digits are perfect square)

first & second digits must be 4,9 respectively ( 49 is perfect square)

third & fourth digits must be 1,6 resp. (16 is pefect square)

fifth & sixth digith should be 2,5 (as there is no other combination from the rest digits which are making a perfect square)

so the six digits are : 491625
(as last three digits is also a pefect square of 25 )

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Meenakshi   9 years AGO

The number is 491625
first digit is perfect square=4
second digit is perfect square=9
third digit is perfect square=1
number formed by 1st and 2nd in order is a perfect square=49=7^2
number formed by 3rd and 4th in order is a perfect square=16=4^2
number formed by 5th and 6th in order is a perfect square=25=5^2
number formed by last 3 digits in order is a perfect square=625=25^2

So,the product of all six digits is:4*9*1*6*2*5=2160

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RAUNAK   9 years AGO

1st 2 dgits should be 49(both individually are perfect squares and if combined a perfect square too..)
3rd digit possible 1...(a perfect square)
3rd and 4th if combined we have only option i.e.16
last 3 digits ...since all digits are diffenrent and non-zero alsoand 4th one is 6 hence it should be 625...
Thus no is 491625..and hence product is 2160

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A M ANKIT KALLURAYA   9 years AGO

number formed is 491625
ans=4*9*1*6*2*5=2160

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Gourab Dutta   9 years AGO

First digit 4, 2nd 9, 3rd 1 4th 6,5th 2,6th 5...so the product is 2160..

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SREENIVASA RAO PALLAPU   9 years AGO

first 3 digits are a perfect squares individually => 1 or 4 or 9
number formed by first and second digit is a perfect square
=> only 2 digit perfect square possible with above three is 49 => first 3 digits are 491
number formed by 3 and 4th also perfect square =>16
and last three digit num also a perfect square =>6_ _ is a perfect square. only choices are 625 and 676
so last condition all digits are different =>491625
sum of digits = 2160

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Revathi   9 years AGO

6 digit perfect square is 491625.
product of above 6 digits is 2160

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Rahul   9 years AGO

here , the first digit is a perfect square therefore it can be either 1 , 4, 9.
the second digit is also a perfect square therefore it may be either 1 , 4 , 9.
but it is said that the first and second digit's number is also a perfect square therefore the 4 and 9 will be the first and second digits.
by this way if we examine the no. will be 4,9,1,6,2,5
4*9*1*6*2*5 = 2160.

Like? Yes (2) | No   

Shubham Banerjee   9 years AGO

the number is 491625 => 4*9*1*6*2*5 = 2160

1) First digit is a perfect square : 4 = 2*2
2) Second digit is a perfect square : 9 = 3*3
3) Third digit is a perfect square : 1 = 1*1
4) Number formed by first and second digit in order is perfect square : 49 = 7*7
5) Number formed by third and fourth digit in order is a perfect square : 16 = 4*4
6) Number formed by fifth and sixth digit in order is a perfect square : 25 = 5*5
7) Number formed by last 3 digit in order is a perfect square : 625 = 25*25
8) All the digits in the number are different and non-zero : 4, 9 , 1, 6, 2, 5 != 0

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abhishek pndey   9 years AGO

491625

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MRITUNJAY   9 years AGO

digits of six digit number=491625

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ABHINAV PUSHPAM   9 years AGO

The required number is 491625. So the product is 2160

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Saurabh Kumar Gupta   9 years AGO

The required number will be 491625.
So 4*9*1*6*2*5= 2160

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Jaspalsingh Parmar   9 years AGO

No is 491625
So option 9 is correct

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Ankit Sirohi   9 years AGO

The number thta satisfies all the conditions is,
491625... i.e 49 16 25 set of squares...the product of digits is 2160...hence answer option 9.

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RAMAKRISHNA   9 years AGO

the number formed by following the points givrn is 491625
product of all the digits gives 2160

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Vamsi Srikanth   9 years AGO

The 6 digit number is 491625. By multiplying all the digits, we'll get 2160

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guru   9 years AGO

The number according to the given conditions is 491625 and the product of the digits is 2160

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TUSHAR    9 years AGO

2160

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g lokesh   9 years AGO

The number is 491625
first three numbers must be 1,4,9
1st and 2nd must be perfect square is 49
3rd and 4th must be 16 and so on.........

Like? Yes (1) | No   

Ajinkya Kulkarni   9 years AGO

491625

Like? Yes (2) | No (1)  

Dr.Dipin Singh   9 years AGO

4*9*1*6*2*5=2160

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SAYAN CHATTERJEE   9 years AGO

the 1st digit , 2nd digit is square and in order they are square so it must be 49
the 3rd is square, and 3rd, 4th in order is square, so this should be 16
the 5th,6 th in order is square as well as 4th, 5th, 6th in order is square, so it is 25
now the no. becomes 491625
so the product of the digits is 2160.

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RAKESH   9 years AGO

no. is 491625

so, product = 2160

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Devendra Marghade   9 years AGO

The number is 491625
So product of all the digits=4*9*1*6*2*5=2160

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sravani   9 years AGO

number is 4 9 1 6 2 5
product is 2160...

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sompon temtheerakij   9 years AGO

A six digit number is 491625.
the product of all the six digit = 4*9*1*6*2*5 = 2160

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Ponni   9 years AGO

The six digit number is 491625
product of 491625=2160 = option 9

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satyam sharma   9 years AGO

the no is 491625
4*9*1*6*2*5=2160

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Paras Jain   9 years AGO

Number is 491625 so product = 2160 Ans.

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manasa   9 years AGO

4*9*1*6*2*5=2160
here 4,6,1 are perfect squares....frst and second number in order 49,third and fourth number in order 16 are also perfect squares.. and last three numbers in order 625 is also a perfect square..

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mayank agarwal   9 years AGO

First place can have only three possible values namely 1, 4 or 9. But 1 and 9 are rejected because if we put them in first place, we will not have any number which is a perfect square and make a perfect square of 1st and 2nd when taken in order. So 1st place can only contains 4.

Now, second place can only contain 9 as only 49 is a perfect square according to rule (4).

Now, 3rd place can only be 1 because according to rule (3), it must be perfect square and all digits must be different, so only 1 is remaining as perfect square. so, third digit will be 1.

4th digit will be 6 as according to rule (4), number formed by 3rd & 4th digit taken in order must be a perfect square and 16 is only perfect square starting with 1.

Now, only 2 & 5 can be 5th & 6th digit respectively which fulfill rule (6) & (7).

So, the number formed is 491625.
And the product of all digits is 2160 (Option 9) Answer.

Thank You

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Mithun Kumar Kesari   9 years AGO

2160

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