Three integers x, y, z such that 1 =< x, y, z =< 9 and x not= y not= z are choosen. The sum of produ

Supriya Mondal   9 years AGO

Numbers will be 2,5 and 9
As, sum of products of numbers taken in pair is=(2*5)+(2*9)+(5*9)=10+18+45=73
and sum of this three numbers is=2+5+9=16
So, product of this three numbers is=2*5*9=90
So, option 4)90 is the right answer

Like? Yes (6) | No   

Saurabh Kumar Gupta   9 years AGO

Perfect square less than 10 are: 1, 4, 9.
So according to the given conditions, the three numbers possible are: 9, 2, 5.
Their sum is 16 and only one of them is a perfect square.
Also (9*2)+(9*5)+(2*5)=73
So the required product is 9*2*5=90

Like? Yes (9) | No (4)  

Abhishek Sumit   9 years AGO

(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
from above formula we get x^2+y^2+z^2=110
and we have x+y+z=16
so we get,three no.s as 5,9,2. and their product is 90

Like? Yes (4) | No (1)  

Surit Datta   9 years AGO

the three integers are 2,5,9
as
there summation is 2 + 5 + 9 = 16
product pair is (2*5 + 5*9 + 2*9) = 73
so there multiple will be
2*5*9 = 90
so option 4
that's it.

Like? Yes (2) | No   

Pradyumna K S   9 years AGO

numbers are 9, 5, 2.
9+5+2=16
(9)(5)+(5)(2)+(2)(9)=73
(9)(5)(2)=90

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JANARTHANAN RAM   9 years AGO

2+9+5=16;
2*9+9*5+2*5=73;
so,2*9*5==90;

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Sameer Kulkarni   9 years AGO

The numbers are 9, 2, 5
and Their product is 90

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A M ANKIT KALLURAYA   9 years AGO

the numbers are 2,9,5 which satisfy all the condition given
so product is 90

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RAKESH   9 years AGO

x^2 + y^2 + z^2 = 16^2 - 2*73 = 110

=> x,y,z = 9,5,2 or xyz = 90

Like? Yes (1) | No   

g lokesh   9 years AGO

Based on the conditions given the numbers will be 2,5,9
and their prodect is 90

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sravani   9 years AGO

one of them must be 1 or 9 or 4
let it be 9 and check the others..
Then 2,5 satisfies..
no other satisfies with1 or 4..
so numbers are 9,2,5
product is 90...
The other way to do this is (x+y+z)^3-(x+y+z)^2.

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Subha Ganesan   9 years AGO

one is perfect square so 9
16-9=7
2+5=7
so 2*5*9=90

Like? Yes (2) | No (1)  

Sravanthi   9 years AGO

x=2
y=9
z=5

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Gurram Mahendra ranganath   9 years AGO

23^23=529
5*2+2*9+5*9=10+18+45=73(satisfied)
5+2+9=16(satisfied)
hence,5*2*9=90

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Satya B   9 years AGO

x=9 y=2 z=5
xyz=90

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Shruthi   9 years AGO

Given: 1=

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apurva katyayni   9 years AGO

259 is the no.

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arush gupta   9 years AGO

ans 90 the no will be 9,5,2

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reddyprasad   9 years AGO

9+2+5=16
9*2+2*5+5*9=73
9*2*5=90

Like? Yes (1) | No   

Anshul Garg   9 years AGO

From the question
x+y+z=16
xy+yz+zx=73
One number is perfect square (say x is the perfect square).

So, the possible value of x are 1,4,9.

We can check by putting the value and solving for other 2 numbers. And we get three numbers are
2,9,5
And product will be 2*9*5 = 90

Like? Yes (1) | No   

manorama rai   9 years AGO

let z=9;
then solving the equation from second condition we will get y=7-x;
hence again solving the equations we will get x=5 or 2;
x can take any value and reverse value will be taken by y
hence product will come to be same and it is 90.

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ANKIT RAMAN   9 years AGO

BECAUSE XY+YZ+ZX=73
AND X+Y+Z=16
SO,BY FORMULA,,X^2+Y^2+Z^2=110.
THEN THE VALUE OF X,Y AND Z WHICH WILL SATISFY THE EQUATION ARE 9,5,2.

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kona chandra reddy   9 years AGO

x=2,y=5,z=9
x*y+y*z+z*x=10+45+18=73
z=9,so z is square of number 3.
then product of x,y,z is x*y*z=2*5*9=90

Like? Yes (1) | No   

Ponni   9 years AGO

the three numbers are: 9,5,2
sum of their products is 9*5 +5*2+2*9 =73
sum = 9+5+2=16
product is 9*5*2=90

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Deepak Kumar Sahu   9 years AGO

2, 5, 9

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anusha   9 years AGO

ans is 90

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anuj gupta   9 years AGO

5,2,9.
5*2*9=90.

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Devendra Marghade   9 years AGO

The three integers are 2,5,9
So product=2*5*9=90

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Ankit Pandey   9 years AGO

xy + yz +zx = 73

x + y + z = 16
Since one no is perfect square so let us x = 9
and y = 5, z = 2
these numbers fulfilled the given conditions.

so product of nos = 9*5*2 = 90

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Vivek Vishal Anand   9 years AGO

x=9, y=2, z=5

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santosh bagathi   9 years AGO

one of three numbers is a perfect square
between 1 to 9 , perfect squares are 4,9

and sum =16

then taking above in to consideration ,possible values of x,y,z are [9,2,5] ,[9,4,3] ,.........etc

of those [9,2,5]satisfies third condition xy+xz+yz=73

thus

ans : (4) 90

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Jaspalsingh Parmar   9 years AGO

295 is the number
Product 90

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ranjithreddy   9 years AGO

x+y+z=16
Xy+yz+zx=73
X^2+Y^2+Z^2=110
one number is a perfect square
Its should be either 1or 4 or 9
By using the given conditions we will get the numbers as 9,5,2
The final product becomes 90.

Like? Yes (1) | No   

Nupur   9 years AGO

We know that x + y + z = 16
We also know xy + yz + xz = 73
Let x = 9 (perfect square)
9y + yz + 9z = 73
USing possible combinations within [1,9]
We get y = 5, z = 2
Hence product = 90

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Ravi Bhushan Mahato   9 years AGO

number are 2 , 5 , 9
so answer is 90

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Swathy Murugan   9 years AGO

option 4

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Shanmugapriya.G   9 years AGO

from given data
xy+yz+zx=73,x+y+z=16;
let z=9 (perfect square)
while solving we get xy=10,z=9;
so the product of number xyz=90

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Awadhesh Singh   9 years AGO

The no. perfect sq can be 1, 4 or 9.
For x=1 or 4, y+z=15 or 12;
eqn xy+yz+zx=73 can not be solved.
for x=9, eqn will be,
y^2 -7y+10=0.
i.e. nos are 2,5,9.
and 2*5*9=90.

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Sivaraman Kumarsamy   9 years AGO

The perfect Squares may be 4 or 9
Let z=9
Sum of the unknowns,
x+y+9=16
Implies,
x+y=7
Therefore
(xy)+(yz)+(zx)=73
Will be,
(xy)+(9y)+(9x)=73
Also, x+y=7
Implies,
y=7-x
(x(7-x))+9(7-x)+9x=73
7x-(x^2)+63-9x+9x=73
7x-(x^2)=10
(x^2)-7x+10=0
solving, x=2 (or) x=5
let x=5
implies, y=2 (since x+y=7)
Therefore,
x=5
y=2
z=9
x+y+z=16
(xy)+(yz)+(xz)=73

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MRITUNJAY KUMAR   9 years AGO

Product of number= 9*2*5=>90
Option)4

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kiranmayee   9 years AGO

i assumed the numbers as 9 , 5, 2.... after the simplification we get the answer as 90

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ramakrishnateja   9 years AGO

given that 1=1,z

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mounika.p   9 years AGO

295 is the number and product is 90

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puneet   9 years AGO

because x+y+z=16
and one is perfect squre so if we take 4 as a perfect sqr that not solve the eqn xy+yz+zx=73
so we take x=2,y=5 and z=9
these values full fill all the conditions
and xyz=90

Like? Yes (1) | No   

Praveen Kumar Soni   9 years AGO

For being a sum of 16 with being perfect square there is only set possible i.e { 5,2,9} and number 529 is a perfect square of 27 as well as there sum is 16 and sum of products be (9*5+5*2+9*2 = 73 ) .And as we have no. so the product of three numbers be 9*5*2 = 90.

Like? Yes (2) | No (1)  

HUSENAIAH   9 years AGO

2*5*9=90

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gunjan maurya   9 years AGO

x+y+z=16
xy+yz+zx=7
perfect square between 1 and 9 can b only 4 and 9.
in sum of their pair products unit digit is 3 whch can b obtained only whn the perfect square is 9.

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Avani Patoria   9 years AGO

It is given that ;
xy + yz + zx = 73 &
x + y + z=16

now one of them is perfect square which is 9
let take z=9
then we'll get rest of the two numbers which is 2 & 5

so the x,y & z will be 2,5,9 and their product is = 90

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BHASKAR MANDAL   9 years AGO

only one combination is possible and that is
2,5,9
so the product will be 2*5*9 = 90
option 4

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ABHINAV PUSHPAM   9 years AGO

295 is the number. So answer is 90. So option 4).

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MRITUNJAY   9 years AGO

number is 295 and product is 90.

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Shamba Mitra   9 years AGO

we have x,y,z ranging between 1 to 9..one of them is a perfect square so it should be a 4 or a 9...lets take z=4 so
x+y=16-4=12
and xy+yz+zx=73
or, xy+4(12)=73
or,xy=25
but as all three numbers are integers and a condition is there that any of them are not equal...so xy=25 is not possible
now we take z=9;
x+y=7;
xy+9(x+y)=73
or,xy=10
perfectly possible
so the answer of xyz=90

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Jitendra Kumar   9 years AGO

2,5,9
2*5+5*9+9*2=73

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SANDIPAN CHOUDHURY   9 years AGO

The integers are 2,5,9
And 2*5+5*9+9*2 = 73
2+5+9=16
where 9 is a perfect square.

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Sourabh Prasad   9 years AGO

xy+yz+zx = 73
x+y+z = 16

Therefore 1 number is either 4 or 9.

solving we get this,
9 2 5
9*2*5=90

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manvi Gupta   9 years AGO

(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
x^2+y^2+z^2=110
x=9
y=10
z=1
x*y*z=90

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rakhi kumari   9 years AGO

9+5+2=16

9*5 + 5*2 + 2*9=73

so 9*5*2=90

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Ajinkya Kulkarni   9 years AGO

90

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P.Swapna   9 years AGO

x,y,z in between 1 to 9 so I picked out 9 as one no and the remaining as 2 and 5 by trail and error method so as it satisfies the equations
1)xy+yz+zx=73
2)x+y+z=16

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Abhishek singh   9 years AGO

there will only maximum 3 solution
4,7,5
9,2,5,
9,6,1
which satisfy the addition statement
and only 9,2,5 satisfy the multiplication statement
therefore 9*2*5=90

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kondalarao   9 years AGO

529.
23*23=529
10+18+45=73
5*2*9=90

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Dusi.Lakshmi Harika   9 years AGO

9+5+2=16 and their pair product and sum=73
9*5=45,5*2=10,9*2=18
45+10+18=73
so product=9*5*2=90

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KUMAR HARSH   9 years AGO

(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
16^2=x^2+y^2+z^2+2*73
256-146=x^2+y^2+z^2=110
put x=2,y=5&z=9
xyz=90

Like? Yes (1) | No