sheikh shahrukh   10 years AGO

let the number be a and b,
now according to given conditions...
a+b=28
and
(a+b)/2 = sqrtof(a*b).......... since geometric mean is equal to square root of product of two number....
28/2=14=sqrtof(a*b)
squaring both sides
14*14=7*2*7*2=a*b
the possible combinations are 49*4=a*b
as 49 and 4 are perfect squares so,
49+4=53
so option 7 is correct

Like? Yes (9) | No (1)  

Supriya Mondal   10 years AGO

Sum of the two number is 28
So arithmetic mean of this two number is =14
Let the perfect square numbers are p1 and p2
then geometrical mean=sqrt(p1*p2)
then we can write,
sqrt(p1*p2)=14
p1*p2=196
so, p1=4 and p2=49 which are perfect square
So sum of p1 and p2=4+49=53
So, option 7)53 is the right answer

Like? Yes (4) | No (1)  

SHAHEEN   10 years AGO

Arithmetic mean of two numbers whose sum=A+B=28
Arithmetic mean of two numbers =geometrical mean of two perfect square numbers
SO
(A+B)/2=SQRT(XY)
BY SOLVING
XY=14^2=>7^2*2^ 2
Sum of these perfect square numbers=49+4
==>53 ans is option 7

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Yathiraj   10 years AGO

If A&B are the two numbers whose sum=28
then (A+B)/2 = 14 = Geo Mean (X, Y)
X & Y are the two perfect square numbers.
There are 2 numbers and hence Geo Mean = (X * Y)^1/2
=> (X * Y) = 14^2 = 196
From above, we get 4 & 49 as the perfect square numbers whose product is 196
X=4
Y=49
and Hence, X+Y => 53

Option 7.

Like? Yes (3) | No (1)  

MRITUNJAY   10 years AGO

a+b/2=(ab)^1/2
28/2=(ab)^1/2
14=(ab)^1/2
196=ab
49*4=ab
sum is 49+4=53
option 7

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Prithwijit Ghosh   10 years AGO

x+y=28
AM of x,y =1/2(x+y)
=14
=gm of a,b
=√ab=14
Ab=196
=49*4

Answer 49+4=53

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nikita agrawal   10 years AGO

a+b=28

(a+b)/2= under root(pq) // let p and q are perfect square number

then 28/2 = under root(pq)

square(14)=pq

14*14 =pq

2*7*2*7 =pq

thn (2*2)* (7*7) = pq

hence, p=4, q=49
adding p and q
we get 53 answer

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RAKESH   10 years AGO

14^2 = x^2*y^2

2^2+7^2= 53

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Devendra Marghade   10 years AGO

If two numbers are x & y ,then
Their Arithmetic Mean=(x+y)/2= 28/2=14 and
Geometric Mean= Sqrt(x*y)
As Arithmetic Mean= Geometric Mean
Sqrt(x*y)=14, x*y=196
The two square numbers x & y can be 4 & 49
So the Sum= 4+49=53
Ans=Option 7)

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SAGNIK PAL   10 years AGO

given, x + y = 28
A.M. = (x + y)/2= 14

14= ?(xy)
xy=196
LCM of 196,
2�2�7�7
the no.s are 4 and 49
sum of the perfect sq 53 ans.

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KALYAN KUMAR REDDY VALLURU   10 years AGO

1,2,4,7,14,28,49,98,196, are factors of 196.
sqrt(ab)=14
ab=196
so a+b = either 197 or 53.

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Surit Datta   10 years AGO

(n1 + n2)/2 = 14
which is arithmetic mean
so according to the problem,
sqrt(n1 * n2) = 14
so,
n1 * n2 = 196
so ,
n1 = 49
n2 = 4
so summation is 53
so option 7
that's it.

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Sakshi Agarwal   10 years AGO

average of two numbers is their sum divided by 2 i.e., 14 . Now geometric mean of two perfect squares is the product of these two perfect squares. we know 14=7*2,
implies no.s are 49 and 4. their sum is 63.

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sindhura   10 years AGO

(a+b)/2=sqrt(x*y)=>14=sqrt(xy),if x=4 & y=49 then x+y=53

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Harish Reddy Namala   10 years AGO

49 & 4 are perfect squares

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NESAB JAFAR   10 years AGO

am>=gm

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alety kiranmai   10 years AGO

Arithmetic mean of two numbers whose sum=A+B=28
Arithmetic mean of two numbers =geometrical mean of two perfect square numbers
SO
(A+B)/2=SQRT(XY)
XY=14^2=>7^2*2^ 2
Sum of these perfect square numbers=49+4
==>53 ans is option 7

Like? Yes (1) | No   

shareef   10 years AGO

sum = a+b = 28
then A.M = (a+b)/2 = 14
AM=GM
so GM = sqrt(x*y) = 14
x*y = 196
x,y are two perfect squares so choose perfect squares...
then x,y are 49 and 4
so ans
x+y = 49+4 =53

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Testing Account   10 years AGO

a+b/2=squareroot of xy then a+b/2=squareroot ofxy then solve we getab=196 which is multiple of 49&4 perfect square no.and sum is 49+4=53

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Josepheena Joseph   10 years AGO

Let the 2 suare nos be a,b
Given a x b = (28/2)^2 = 196
49 x 4 = 196
Therefore sum = 49+4 = 53

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CHAYAN KUMAR   10 years AGO

take two perfect square as 49 & 4

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SUSHANT KUMAR   10 years AGO

a+b=28
(a+b)/2=sqrt(c.d)
c.d=196
so c=4
d=49
hence c+d=53

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darshana kumrawat   10 years AGO

(a+b)/2=sqrt(p^2+q^2)=14
p*q=14
p=2, q=7
p^2=4, q^2=49
therefore no. is 53

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Vishakha Tinkhede   10 years AGO

let x+y = 28 and acording to given condition,
let (x+y)/2 = (ab)^1/2
=>ab = 196 and since a and b are perfect squares that'why a = 4 and b = 49 and vice versa ..and hence 4+49 = 53

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shivam goyal   10 years AGO

arithmetic mean be = ((X+Y)/2)

geometric mean be = sqrt(ZK)

equate both of them.

we get (ZK= 196)

then, comparing you will get 53 is the answer...

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KUMAR HARSH   10 years AGO

let first no. is x and 2'nd is y for AM
let 1'st perfact square no. is O and 2'nd perfact square no is S for GM
by Q,
x+y=28 & (x+y)/2=sqrt(O*S)
so, 14=O*S because O & S is perfact square no.
put O=7 & S=2
7*2=14
7^2+2^2=49+4=53
ans is 53

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PRASHANT KUMAR   10 years AGO

28/2=(xy)^.5
so factor of 14 is 7 and 2 hence sqr7+sqr2=53

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PAWAN KUMAR   10 years AGO

Sum = 28 ,so A.M. = 14 = G.M.
So, product of nos = 14^2 = 196
On looking at the options, we could say that the nos are 49 and 4. so thier sum = 53. Ans

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madhusudhana   10 years AGO

Using AP, GP formulas and first 10 prefect square numbers.

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Srinivas   10 years AGO

A m is 28/2=14
Gm =14*14=4*49
49+4=53

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SHREY KASERA   10 years AGO

let two no. be x, y respectively....& a ,c be two perfect sq. no.
As given,
x+y=28
(x+y)/2=root of a*c
root of a*c=196
a & c should be 4 & 49
sum of a & c=53

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praveen kumar   10 years AGO

14= sqrt(49*4)
s0 49+4 = 53

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Yallapu Uday tarun kumar   10 years AGO

let the two numbers be a & b
sum of a & b is 28
given Arithmetic mean of two numbers is equal to the geometrical mean of two perfect square numbers
and let the two perfect square numbers be x & y
so, (a+b)/2=sqrt(x^2*y^2)
14=xy[since a+b=28]
there is only one possibility of xy=14 ie., x=7 & y=2
and sum is x^2+y^2=53

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Thirupathi Reddy   10 years AGO

x+y/2=xy
given x+y=28
Hence xy=14
factors of 14 are 2,7
2^2+7^2=53

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Ranajit Banerjee   10 years AGO

let no.s be a and b
so a.m=a+b/2=28/2=14
this is equal to g.m of the perfect square numbers
and g.m=root(x*y)
so x*y=196
x and y will be 49 and 4 so sum=49+4=53

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siddharth prakash singh   10 years AGO

since sum of two numbers=28
therefore mean=14
so,GM=14
let numbers be a and b
so ab=196 (as GM=14)
196=4*49
therefore required nos a and b be 4 and 49.
their sum=53

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shivom pandey   10 years AGO

as geometric mean comes out to be 14*14 which says that numbers are 49 and 4 whose sum equals to 53

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Hemant Singh   10 years AGO

** a mean =28/2=14
** let two perfect sq nos be x=a^2 and y=b^2
** g mean=Sq.root(xy) i.e, 14
** so xy=14x14=196
** and 196=2x2x7x7
** (2x2) + (7x7)=53

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Abhik Das   10 years AGO

simple the AM of the two numbers will be 28/2=14
so the geometric mean will be(14*14)=196
so the two numbers will be=49 and 4 which are perfect square
So the sum is (49+4)=53

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CH NEERAJ   10 years AGO

(p.q)^1/2=14 => p.q=196 => p=49=7^2 and q=4=2^2.

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ABHINAV PUSHPAM   10 years AGO

28/2=√4*49
So 4+49= 53
Option 7)

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Jitendra Kumar   10 years AGO

(49*4)^(0.5)=14
hence 49+4
53

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mukund   10 years AGO

a+b=28
(a+b)/2=(x*y)^1/2
x*y=196
196=49*4
49+4=53 answer

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deepak mistry   10 years AGO

a+b=28--> a+b/2=14--->2*7-for perfect square---->4+49=53

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RAVI KUMAR   10 years AGO

ar mean =28/2=14
14 is geometric mean of to perfect square number
14=sqrt(196
=>sqrt(49*4)
sum=49+4
=53

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surbhi mittal   10 years AGO

let numbers be x and y
(xy)^ (1/2) = 14
xy= 196
so x and y will be 49 and 4
so sum is 53

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Bikash sahu   10 years AGO

196=2*2*7*7=4+49=53

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Jay parmar   10 years AGO

Option 7 is correct

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Jaspalsingh Parmar   10 years AGO

Option 7 is correct

Like? Yes (1) | No