Arithmetic mean of two numbers whose sum is equal to 28, is equal to the geometrical mean of two perfect square numbers. Sum of these perfect square number out of given ten option will be

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18 Mar 2015 Arithmetic mean Arithmetic mean of two numbers whose sum is equal to 28, is equal to the geometrical mean of two perfect square numbers. Sum of these perfect square number out of given ten option will be: OPtion
1) 42
2) 45
3) 48
4) 49
5) 51
6) 52
7) 53
8) 56
9) 58
10)60; Correct Option: 7 Best Solution (49)

sheikh shahrukh 9 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 9 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 9 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

Like? Yes (2) | No

Yathiraj 9 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 9 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

Like? Yes (2) | No

Prithwijit Ghosh 9 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

Like? Yes (2) | No

nikita agrawal 9 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 9 years AGO

14^2 = x^2*y^2

2^2+7^2= 53

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Devendra Marghade 9 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)

Like? Yes (1) | No

SAGNIK PAL 9 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.

Like? Yes (1) | No

KALYAN KUMAR REDDY VALLURU 9 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 9 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.

Like? Yes (1) | No

Sakshi Agarwal 9 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 9 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 9 years AGO

49 & 4 are perfect squares

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NESAB JAFAR 9 years AGO

am>=gm

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alety kiranmai 9 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 9 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

Like? Yes (1) | No

Testing Account 9 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 9 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 9 years AGO

take two perfect square as 49 & 4

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SUSHANT KUMAR 9 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 9 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 9 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 9 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 9 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 9 years AGO

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

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PAWAN KUMAR 9 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 9 years AGO

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

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Srinivas 9 years AGO

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

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SHREY KASERA 9 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 9 years AGO

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

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Yallapu Uday tarun kumar 9 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 9 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 9 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 9 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 9 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 9 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 9 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 9 years AGO