Latest Elitmus Aptitude Question SOLUTION: If n+x and n+y both are perfect square and x=18, y=90, then how many values of n will satisfied above condition

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(#M40022341) ELITMUS Numerical Ability question Apptitude Keep an EYE

If n+x and n+y both are perfect square and x=18, y=90, then how many values of n will satisfied above condition

Asked In Elitmus prayas goel (10 years ago)

Solved SHUBHAM KUMAR Read Solution (9)

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manikanta  (10 years ago)

let n+18= a^2 ........(1)
n+90= b^2 ........(2)

b^2 = n+90
= n+18+72
= a^2+72 (from 1)
b^2-a^2 = 72
(b+a)(b-a)=72.......(3)
factorize 72
1*72 (a,b will be fractions)
2*36 [(19-17)(19+17) then substitute a = 17 and b = 19 then n=271]
3*24 (a,b will be fractions)
4*18 [(11+7)(11-7) then substitute a = 7 and b = 11 then n=31]
6*12 [(9+3)(9-3) then substitute a = 3 and b = 9 then n=-9]
8*9 (a,b will be fractions)

Is this solution Helpfull? Yes (77) | No (2)  

ranjeet singh chauhan  (10 years ago)

fOR 3 VALUES OF N.

ie. n=31, n=271, n=-9.

Is this solution Helpfull? Yes (24) | No (3)  

SHUBHAM KUMAR  (10 years ago)

for 3 values of n.
i.e. n=31, n=271, n=-9
for n=31
31+18=49=7
31+90=121=11

for n=271
271+18=289=17
271+90=361=19

for n=-9
-9+18=9 =3
-9+90=81 =9

Is this solution Helpfull? Yes (11) | No (1)  

vaibhav sharma  (10 years ago)

for n=31 n+x=49 and n+y=121
for n=271 n+x=289 and n+y=361

Is this solution Helpfull? Yes (3) | No (6)  

Tanvi  (10 years ago)

only 1 value i.e. n=31

Is this solution Helpfull? Yes (2) | No (16)  

Amit Singh Shekhawat  (10 years ago)

n=31 and n=-9

Is this solution Helpfull? Yes (2) | No (7)  

sravan  (10 years ago)

31+18=49
31+90=121
Are the Perfect squares.
Ans: n=31

Is this solution Helpfull? Yes (1) | No (7)  

vaibhav sharma  (10 years ago)

yes only one solution n=31
for n=271 n+y=351.I wrote 2 soltions earlier by mistake.
only one solution is possible

Is this solution Helpfull? Yes (1) | No (9)  

pawann raj chauhan  (10 years ago)

only one ......n =31
31+18=49 (perfect square of 7)
31+90=121 (perfect sqaure of 11)

Is this solution Helpfull? Yes (1) | No (4)  

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