Latest Elitmus Aptitude Question SOLUTION: It is given that n+x and n+y both are perfect square. and x=18 & y=90. How many such number exist for n ? a) 1 b)3 c) don't know d)none

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(#M40037984) ELITMUS Numerical Ability question Keep an EYE

It is given that n+x and n+y both are perfect square. and x=18 & y=90. How many such number exist for n ?
a) 1
b)3
c) don't know
d)none

Asked In Elitmus Rajat (9 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

Pranami Buragohain  (9 years ago)

n+18 = a^2
n+90 = b^2
subtract the two
b^2 - a^2 = 72
(b-a)(b+a) = 72
Look at factors of 72
1*72
2*36
3*24
4*18
6*12
8*9

How many of these have an a and b such that (b-a) is the small number and (b+a) is the large?
b-a = 1
b+a = 72
add the two
2b = 73 (no... needs to be whole numbers)
b-a = 2
b+a = 36
2b = 38
b = 19, a = 17, b^2 = 361, n + 90 = 361 so n = 271
n should also equal 17^2 - 18 = 271 (so that's 1)

we notice the sum of the factors must be even and the average of the factors is b

3*24 sum is 27
4*18 sum is 22, the average is 11
b = 11
n = 11^2 - 90 = 31
a = b - small factor = 11-4 = 7
check : 31+18 = 49 = 7^2 (so that's 2)

6*12 sum is 18, average is 9
b = 9, a = 9-6 = 3
n= 9^2 - 90 = -9
-9 + 18 = 9 = 3^2 (that's 3)

8*9 sum is odd

Is this solution Helpfull? Yes (23) | No (1)  

amrita kumari  (9 years ago)

b) 3
31, -9, 271

Is this solution Helpfull? Yes (13) | No (6)  

Awantika singh  (9 years ago)

how should we know that there are 3 such no. -like we can go on couinting after 271?Where should we stop.Option could be D.none

Is this solution Helpfull? Yes (9) | No (3)  

subhash kumar  (9 years ago)

@PRANAMI BURAGOHAIN.. your solution was very helpful... Thanks!!!

Is this solution Helpfull? Yes (5) | No   

Riya Banerjee  (9 years ago)

Ans) (a) 1

Is this solution Helpfull? Yes (1) | No (5)  

RAJESH YADAV  (9 years ago)

a) 1

31 + 18 = 49
31 + 90 = 121

Is this solution Helpfull? Yes (1) | No (3)  

priyanka kumari  (9 years ago)

b) 31,126,271

Is this solution Helpfull? Yes (1) | No (12)  

Kaustubh  (9 years ago)

a) 49 and 121

Is this solution Helpfull? Yes | No (3)  

Kumar Vikash  (9 years ago)

49 and 121,
9 and 81 where n= -9

Is this solution Helpfull? Yes | No (2)  

LOKESH RANJAN  (9 years ago)

c,as we didn't find the actual no.

Is this solution Helpfull? Yes | No   

nilanjan das  (9 years ago)

the difference between two square is 72.now u hv to find the suc no's of square diffrnce 72.answer wil be 2

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Ranjeet  (9 years ago)

3--31,-9,271

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