Latest Elitmus Aptitude Question SOLUTION: ABC is a right-angle triangle with sides R1, R2 and R3 such that no sides are even simultaneously. If 102 is added to all sides and then squared we get S1, S2, S3 (Sn=square of (Rn

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(#M40152532) ELITMUS Numerical Ability question APTITUDE Keep an EYE

ABC is a right-angle triangle with sides R1, R2 and R3 such that no sides are even simultaneously. If 102 is added to all sides and then squared we get S1, S2, S3 (Sn=square of (Rn+102)). If T= S1+S2+S3.
Then, which is always true for T.
1. divisible by 2 but not by 4
2. divisible by 4 not by 8
3. divisible by 8 not by 4
4. none of the above

Asked In Elitmus raksha singh (8 years ago)

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Rahul Navariya  (8 years ago)

divisible by 2 but not by 4

letR1= 3 R2=4 R3=5 (because no side of right angle triangle same)
add (102) in R1 R2&R3 and then squire and at add them so
[(105)*(105) + 106*106 + 107*107]=33710 that divisable by 2 but not by 4

Is this solution Helpfull? Yes (27) | No (5)  

Abhishek Mohanty  (8 years ago)

ANS-(4) none of the above

T=(R1+102)^2 + (R2+102)^2 + (R3+102)^2
T= R1^2 + R2^2 + R3^2 + [(102^2 + 102^2 + 102^2) + (2*R1*102 + 2*R2*102 + 2*R3*102)].

Now the expression inside the square bracket is always divisible by 4 and 2.

But if R1, R2, R3 are three odd numbers then their squares are also odd and also the sum of three odd numbers is always odd.

Hence R1^2 + R2^2 + R3^2 may be odd so the total expression may be odd hence they might not be divisible by 2, 4 , or 8.

Is this solution Helpfull? Yes (3) | No (8)  

Abhishek jha  (8 years ago)

ans: None of the above..
coz if we take right angled triangle then generally it is impossible to take all side as odd..
if we want to solve this question logically then 1. odd+odd+odd=odd, 2. odd+102(even)=odd, 3.odd*odd=odd.so it is not divisible by 2 . bt it may or may not divisible by 4 & 8.. bt there are no such a option like this.. so answer will be (NONE OF THESE)..

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chhaya  (8 years ago)

@ raksha singh plz tell me ,is it no sides are even simultaneously or no two sides

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NAVEEN  (8 years ago)

which one is the right answer plz explain

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satyam  (8 years ago)

divisible by 4 not by 8

taken R1=2
R2=3
R3=5

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Poonam  (8 years ago)

2.divisible by 4 but not by 8.

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avinash kumar jha  (8 years ago)

this pair is impossible.that's why option(4).

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RAKESH RANJAN  (8 years ago)

I think answer is option d.
As question says that R1,R2,R3 are not even it means it is odd.
Because if we add odd to even then result is odd,and squaring of odd will give odd.
And odd is not divisble by 2,4,8.

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shilpa  (7 years ago)

1. 102*3+3+4+5

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Rajat Tripathi  (7 years ago)

divisible by 2 but not by 4

S1+S2+S3 = S3+S3 (Uing pythagoras theorm)
=> 2S3

Which is divisible by 2 .

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