Divisibility DS

Question

DS

ywilfred · Answer

St1:
N is divisible by 11. If N = 11m, then N^2-N = 121m^2 - 11m = m(121m-11). So N^2-N is divisible by 12 only if m is a multiple of 12. Insufficient.

St2:
N is divisible by 19. If N = 19q, then N^2-N = 361q^2 - 19q = q(361q-19). So N^2-N is divisible by 19 only if q is a multiple of 19. Insufficient.

Using both, N is a multiple of 209. N = 209a. so N^2-N is divisible by 12 only if a is a multiple of 12. Insufficient.

Ans E

Ravshonbek · Answer

Is N^2-N divisible by 12, we have to say YES or NO

N^2-N=N(N-1)=(N-1)N

As u can see N-1 and N are two consequtive numbers.
I think non of the multiples of 11 or 19 can be multiple of 12. So N cannot be multiple of 12.

1. N is divisible by 11. now start plugging 11,22, 33, 44, or any other mulitple of 11. it gives u 10*11, 21*22 or so. sufficient to say NO

2. N is divisible by 19, now start doin the same 19, 38 or so. 18*19, 37*38,... or so. non of these products are divisible by 12 so sufficient to say No to the queston.

I think it is then sufficient to say NO by using each statment alone 


any ideas.

Fig · Answer

For 1, u could try: o N = 11*12... N*(N-1) = 11*12 * (11*12 - 1) .... divisable by 12 o N = 11.... N*(N-1) = 11*10.... not divisable by 12 For 2, u could try o N = 19*12... N*(N-1) = 19*12 * (19*12 - 1) .... divisable by 12 o N = 19.... N*(N-1) = 19*18.... not divisable by 12 For 1 & 2, u could try o N = 19*11*12 o N = 19*11 So, E it is

dahcrap · Answer

The question here is more abt whether n = 4 or n = multiples of 12. Being a multiple of 11 or 19 or both does not answer the question. So E

Divisibility DS

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