Took an online CAT an encountered a DS problem that I have

Question

Took an online CAT an encountered a DS problem that I have been dreading 
Can someone help me with strategies to kill these types of problems because I think I can master this stuff.

Ques: Is N / 18 an integer?

 1) 5N / 18 is an integer

 2) 3N / 18 is an integer

Thank you so much.

SimaQ · Answer

Do prime factorization for such problems:

Is n/18 an interger or
is n/2*3*3 an interger?

1)5*n/18 is an interger or,
5*n/2*3*3 is an interger, this means n must have 2*3*3 as its factors and n/18 must be an interger... sufficient

2)3*n/18 is an interger or,

3*n/2*3*3....cancel out 3
n/2*3 is an interger... so n could be 6 for example or 18.... not sufficient

A

Fig · Answer

(C) for me

N/18 integer? Stat1 5*N / 18 = k <=> N = 18/5 * k where k is an integer 2 cases : o If k = 5*i (i an integer), then N/18 is an integer o If k != 5*i (i an integer), then N/18 is not an integer INSUFF. Stat2 3*N / 18 = j <=> N = 6*j 2 cases : o If j=-2, -1, 1 or 2, then N/18 is not an integer o If |j| > 2 or j=0, then N/18 is an integer INSUFF. Both 1 and 2 o N = 18/5 * k o N = 6*j That inplies, 18/5 * k = 6*j <=> k = 5/3 * j As k must be an integer, we are force to have j = 3*l where l is an integer. We are in the second case of stat2 with j=0 or |j| > 2. Thus, N/18 is an integer. SUFF.

chud01 · Answer

thanks fig. You are correct. I am having a little trouble understanding your notation - Can you dumb it down for me?

Thanks.

kevincan · Answer

(1) N is either a multiple of 18 (and therefore an integer) or an non-integer of the form 18k/5 where k is an integer than is not a multiple of 5. So N/18 could be an integer or a non-integer

NOT SUFF

(2) N/6 is an integer- N is a multiple of 6- N/18 may or may not be an integer.

NOT SUFF

(1) and (2) From (2), we know that N is an integer. (1) tells us that 
N is a multiple of 18 and therefore N/18 is an integer.

C

chud01 · Answer

So 1 shows it is either an integer multiple of 18 or a non integer 18/5 and 2 shows that it is an integer. Combined, it's an integer and it is a multiple of 18

Thanks!

SimaQ · Answer

Could somebody explain, what i missed in my method?

Fig · Answer

it's (5*n) that has 3*2*2 as prime factors and not n

SimaQ · Answer

But if 5n is divisable by 18, n must have 3*3*2 it does not really matter whether it has another 5 or 7 or whatever....

Fig · Answer

We can take an example

If n=18/5, then 5*n/18 = 1, an integer, but n is not

SimaQ · Answer

We can take an example

If n=18/5, then 5*n/18 = 1, an integer, but n is not

Yeah i am aware of that, just i am interested why we could not solve it by prime factorization... Anyway, i would use prime factorization on any "multiple", "factor", "divisable" type question... Guess it is not good to use it on "is it an interger" questions...

Took an online CAT an encountered a DS problem that I have

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