mohit11 wrote:Is X divisible by 15?

1)When X is divided by 10, the result is an integer
2)X^2 is a multiple of 30

Source: GMATclub Test

OA:C .. Please explain your answer

Mohit Bhai,

I have seen hundereds of examples ..but i feel plugging in is the easiest and direct method..
WHy becox in real test at the maxu u can get 3 /4 DS of this types dealing with Number theory..so I dont see any harm of using "Plugging In numbers"

St 1: 1)When X is divided by 10, the result is an integer

case 1: x = 20, remainder is zero. But 20 is not Divisible by 15.---No

case 2: X = 30 remainder is zero when divided by 10. Moreover when didvided by 15, remainder is zero. SO divisible by 15--YES

Inconsistent..SO Insufficient!!

St 2 :

case 1: X= 30
X^2 is divisible by 30
and even X is divisble by 15---YES

Case 2: X= Sqrt(30)

X^2 = 30, it is divisible by 30 where as X is NOT divisible by 15 --NO

Again Inconsistent--So Insuficient

So we are left with C or E!!

Lets try x= 30 (which is both divisible by 10 & X^2 is divisible by 30)

Yeah it is very well divisible by 15.

One more: X = 60 (which is both divisible by 10 & X^2 is divisible by 30)
Yeah it is very well divisible by 15.

So pick C

I am also looking for some formula method apart from Plugging numbers....as this method is time consuming!!

That's a great approach, Govi.

We can also solve by considering prime factors.

Is x divisible by 15?

Well, if x were divisible by 15, then x would contain 3 and 5 in its prime factorization.

(1) tells us that x is a multiple of 10. This means x contains 5 in its prime factorization. But we don't know if it has 3. Insufficient.

(2) tells us that x^2 is a multiple of 30. Now, if we knew that x were an integer, then this would mean that x contains 2, 3 and 5 in its prime factorization, and (2) would be sufficient. But as gmatmachoman rightly points out x may easily be a non-integer, such as sqrt 30.
Insufficient.

From (1) we know that x is divisible by 10--thus, x is an integer....choose C.

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For these number property DS questions, if the theory/concepts jump out at you, then solve that way. If not, then pick numbers. But quite often you can pick numbers and use/discover a bit of theory at the same time. In yes/no questions, through picking numbers, you can prove insufficiency by getting different answers (yes vs no). While you can't prove sufficiency, if you keep getting "yes" or keep getting "no" using different kinds of numbers, then you can convince yourself of sufficiency.