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


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Could u plz provide explanation

C.
From 1 ) X is an integer =>NSF
From 2) X has atleast one 2,5 and 3 as factors.

1 + 2. X is divisible by 15.

Hi,

This is Data Sufficiency (DS) GMAT quant question. DS questions have 2 statements (1) and (2). Here are the options for DS questions:

(A) Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
(B) Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient
(E) Statements (1) and (2) TOGETHER are NOT sufficient

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Is X divisible by 15?

1. When X is divided by 10, the result is an integer -- X=K*2*5--- NOt sufficient
2. X^2 is a multiple of 30 -- X^2= K1*2*3*5 since X might not be integer..Not sufficeint

Combining both .. sufficient Ans C

With B you can have X = square root (30) also as a possibility, which is not divisible by 15.

I thought the answer is 'B'
second statement says
2. X^2 is a multiple of 30

I guessed this would mean any multiple of 30 which is a square number would satisfy the equation x^2=30n.
for example 900 or 3600.
Please suggest .

hey,
S1: 10 i.e is not divisible but 30 is. 20 isn't and 60 is NS
S2: you said that x^2=30n so:
x^2 can be 30*30 which means that x=30 hence divisible by 15, but

x^2 cab be 30*2 which means that x=root 60 , hence not divisible by 15. NS

combining:

x^2=30A
x=10B

X^2/X=30A/10B
X= 3*(A/B)
since x has 3 in it and from S1 we know that A/B must be 10(0r 2*5) or else it wont be an integer

x=3* 2something*5 something. which means 30;60;90 etc.. allways divisible by 15

10\sqrt{30} doesn't satisfy statement 1. Per statement 1 X has to be ....-20,-10,0,10,20,30... A multiple of 10. 10\sqrt{30} is NOT a multiple of 10.
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Bunuel, please throw some light here,
(c) is right as per many of us but why not (E)?
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Is x divisible by 15?

(1) When x is divided by 10, the result is an integer --> \frac{x}{10}=integer --> x=10*integer. Now, if x=0 (in case integer=0), then the answer is YES but if x=10 (in case integer=1), then the answer is NO. Not sufficient.

From this statement though we can deduce that x is an integer (since x=10*integer=integer).

(2) x^2 is a multiple of 30 --> if x=0, then the answer is YES but if x=\sqrt{30}, then the answer is NO. Not sufficient.

(1)+(2) Since from (1) x=integer then x^2=integer, and in order x^2 to be divisible by 30=2*3*5, x must be divisible by 30 (x must be a multiple of 2, 3 and 5, else how can this primes appear in x^2?), hence x is divisible by 15 too. Sufficient.

Notice that x can be positive, negative or even zero, but in any case it'll be divisible by 30.

Answer: C.

Next, every GMAT divisibility question will tell you in advance that any unknowns represent positive integers (ALL GMAT divisibility questions are limited to positive integers only). So, we edited this question and in the new GMAT Club tests this question reads:

If x is a positive integer, is x divisible by 15?

(1) x is a multiple of 10 --> if x=10, then the answer is NO but if x=30, then the answer is YES. Not sufficient

(2) x^2 is a multiple of 12 --> since x is an integer, then x^2 is a perfect square. The least perfect square which is a multiple of 12 is 36. Hence, the least value of x is 6 and in this case the answer is NO, but if for example x=12*15 then the answer is YES. Not sufficient.

Notice that from this statement we can deduce that x must be a multiple of 3 (else how can this prime appear in x^2?).

(1)+(2) x is a multiple of both 10 and 3, hence it's a multiple of 30, so x must be divisible by 15. Sufficient.

Answer: C.

Hope it's clear.
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