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I. If x+3 divisible by 3 => x divisible by 3 but it doesn't say that is divisible by 2 also. Not suff II. x+3 odd => x must be even. Alone is not sufficient

I and II say X is an even number (which we know must be divisible by 2) and x divisible by 3. From here we can conclude that x is divisible by 6.

Re: Is the integer X divisible by 6? 1. x+3 is divisible by 3 2. [#permalink]

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12 Jun 2014, 10:10

jackychamp wrote:

Is the integer X divisible by 6? 1. x+3 is divisible by 3 2. x+3 is an odd number.

I get C. As, say x = 6. x+3 = 9 which is odd and divisible by 3.

But what is we put in x as "0". x + 3 is 3 which is also odd and divisible by 3 but not 6.

Any idea what am I missing?

You are answering yourself.

In II) You do not know that X+3 is divisible by 3, so, if you put 0, the answer is no, because 0+3 is odd but is not divisible by 6. However, you can put 6+3=9 that is odd and divisible by 6 (X=6) so, that's why II) is not sufficient. We have found two numbers that fit with the statement but we can not answer the main question.

(1) x + 3 is divisible by 3. This basically means that x is divisible by 3 (x = {a multiple of 3} - 3 = {a multiple of 3}), which is not sufficient to say whether it's divisible by 6.

(2) x + 3 is an odd number. This means that x is even (\(x=odd-3=odd-odd=even\)). Not sufficient.

(1)+(2) x is an even multiple of 3, hence it's a multiple of 6. Sufficient.

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Is the integer x divisible by 6?

(1) x + 3 is divisible by 3 (2) x + 3 is an odd number

In the original condition there is 1 variable and we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D is likely the answer.

In case of 1), x+3=3t(t:some integer) thus x=multiple of 3. If x=3 the answer is no, if x=6 the answer is yes. Therefore the condition is not sufficient. In case of 2), if x+3=odd, x=odd-3=even, x=2 then the answer is no. If x=6 the answre is yes, therefore the condition is not sufficient. Using both 1) & 2) together, if x=multiple of 3 and even, it must be a multiple of 6 and thus the answer is yes. Therefore the answer is C.
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(1) x + 3 is divisible by 3 (2) x + 3 is an odd number

Question asks whether x is divisible by 6 i.e. x is divisible by 3 AND x is divisible by 2.

Statement 1, x + 3 is divisible by 3 => i.e . x is divisible by 3, but no information about x divisible by 2. So insufficient.

Statement 2, x+3 is odd number => i.e. x must be even number. So any even number must be divisible by 2. But no information about x divisible by 3. Clearly insufficient.

combining statement 1 & 2, X is divisible by 3 AND x is divisible by 2. So Answer is D.

[quote="jackychamp"]Is the integer x divisible by 6?

(1) x + 3 is divisible by 3 (2) x + 3 is an odd number

Solution :

Statement 1: Case 1: x=6. We get x to be a divisible of 6.

Case 2: x=15. We get x not to be a divisible of 6. Therefore this statement is not sufficient on its own.

Statement 2: Case 1: If x=10. We get x not to be a divisible of 6. Case 2: If x=12. We get x not to be a divisible of 6. Therefore this statement is not sufficient on its own.

Combining St1 and St2, We get x to be divisible by 6.

(1) x + 3 is divisible by 3 (2) x + 3 is an odd number

Question asks whether x is divisible by 6 i.e. x is divisible by 3 AND x is divisible by 2.

Statement 1, x + 3 is divisible by 3 => i.e . x is divisible by 3, but no information about x divisible by 2. So insufficient.

Statement 2, x+3 is odd number => i.e. x must be even number. So any even number must be divisible by 2. But no information about x divisible by 3. Clearly insufficient.

combining statement 1 & 2, X is divisible by 3 AND x is divisible by 2. So Answer is D.

No its wrong. You are assuming things. Try to get a scenario that makes the statements invalid. Please go through my solution if required. Thanks

I get C. As, say x = 6. x+3 = 9 which is odd and divisible by 3.

But what is we put in x as "0". x + 3 is 3 which is also odd and divisible by 3 but not 6.

Any idea what am I missing?

St 1 (X +3) /3= some integer k this just implies that X has to be a multiple of 3 but it could be exactly 3- in which case X is too small to be divisible by 6 insufficient St 2 X+3 = odd - this just means that X has to be an even number insufficient

St 1 and St 2

Using inferences from St 1 and St 2 - X must be an even multiple of 3- the smallest of which is 6 which is clearly divisible by 6 - any even multiple of 3 is divisible by 6

(1) x + 3 is divisible by 3 (2) x + 3 is an odd number

We need to determine whether x/6 = integer.

Statement One Alone:

x + 3 is divisible by 3.

Statement one is not sufficient to answer the question. If x = 3, then x is not divisible by 6; however, if x = 6, then x is divisible by 6.

Statement Two Alone:

x + 3 is an odd number.

Statement two is not sufficient to answer the question. If x = 2, then x is not divisible by 6; however, if x = 6, then x is divisible by 6.

Statements One and Two Together:

Using statements one and two, we see that x + 3 is an odd multiple of 3, such as 3, 9, 15, etc. Thus, x must be an even multiple of 3. Since all even multiples of 3 are multiples of 6, x/6 is an integer.

Answer: C
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(1) x + 3 is divisible by 3. This basically means that x is divisible by 3 (x = {a multiple of 3} - 3 = {a multiple of 3}), which is not sufficient to say whether it's divisible by 6.

(2) x + 3 is an odd number. This means that x is even (\(x=odd-3=odd-odd=even\)). Not sufficient.

(1)+(2) x is an even multiple of 3, hence it's a multiple of 6. Sufficient.

Answer: C.

Hi Bunuel, Do we need to consider negative integer for statement (1)?
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(1) x + 3 is divisible by 3. This basically means that x is divisible by 3 (x = {a multiple of 3} - 3 = {a multiple of 3}), which is not sufficient to say whether it's divisible by 6.

(2) x + 3 is an odd number. This means that x is even (\(x=odd-3=odd-odd=even\)). Not sufficient.

(1)+(2) x is an even multiple of 3, hence it's a multiple of 6. Sufficient.

Answer: C.

Hi Bunuel, Do we need to consider negative integer for statement (1)?

x could be a negative integer for (1) or/and (2) but it does not affect the answer. For example, when we consider the statements together, we get that x is an even multiple of 3, so x could be ..., -12, -6, 0, 6, 12, ... As you can see x is indeed divisible by 6 for all possible values of x.
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