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# Is x+1 a factor of 12?

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General Discussion
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divisor, multiple and factor can be tricky when we are short of time...best is to write factors..

Question is Is x+1 = 1,2,3,4,6,12?
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Bunuel wrote:
agnok wrote:
Is x+1 a factor of 12?

1. x+1 is even
2. x+1 is a factor of 2 and 3

Good question.

(1) x+1 is even --> clearly insufficient, x+1 could be 2 or 30.

(2) x+1 is a factor of 2 and 3 --> 2 and 3 are consecutive integers, consecutive integers are co-prime, which means that they do not share ANY common factor but 1 (for example 5 and 6, two consecutive integers share only one common factor: 1). So as x+1 is a factor of BOTH 2 and 3 then x+1=1 and 1 is a factor of 12. Sufficient.

Bunuel,

The reason I chose E was because of the case where x = 5

x + 1 - even
x + 1 = 6 is factor of both 2 & 3

But 12 is not a factor of 6
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eaakbari wrote:
Bunuel wrote:
agnok wrote:
Is x+1 a factor of 12?

1. x+1 is even
2. x+1 is a factor of 2 and 3

Good question.

(1) x+1 is even --> clearly insufficient, x+1 could be 2 or 30.

(2) x+1 is a factor of 2 and 3 --> 2 and 3 are consecutive integers, consecutive integers are co-prime, which means that they do not share ANY common factor but 1 (for example 5 and 6, two consecutive integers share only one common factor: 1). So as x+1 is a factor of BOTH 2 and 3 then x+1=1 and 1 is a factor of 12. Sufficient.

Bunuel,

The reason I chose E was because of the case where x = 5

x + 1 - even
x + 1 = 6 is factor of both 2 & 3

But 12 is not a factor of 6

6 is NOT a factor (divisor) of neither 2 nor 3.
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Yes, I mixed multiple and factors and made a massive mess.

Thanks Bro. Much appreciated.
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Re: Is x+1 a factor of 12? [#permalink]
Hi everyone!

I might've missed something. But I got a question.

Isn't statement (1) contradicting statement (2)?

(1) -> x+1 = even

(2) -> x+1 is a factor of 2 and 3. (Which gives us x+1 = 1)

Wouldn't that mean that statement (1) is false?

Again, I might've missed something.
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Re: Is x+1 a factor of 12? [#permalink]
Hiho wrote:
Hi everyone!

I might've missed something. But I got a question.

Isn't statement (1) contradicting statement (2)?

(1) -> x+1 = even

(2) -> x+1 is a factor of 2 and 3. (Which gives us x+1 = 1)

Wouldn't that mean that statement (1) is false?

Again, I might've missed something.

Not at all

6,12,18,24,36...

all are even numbers which have factors as 2 & 3
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Re: Is x+1 a factor of 12? [#permalink]
eaakbari wrote:
Hiho wrote:
Hi everyone!

I might've missed something. But I got a question.

Isn't statement (1) contradicting statement (2)?

(1) -> x+1 = even

(2) -> x+1 is a factor of 2 and 3. (Which gives us x+1 = 1)

Wouldn't that mean that statement (1) is false?

Again, I might've missed something.

Not at all

6,12,18,24,36...

all are even numbers which have factors as 2 & 3

I'm not quite sure that I understand.

x+1 is a factor of both 2 and 3. The only factor 2 and 3 shares is 1. Therefore x+1 = 1.

Now what I don't understand is why statement (1) says that x+1 is even, when statement 2 gives us the solution that makes its odd.
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Re: Is x+1 a factor of 12? [#permalink]
Hiho wrote:
eaakbari wrote:
Hiho wrote:
Hi everyone!

I might've missed something. But I got a question.

Isn't statement (1) contradicting statement (2)?

(1) -> x+1 = even

(2) -> x+1 is a factor of 2 and 3. (Which gives us x+1 = 1)

Wouldn't that mean that statement (1) is false?

Again, I might've missed something.

Not at all

6,12,18,24,36...

all are even numbers which have factors as 2 & 3

I'm not quite sure that I understand.

x+1 is a factor of both 2 and 3. The only factor 2 and 3 shares is 1. Therefore x+1 = 1.

Now what I don't understand is why statement (1) says that x+1 is even, when statement 2 gives us the solution that makes its odd.

Yes , you are correct.

Maybe statement B should read 'x+1 has factors 2 and 3'

Its probably not a good source.

Let Bunuel solve this confusion...XD
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Re: Is x+1 a factor of 12? [#permalink]
eaakbari wrote:
Hiho wrote:
eaakbari wrote:

Not at all

6,12,18,24,36...

all are even numbers which have factors as 2 & 3

I'm not quite sure that I understand.

x+1 is a factor of both 2 and 3. The only factor 2 and 3 shares is 1. Therefore x+1 = 1.

Now what I don't understand is why statement (1) says that x+1 is even, when statement 2 gives us the solution that makes its odd.

Yes , you are correct.

Maybe statement B should read 'x+1 has factors 2 and 3'

Its probably not a good source.

Let Bunuel solve this confusion...XD

I think it would be better if (1) would read ' x+1 = odd' instead.

Your statement would make the question unsolvable because x+1 would have too many possible outcomes.
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Bunnel according to statement1 X+1 is even but in our second statement we have derived X+1=1 which is an odd number .In real GMAT questions i do u think this kind of contradiction will be there in the two statements given ???
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Re: Is x+1 a factor of 12? [#permalink]
Hiho wrote:
Hi everyone!

I might've missed something. But I got a question.

Isn't statement (1) contradicting statement (2)?

(1) -> x+1 = even

(2) -> x+1 is a factor of 2 and 3. (Which gives us x+1 = 1)

Wouldn't that mean that statement (1) is false?

Again, I might've missed something.

x+1 is a factor of both 2 and 3 that means the sum of x+1 can divide both 2 and 3 three. You see three no value common that divide both 2 and 3 other than 1 .
12 is also divisible by 1.
Ans. B
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skamal7 wrote:
Bunnel according to statement1 X+1 is even but in our second statement we have derived X+1=1 which is an odd number .In real GMAT questions i do u think this kind of contradiction will be there in the two statements given ???

On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

(1) should read: x+1 is odd.

Hope it's clear.
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Re: Is x+1 a factor of 12? [#permalink]
Option B.
S1: If x+1 is even
x+1 could be 2 in which case answer is yes.
x+1 could be 14 in which case answer is no.
Not suff.

From S2:x+1 could only be 1,2 or 3 each of which is a factor of 12.So answer is yes.Suff.

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Re: Is x+1 a factor of 12? [#permalink]
agnok wrote:
Is x+1 a factor of 12?

(1) x+1 is even
(2) x+1 is a factor of 2 and 3

Statement I is insufficient:

x + 1 = 8, x + 1 = 4

Statement II is sufficient:

If x + 1 is a factor of 2 and 3 it has to be equal to 1. Hence x + 1 is a factor of 12
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Re: Is x+1 a factor of 12? [#permalink]
Excellent Question
here statement 1 is not sufficient as x+1 can be 8 or 2 or 500
statement 2 tells us that x+1 is a factor of both 2 and 3
hence x+1=1 => x=0
thus as one is the FACTOR of every number => sufficient
hence B
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Is x+1 a factor of 12? [#permalink]
Is x+1 a factor of 12?

(1) x+1 is even
(2) x+1 is a factor of 2 and 3

Silly mistakes all round, but gaps in my knowledge have been brought to light.

First I rewrote as is 12/(x+1) = int?

Stat.(1) I didn't put a constraint on the potential range of factors

Stat.(2) I actually interpreted as "x+1 is a factor of 2 and 3" therefore x is a factor of 6.

Applying the rules put forward by Bunuel:

(2) Two consecutive integers will never share the same prime factors, therefore the GCF of two consecutive integers is 1
Since x+1 is a factor of two consecutive integers (2 and 3), x+1 must be 1.

1 is a factor of 12. Thus Stat.(2) --> Sufficient
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Re: Is x+1 a factor of 12? [#permalink]
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