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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   35% (medium)

Question Stats: 67% (01:20) correct 33% (01:19) wrong based on 306 sessions

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If the remainder is 2 when $$x$$ is divided by 5, then is $$x$$ divisible by 7?

(1) $$x$$ is a prime number

(2) $$x + 3$$ is a multiple of 10

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Math Expert V
Joined: 02 Sep 2009
Posts: 55635

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Official Solution:

Statement (1) by itself is insufficient. If $$x$$ is a prime number, then $$x$$ can be 7, 17, 37, and so on. 7 is divisible by 7, but 17 and 37 are not.

Statement (2) by itself is insufficient. If $$x = 7$$, then the answer to the question is yes. If $$x = 17$$ then the answer is no; if $$x = 37$$ then the answer is no.

Statements (1) and (2) combined are insufficient. $$x$$ can still be 7, 17, 37, etc.

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Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. If $$x$$ is a prime number, then $$x$$ can be 7, 17, 37, and so on. 7 is divisible by 7, but 17 and 37 are not.

Statement (2) by itself is insufficient. If $$x = 7$$, then the answer to the question is yes. If $$x = 17$$ then the answer is no; if $$x = 37$$ then the answer is no.

Statements (1) and (2) combined are insufficient. $$x$$ can still be 7, 17, 37, etc.

Hi Brunel, I got the same answer, but it took me more than 3 minutes to confirme my answer. Do you know if is it possible to do the question in a faster way?

Regards,
Gonzalo
Intern  Joined: 18 Apr 2015
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Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. If $$x$$ is a prime number, then $$x$$ can be 7, 17, 37, and so on. 7 is divisible by 7, but 17 and 37 are not.

Statement (2) by itself is insufficient. If $$x = 7$$, then the answer to the question is yes. If $$x = 17$$ then the answer is no; if $$x = 37$$ then the answer is no.

Statements (1) and (2) combined are insufficient. $$x$$ can still be 7, 17, 37, etc.

Hi Bunuel,

Statement (1) Says X is prime. How is one of the answers then 7? 1 is not a prime number please help me understand then how 5(1) +2 is in this range then? I'm likely misunderstanding your given solution.

Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 55635

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stov10 wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. If $$x$$ is a prime number, then $$x$$ can be 7, 17, 37, and so on. 7 is divisible by 7, but 17 and 37 are not.

Statement (2) by itself is insufficient. If $$x = 7$$, then the answer to the question is yes. If $$x = 17$$ then the answer is no; if $$x = 37$$ then the answer is no.

Statements (1) and (2) combined are insufficient. $$x$$ can still be 7, 17, 37, etc.

Hi Bunuel,

Statement (1) Says X is prime. How is one of the answers then 7? 1 is not a prime number please help me understand then how 5(1) +2 is in this range then? I'm likely misunderstanding your given solution.

Thanks

The stem says that the remainder is 2 when x is divided by 5.
(1) says that x is a prime number.

x can be 7 because 7 is a prime and 7 divided by 5 gives the remainder of 2.
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Hi Bunuel

From the question we can make out that x has ones digit of 2 or 7.

1. This eliminates all the nos. with 2 as units digit.
So, as you said the no. could be 7, 17, 37, 57 etc. But none of these, or any of the greater prime nos. with units digit as 7, are divisible by 7.
Hence, sufficient.

2. Statement one is a subset of statement 2, without the "prime no. condition", therefore can also have a no. like 77.
Hence, not sufficient.

Ans: Option 1

Math Expert V
Joined: 02 Sep 2009
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bibinphilips wrote:
Hi Bunuel

From the question we can make out that x has ones digit of 2 or 7.

1. This eliminates all the nos. with 2 as units digit.
So, as you said the no. could be 7, 17, 37, 57 etc. But none of these, or any of the greater prime nos. with units digit as 7, are divisible by 7.
Hence, sufficient.

2. Statement one is a subset of statement 2, without the "prime no. condition", therefore can also have a no. like 77.
Hence, not sufficient.

Ans: Option 1

I don't understand what you mean by the red part.

For (1): x can be 7 so divisible by 7 or say 17, so not divisible by 7. Two different answers not sufficient.
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Bunuel wrote:
If the remainder is 2 when $$x$$ is divided by 5, then is $$x$$ divisible by 7?

(1) $$x$$ is a prime number

(2) $$x + 3$$ is a multiple of 10

Hey Bunuel

Just to understand, x can be 2 also in general and even for answer choice 1. 2 divided by 5 will leave the remainder as 2. Am I missing something?

Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 55635

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gmatlife wrote:
Bunuel wrote:
If the remainder is 2 when $$x$$ is divided by 5, then is $$x$$ divisible by 7?

(1) $$x$$ is a prime number

(2) $$x + 3$$ is a multiple of 10

Hey Bunuel

Just to understand, x can be 2 also in general and even for answer choice 1. 2 divided by 5 will leave the remainder as 2. Am I missing something?

Thanks

Yes, x can be 2, for (1) because 2 divided by 7 gives the remainder of 2.
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When divided by five there's a remainder of 2,and when added with 3 it is divisible by 7.
Math Expert V
Joined: 02 Sep 2009
Posts: 55635

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Rishab30 wrote:
When divided by five there's a remainder of 2,and when added with 3 it is divisible by 7.

What about it? The answer is E, which means that we can have both an YES and a NO answer to the question. For example, if x = 7, then the answer is YES but if x = 67, then the answer is NO.
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