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# When positive integer p is divided by 7 the remainder is 2.

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Manager
Joined: 02 Aug 2007
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When positive integer p is divided by 7 the remainder is 2.  [#permalink]

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Updated on: 05 Jun 2014, 01:17
1
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65% (hard)

Question Stats:

58% (02:04) correct 42% (02:21) wrong based on 314 sessions

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When positive integer p is divided by 7, the remainder is 2. Is p divisible by 8?

(1) p is divisible by 2 and 3

(2) p<100

M05-20

Originally posted by xALIx on 01 Feb 2009, 13:23.
Last edited by Bunuel on 05 Jun 2014, 01:17, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: When integer p is divided by 7  [#permalink]

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01 Feb 2009, 13:57
2
1
x-ALI-x wrote:
When integer p is divided by 7, the remainder is 2. Is p divisible by 8?

1. p is divisible by 2 and 3
2. p < 100

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

p= 7k+2

p values when k=0,1,2,3,4,..

p=2,9,16,23,30,37,44,51,58,65,72,79,86,93,100

1)
p is divided by 2 and 3 = p is dived by 6
possible values are
30 -- remainder when divided by 8 --6
72-- remainder when divided by 8 --0.

not sufficient

2)
p<100

not sufficient.

commbined not sufficient see statement1

E
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Re: When integer p is divided by 7  [#permalink]

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01 Feb 2009, 19:17
how did you get from this step:
p is divided by 2 and 3 = p is dived by 6
To this step:
possible values are
30 -- remainder when divided by 8 --6
72-- remainder when divided by 8 --0.

Could someone explain the logic behind it?
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Re: When integer p is divided by 7  [#permalink]

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01 Feb 2009, 23:44
wcgmat,

of the sample values mentioned, there are only 2 numbers - 30, 72, that are divisible by both 2 and 3

Cheers,
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Re: When integer p is divided by 7  [#permalink]

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02 Feb 2009, 17:38
x2suresh wrote:
x-ALI-x wrote:
When integer p is divided by 7, the remainder is 2. Is p divisible by 8?

1. p is divisible by 2 and 3
2. p < 100

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

p= 7k+2

p values when k=0,1,2,3,4,..

p=2,9,16,23,30,37,44,51,58,65,72,79,86,93,100

1)
p is divided by 2 and 3 = p is dived by 6
possible values are
30 -- remainder when divided by 8 --6
72-- remainder when divided by 8 --0.

not sufficient

2)
p<100

not sufficient.

commbined not sufficient see statement1

E

Great explanation Suresh!!! I've always considered it 7p+2, but you're correct in noting it as 7k+2.
Thanks!
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Re: When integer p is divided by 7  [#permalink]

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04 Feb 2009, 15:47
unplugged wrote:
wcgmat,

of the sample values mentioned, there are only 2 numbers - 30, 72, that are divisible by both 2 and 3

Cheers,
Unplugged

Ok, I see that in this example, 30 and 72 is obtained when we count out a bunch of numbers that fit the remainder equation that was provided. But when you encounter remainder type of problems like this, do you always just calculate out a bunch of sample numbers according to the equation provided? Is this the best strategy to use? Or are there mathematical ways to obtain numbers like 30 and 72?
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Posts: 736
Re: When integer p is divided by 7  [#permalink]

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12 Feb 2009, 14:24
x2suresh wrote:
x-ALI-x wrote:
When integer p is divided by 7, the remainder is 2. Is p divisible by 8?

1. p is divisible by 2 and 3
2. p < 100

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

p= 7k+2

p values when k=0,1,2,3,4,..

p=2,9,16,23,30,37,44,51,58,65,72,79,86,93,100

1)
p is divided by 2 and 3 = p is dived by 6
possible values are
30 -- remainder when divided by 8 --6
72-- remainder when divided by 8 --0.

not sufficient

2)
p<100

not sufficient.

commbined not sufficient see statement1

E

As p is even, one can shorten the iteration by calculating p for even values of k.
Any more shortcuts?
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Re: When integer p is divided by 7  [#permalink]

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04 Jun 2014, 20:20
I got the answer by listing down multiples of 6 and ( multiples of 7 ) + 2 till i found a match for 2 numbers is there a faster way of doing this ?

Since in the gmat time matters the most !!!
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Re: When integer p is divided by 7  [#permalink]

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04 Jun 2014, 20:55
1
2
shelrod007 wrote:
I got the answer by listing down multiples of 6 and ( multiples of 7 ) + 2 till i found a match for 2 numbers is there a faster way of doing this ?

Since in the gmat time matters the most !!!

When you are given different remainders - 2 when divided by 7 and 0 when divided by 6 (using stmnt 1), you have to find the first such common number. Some tips and tricks of this method are discussed here:
http://www.veritasprep.com/blog/2011/05 ... s-part-ii/

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Re: When positive integer p is divided by 7 the remainder is 2.  [#permalink]

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05 Jun 2014, 01:18
When positive integer p is divided by 7, the remainder is 2. Is p divisible by 8?

When positive integer p is divided by 7 the remainder is 2: $$p=7q+2$$, so p can be: 2, 9, 16, 23, 30, 37, 44, 51, 58, 65, 72, ...

(1) p is divisible by 2 and 3 --> p is a multiple of 6 --> p can be 30 (answer NO) or 72 (answer YES). Not sufficient.

(2) p < 100. Clearly insufficient.

(1)+(2) p can still be 30 (answer NO) or 72 (answer YES). Not sufficient.

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Re: When positive integer p is divided by 7 the remainder is 2.  [#permalink]

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24 Feb 2016, 16:25
if P is divided by 7 then remainder is 2, then what will be the remainder if p is divided by 8

Statement 1:

p is divisible by 2 and 3
so we can say that p is divisible by all the multiples of 6

now we have to take the multiple of 6 which when divided by 7 gives remainder 2.
so the values are 30, 72 and so on

and when we divide 30 with 8 we get 6 as remainder but when we divide 72 with 8 we get o as remainder.

so this statement is clearly insufficient

Statement 2: p < 100

clearly insufficient as p can be any value and thus can give any remainder from 0 to 9 when divided by 8

Combining both the statements

Clearly insufficient as we already know that there are 2 possible values of p under 100 and both are giving different remainder( i.e 6 and 0 resp.)

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Re: When positive integer p is divided by 7 the remainder is 2.  [#permalink]

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22 Mar 2016, 03:43
Choose 72 and 30 as the two numbers and we can discard both the statements
Hence E
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Re: When positive integer p is divided by 7 the remainder is 2.  [#permalink]

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19 Oct 2018, 10:05
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Re: When positive integer p is divided by 7 the remainder is 2.   [#permalink] 19 Oct 2018, 10:05
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