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Manager  Joined: 02 Aug 2007
Posts: 203
Schools: Life
When positive integer p is divided by 7 the remainder is 2.  [#permalink]

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Difficulty:   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.
SVP  Joined: 07 Nov 2007
Posts: 1569
Location: New York
Re: When integer p is divided by 7  [#permalink]

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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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Intern  Joined: 15 Jan 2009
Posts: 44
Schools: Marshall '11
Re: When integer p is divided by 7  [#permalink]

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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?
Senior Manager  Joined: 26 May 2008
Posts: 361
Schools: Kellogg Class of 2012
Re: When integer p is divided by 7  [#permalink]

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wcgmat,

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

Cheers,
Unplugged
Manager  Joined: 02 Aug 2007
Posts: 203
Schools: Life
Re: When integer p is divided by 7  [#permalink]

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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!
Intern  Joined: 15 Jan 2009
Posts: 44
Schools: Marshall '11
Re: When integer p is divided by 7  [#permalink]

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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?
Director  Joined: 29 Aug 2005
Posts: 736
Re: When integer p is divided by 7  [#permalink]

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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?
Manager  Joined: 23 Jan 2013
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Schools: Berkeley Haas
GMAT Date: 01-14-2015
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Re: When integer p is divided by 7  [#permalink]

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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 !!!
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9330
Location: Pune, India
Re: When integer p is divided by 7  [#permalink]

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 55668
Re: When positive integer p is divided by 7 the remainder is 2.  [#permalink]

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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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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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GRE 1: Q169 V154 Re: When positive integer p is divided by 7 the remainder is 2.  [#permalink]

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