Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 02:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# M05-20

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56255

### Show Tags

16 Sep 2014, 00:25
1
9
00:00

Difficulty:

55% (hard)

Question Stats:

60% (02:03) correct 40% (02:25) wrong based on 126 sessions

### HideShow timer Statistics

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) $$p \lt 100$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 56255

### Show Tags

16 Sep 2014, 00:25
1
1
Official Solution:

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. This statement tells that $$p$$ is a multiple of 6, so $$p$$ could be 30 (answer NO) or 72 (answer YES). Not sufficient.

(2) $$p \lt 100$$. Clearly insufficient.

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

_________________
Manager
Joined: 31 Oct 2011
Posts: 50
Location: India
GMAT 1: 660 Q48 V32
GPA: 3.56
WE: Programming (Computer Software)

### Show Tags

28 Sep 2016, 10:11
Is there an algebraic solution to this, rather than having to write the first 10 possible values of p?
Intern
Joined: 12 Sep 2016
Posts: 12

### Show Tags

11 Jan 2017, 18:03
rajarams wrote:
Is there an algebraic solution to this, rather than having to write the first 10 possible values of p?

Experts - Please suggest if this can be solved by some other method

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 56255

### Show Tags

11 Jan 2017, 21:59
ankur2710 wrote:
rajarams wrote:
Is there an algebraic solution to this, rather than having to write the first 10 possible values of p?

Experts - Please suggest if this can be solved by some other method

Thanks

Check here: when-positive-integer-p-is-divided-by-7-the-remainder-is-75299.html
_________________
Director
Joined: 14 Feb 2017
Posts: 702
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GPA: 2.61
WE: Management Consulting (Consulting)

### Show Tags

09 Dec 2018, 16:20
When positive integer p is divided by 7 the remainder is 2.

Algebraically this means
Step 1. p/7 = Q +2/7 (p divided by 7 equals some quotient + remainder 2 (always express over divisor))
Step 2. multiply by 7
7*(p/7 = Q +2/7)
P = 7Q +2 where Q can be 0
_________________
Goal: Q49, V41

+1 Kudos if you like my post pls!
Intern
Joined: 04 Jun 2019
Posts: 5

### Show Tags

30 Jun 2019, 14:18
I understand the step in (1) where the numbers come out to be 30 and 72 because they fit the criteria, but what does the remainders 72 and 30 when they're divided by 8 have to do with it? Nowhere in the questions does it mention that the remainder of p/8 has to be 2.

Though, I do think it makes sense that (1) does not suffice because 30 and 72 could both be answers, so isn't sufficient.

Am I on the right track?

Posted from my mobile device
Re: M05-20   [#permalink] 30 Jun 2019, 14:18
Display posts from previous: Sort by

# M05-20

Moderators: chetan2u, Bunuel