GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 10 Dec 2018, 12:44

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

# If ‘p’ is a positive integer, for what minimum value of ‘p’ is

Author Message
TAGS:

### Hide Tags

Manager
Joined: 07 Jun 2017
Posts: 175
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
If ‘p’ is a positive integer, for what minimum value of ‘p’ is  [#permalink]

### Show Tags

25 Oct 2017, 22:42
1
6
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:16) correct 24% (01:50) wrong based on 130 sessions

### HideShow timer Statistics

If ‘$$p$$’ is a positive integer, for what minimum value of ‘$$p$$’ is [$$7 * 10^p + 4p$$] divisible by 9?

A. 3
B. 5
C. 11
D. 14
E. 19

_________________

Regards,
Naveen
email: nkmungila@gmail.com
Please press kudos if you like this post

Intern
Joined: 08 Jul 2017
Posts: 5
If ‘p’ is a positive integer, for what minimum value of ‘p’ is  [#permalink]

### Show Tags

25 Oct 2017, 23:09
A number is divisible by 9 if the sum of all of its digits is divisible by 9.
Example- 126783 is divisible by 9 since the sum of its digits is 27, which is divisible by 9.

Here (7*10^p + 4p) can be seen as made up of the parts 7*10^p and 4p.
For any value of p, 7*10^p will only have one non zero digit and that will be 7 itself. (Followed by p number of zeroes)

4p on the other hand depends on the value of p.
We go by plugging in options. The correct answer is 5, so I’ll prove it works for that. You should do option A first.

Consider option B. p=5
4p=20
Then 700000+20 will have just 7 and 2 as non zero digits. So the sum of all the digits will be 9, which is divisible by 9.

Sent from my iPhone using GMAT Club Forum mobile app
Senior SC Moderator
Joined: 22 May 2016
Posts: 2201
If ‘p’ is a positive integer, for what minimum value of ‘p’ is  [#permalink]

### Show Tags

26 Oct 2017, 15:28
nkmungila wrote:
If $$p$$ is a positive integer, for what minimum value of $$p$$ is $$7 * 10^p + 4p$$ divisible by 9?

A. 3
B. 5
C. 11
D. 14
E. 19

We need a multiple of 9. So the number's nonzero digits must total 9 or a multiple of 9.

The key is the term +$$4p$$

7 * 10 to ANY power (70; 7,000; 7,000,000) leaves one nonzero integer: 7
7 + 4p's digits must = 9 / multiple of 9

So $$4p$$ must, e.g., equal 2 or 11 or 20 or 38. . . to yield a multiple of 9, thus:
7 + 2 = 9
7 + 3 + 8 = 18

$$10^{p}$$ does not matter.

Answer choices, checking only to see if 4p + 7 = multiple of 9

A) p = 3
(4)(3) = 12
(1 + 2 + 7) = 10, and (1 + 0 = 1)
Not divisible by 9. NO
Number = $$7 * 10^3 + (4)(3)= 7,012$$

B) p = 5
(4)(5) = 20
7 + 2 + 0 = 9
That works. YES
Number = $$7 * 10^5 + (4)(5)= 70,020$$

C. 11. (7 + 4*11) = 51. NO

D. 14. (7 + 4*14) = 63. YES

E. 19. (7 + 4*19) = 83. NO

Answers B and D work. But the prompt asks for the minimum value of p: 5 < 14

Senior Manager
Joined: 07 Jul 2012
Posts: 378
Location: India
Concentration: Finance, Accounting
GPA: 3.5
Re: If ‘p’ is a positive integer, for what minimum value of ‘p’ is  [#permalink]

### Show Tags

26 Oct 2017, 18:13
1
A number is divisible by 9 when the sum of all of its digits is divisible by 9.

7*$$10^p$$= 70, 700, 7000....... (for p= 1,2,3......)

Now 7+4p should be divisible by 9

(A) 7+4*3= 19
(B) 7+4*5= 27 (Divisible by 9)

_________________

Kindly hit kudos if my post helps!

Intern
Joined: 09 Dec 2015
Posts: 6
Re: If ‘p’ is a positive integer, for what minimum value of ‘p’ is  [#permalink]

### Show Tags

26 Oct 2017, 18:23
This is little bit time saving.

When 7*10^p is divided by 9 reminder will be 7 (always). Now if (7*10^p +4p) is divisible with then 4p/9 reminder should be 2 so, addition of both reminder (7+2=9) will divisible by 9.

Now if p=3 then 4p=12 reminder (4p/9) is 3 this means at p=3 not possible here.

If p=5 then 4p=20, reminder 2 so, this is the correct Answer.

Continue with option 3 , 4 and 5.

Sent from my Lenovo K8 Plus using GMAT Club Forum mobile app
Non-Human User
Joined: 09 Sep 2013
Posts: 9097
Re: If ‘p’ is a positive integer, for what minimum value of ‘p’ is  [#permalink]

### Show Tags

17 Nov 2018, 00:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If ‘p’ is a positive integer, for what minimum value of ‘p’ is &nbs [#permalink] 17 Nov 2018, 00:28
Display posts from previous: Sort by