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

 It is currently 12 Dec 2019, 11:30

### 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

# Positive integer m is defined such that m=10n−36. Positive integer k

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59712
Positive integer m is defined such that m=10n−36. Positive integer k  [#permalink]

### Show Tags

12 Feb 2017, 14:27
1
8
00:00

Difficulty:

85% (hard)

Question Stats:

60% (02:32) correct 40% (02:42) wrong based on 174 sessions

### HideShow timer Statistics

Positive integer m is defined such that $$m=10^n−36$$. Positive integer k is defined such that k equals the sum of the digits of integer m. For which of the following values of n is k a multiple of 5?

A. 107
B. 108
C. 109
D. 110
E. 111

_________________
Director
Joined: 05 Mar 2015
Posts: 978
Re: Positive integer m is defined such that m=10n−36. Positive integer k  [#permalink]

### Show Tags

12 Feb 2017, 21:20
1
2
Bunuel wrote:
Positive integer m is defined such that $$m=10^n−36$$. Positive integer k is defined such that k equals the sum of the digits of integer m. For which of the following values of n is k a multiple of 5?

A. 107
B. 108
C. 109
D. 110
E. 111

Last two digits are 64

and the rest digits of m will be 9's
so how many 9's...its n-2 nos. of 9
suppose n=4 or 10^n= 10^n =10000
then 10000-36 = 9964
thus sum will be 2*9 +6+4= 28
Lets check options
(a) n=107 thus sum = 9*105+6+4 =945+10=955
(b) n=108 thus sum = 9*106+6+4 =954+10=964
(c) n=109 thus sum = 9*107+6+4 =963+10=973
(d) n=110 thus sum = 9*108+6+4 =972+10=982
(e) n=111 thus sum = 9*109+6+4 =981+10=991

only option (a) is resulting as 955 ,divisible by 5

Ans A
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1683
Location: India
Re: Positive integer m is defined such that m=10n−36. Positive integer k  [#permalink]

### Show Tags

12 Feb 2017, 21:33
m = 10^n - 36

k = sum of digits of m.

n = 2 --> m = 64
n = 3 --> m = 964
n = 4 --> m = 9964
n = 5 --> m = 99964

The last 2 digits of m is 6 and 4 and 6 + 4 = 10.
The number of 9's in m = value of n - 2

For k to be a multiple of 9, the number of 9's in 'm' must be a multiple of multiple of 5.

A. 107 --> 105 9's

Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 275
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE: Information Technology (Consulting)
Re: Positive integer m is defined such that m=10n−36. Positive integer k  [#permalink]

### Show Tags

12 Feb 2017, 21:39
Bunuel wrote:
Positive integer m is defined such that $$m=10^n−36$$. Positive integer k is defined such that k equals the sum of the digits of integer m. For which of the following values of n is k a multiple of 5?

A. 107
B. 108
C. 109
D. 110
E. 111

For any n>2 $$10^n-36$$ will have last two digits as 64, sum of which is divisible by 5.

for n=3 m=964, n=4 m=9964. So m has (n-2)number of 9 in it.

Only option A gives n-2 as multiple of 5.
Intern
Joined: 03 Feb 2017
Posts: 25
Re: Positive integer m is defined such that m=10n−36. Positive integer k  [#permalink]

### Show Tags

30 Jul 2017, 22:12
$$10^n -36$$ gives 6 and 4 at tens and unit place respectively and rest of the digits are $$9$$

$$6 + 4 = 10$$ which is a multiple of 5 already. So, to make the sum multiple of 5, we need atleast five 9s (or in multiple of 5) along with 64 to make the sum multiple of 5 as $$9+9+9+9+9=45$$.

Only answer choice A give 105 nines (9s in multiple of 5) and leaves two slots for 64 to fit in
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: Positive integer m is defined such that m=10n−36. Positive integer k  [#permalink]

### Show Tags

01 Aug 2017, 17:13
Bunuel wrote:
Positive integer m is defined such that $$m=10^n−36$$. Positive integer k is defined such that k equals the sum of the digits of integer m. For which of the following values of n is k a multiple of 5?

A. 107
B. 108
C. 109
D. 110
E. 111

Since m is a positive integer, we see that the least integer value of n is 2.

If n = 2, we see that m = 10^2 - 36 = 100 - 36 = 64.

If n = 3, we see that m = 10^3 - 36 = 1,000 - 36 = 964.

If n = 4, we see that m = 10^4 - 36 = 10,000 - 36 = 9,964.

If n = 5, we see that m = 10^5 - 36 = 100,000 - 36 = 99,964.

We see that if n > 2, m is the number consisting of a sequence of 9s followed by 64. In fact, the number of 9s is 2 less than n. For example, if n = 5, we have a sequence of three 9s followed by 64. Thus k, the sum of the digits of m, is the sum of these 9s and the digits 6 and 4, i.e., k = 9(n - 2) + 6 + 4 or k = 9(n - 2) + 10.

Since 10 is already a multiple of 5, in order for k to be a multiple of 5, 9(n - 2) also has to be a multiple of 5. Since 9 isn’t a multiple of 5, we know that (n - 2) must be a multiple of 5. This means that the units digit of n must be either 2 or 7. Of the answer choices given, only 107 has the desirable units digit, so choice A is the answer.

_________________

# Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Senior Manager
Joined: 02 Apr 2014
Posts: 462
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
Re: Positive integer m is defined such that m=10n−36. Positive integer k  [#permalink]

### Show Tags

11 Jan 2018, 06:41
Let us find pattern of k, when m = $$10^n - 36$$

suppose n = 4, then m = 10000 - 36 = 9964
suppose n = 4, then m = 100000 - 36 = 99964

so sum of digits = k = $$(n-2) * 9 + 10$$ => 10 is already multiple of 5 => we have to check if $$(n-2)$$ is multiple of 5
going by choices, if we fit choice A, n = 107, n - 2 = 105 (which is multiple of 5), we have found the answer (A)
Re: Positive integer m is defined such that m=10n−36. Positive integer k   [#permalink] 11 Jan 2018, 06:41
Display posts from previous: Sort by

# Positive integer m is defined such that m=10n−36. Positive integer k

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne