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

 It is currently 08 Dec 2019, 14:02

### 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

# What is the remainder when 99009900990099000065 is divided by 32

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 12 Aug 2015
Posts: 2549
Schools: Boston U '20 (M)
GRE 1: Q169 V154
What is the remainder when 99009900990099000065 is divided by 32  [#permalink]

### Show Tags

30 Nov 2016, 19:09
1
3
00:00

Difficulty:

5% (low)

Question Stats:

86% (00:56) correct 14% (02:12) wrong based on 78 sessions

### HideShow timer Statistics

What is the remainder when 99009900990099000065 is divided by 32

A)zero
B)one
C)two
D)three
E)four

_________________
Manager
Joined: 28 Jun 2016
Posts: 205
Concentration: Operations, Entrepreneurship
Re: What is the remainder when 99009900990099000065 is divided by 32  [#permalink]

### Show Tags

30 Nov 2016, 21:00
stonecold wrote:
What is the remainder when 99009900990099000065 is divided by 32

A)zero
B)one
C)two
D)three
E)four

99009900990099000065 = 99009900990099000064 + 1 = 32q+1

Therefore remainder = 1

B
Intern
Joined: 28 May 2015
Posts: 1
Re: What is the remainder when 99009900990099000065 is divided by 32  [#permalink]

### Show Tags

30 Nov 2016, 21:07
Ans B

thats the answer i got.. even digit answers are ruled out .. only 1 and 3 remain.. ans comes to be 1
Senior Manager
Joined: 13 Oct 2016
Posts: 354
GPA: 3.98
Re: What is the remainder when 99009900990099000065 is divided by 32  [#permalink]

### Show Tags

03 Dec 2016, 06:37
2
2
stonecold wrote:
What is the remainder when 99009900990099000065 is divided by 32

A)zero
B)one
C)two
D)three
E)four

Imagine we have number

N = abcdefgh … vwxyz where abc… are single digits.

Now we need to find remainder when we divide this number by $$2^x$$

In order to do so we need to pay attention only to last $$x$$ digits. If $$x=1$$ ---> $$2^1$$ (z), if $$x=2$$ ---> $$2^2=4$$ (yz) (divisibility rule for 4 is just a single case) and so on.

Back to our question:

$$32 = 2^5$$ and we need to take into account only last 5 digits of 99009900990099000065.

Discarding the preceding zeros we have:

65/32 remainder is 1.

Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1323
Location: Viet Nam
Re: What is the remainder when 99009900990099000065 is divided by 32  [#permalink]

### Show Tags

03 Dec 2016, 11:49
stonecold wrote:
What is the remainder when 99009900990099000065 is divided by 32

A)zero
B)one
C)two
D)three
E)four

Simply, 99009900990099000000=99009900990099 * 10^6 is divisible by 2^6=64.

Hence, the remainder of 99009900990099000065/32 = the remainder of 65/32=1.
_________________
Board of Directors
Joined: 17 Jul 2014
Posts: 2492
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
What is the remainder when 99009900990099000065 is divided by 32  [#permalink]

### Show Tags

03 Dec 2016, 12:03
stonecold wrote:
What is the remainder when 99009900990099000065 is divided by 32

A)zero
B)one
C)two
D)three
E)four

we could easily eliminate few choices...
it can't be zero, as 32 multiplied by any number would not yield another number with units digit equal to 5.
Moreover, it can't be any EVEN number as a remainder, because odd - even = odd.
C and E are out.

between B and D:
32 * xx2 - then one
32 * xx1 - then three

to be divisible by 32, it must be divisible by 2 four times.
99009900990099000000 is clearly divisible by 32.
64 is divisible by 32 too
therefore, 99009900990099000064 is divisible by 32. therefore, one is the remainder.
Non-Human User
Joined: 09 Sep 2013
Posts: 13727
Re: What is the remainder when 99009900990099000065 is divided by 32  [#permalink]

### Show Tags

27 Sep 2018, 23:31
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: What is the remainder when 99009900990099000065 is divided by 32   [#permalink] 27 Sep 2018, 23:31
Display posts from previous: Sort by