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

It is currently 24 Aug 2019, 13:21

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

q is a three-digit number, in which the hundreds digit is greater than

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

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
B
Joined: 08 Jul 2019
Posts: 5
Location: India
q is a three-digit number, in which the hundreds digit is greater than  [#permalink]

Show Tags

New post 10 Jul 2019, 01:10
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

34% (02:48) correct 66% (03:26) wrong based on 50 sessions

HideShow timer Statistics

q is a three-digit number, in which the hundreds digit is greater than the units digit, and the units digit is equal to the tens digit. If 10\(99\)-q is divisible by 9, then what is the number of possible values of q?
a)4
b)5
c)6
d)9
e)10

PS its 10^99 -q
Manager
Manager
avatar
S
Joined: 08 Jan 2018
Posts: 98
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: q is a three-digit number, in which the hundreds digit is greater than  [#permalink]

Show Tags

New post 10 Jul 2019, 01:37
Let the q = 100x + 10y +z
where x >z and y = z
Other condition: \(10^{99}\) - q is divisible by 9
=> Remainder when 10^{99} divided by 9 : \(\frac{1^{99}}{9}\)= 1 (Remainder)
So, the \(\frac{q}{9}\) should also have 1 as a remainder.
then only the number is divisible by 9.

Thus, going through possible combinations, we get following numbers which when divided by 9 leaves a remainder of 1:
100,433,622,766,811,955

Thus q can have 6 possible values.

Please hit kudos if you like the solution.
Manager
Manager
avatar
S
Joined: 06 Feb 2019
Posts: 107
Re: q is a three-digit number, in which the hundreds digit is greater than  [#permalink]

Show Tags

New post 10 Jul 2019, 04:33
RajatVerma1392, I really didn't get how you've figured out the possible solutions.

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 24 Oct 2017
Posts: 32
Location: India
GMAT 1: 710 Q48 V39
GPA: 3.39
GMAT ToolKit User CAT Tests
Re: q is a three-digit number, in which the hundreds digit is greater than  [#permalink]

Show Tags

New post 11 Jul 2019, 00:14
Please help:

If 10^99q needs to be divisible by 9 -> q must be divisible by 9.

Which means the digits of q must add up to a multiple of 9. The possible numbers with yxx format (y>x) are 522, 711, 855, 900 -> 4 numbers. What am I doing wrong here? TIA
Intern
Intern
avatar
B
Joined: 26 Oct 2010
Posts: 13
q is a three-digit number, in which the hundreds digit is greater than  [#permalink]

Show Tags

New post 11 Jul 2019, 09:01
2
the question says that if (10^99 - Q) is divisible by 9, what are the possible values of Q.

So, we need to figure out the values of Q such that (10^99 - Q) is divisible by 9.

The above equation can be written as (10^99)/9 - Q/9. In other words, the reminder for equation must be 0.

Now, for the 1st term, we can use the reminder theorem. It states that if f(x) is divided by x-a, the reminder is f(a).

So, 10^99/9 can be written as 10^99 / (10 - 1). hence the reminder is f(1) = (1)^99 = 1. So, the reminder of the first term is 1.

Now, the reminder of the 2nd term (Q/9) should also be 1 so that the reminder of the entire equation is 0.

for Q we totally have 45 options: x00 to x88. among that, we need to find out in how many options the 3 numbers add to 10 or 19 or 28.

for x00: only 100
for x11: only 811
for x22: only 622
for x33: only 433
for x44: none
for x55: only 955
for x66: only 766
for x77: none
for x88: none

for totally 6 values.

Hope it is clear.

Bunuel, EgmatQuantExpert Please let us know if there is a shorter procedure. This is way too time consuming for the GMAT.
Manager
Manager
avatar
B
Joined: 27 Mar 2017
Posts: 63
Re: q is a three-digit number, in which the hundreds digit is greater than  [#permalink]

Show Tags

New post 06 Aug 2019, 20:15
No matter how I try to solve this, I have to look into all the possible ways the number XYY can be written, which is too time consuming.

Is this even GMAT worthy ?
GMAT Club Bot
Re: q is a three-digit number, in which the hundreds digit is greater than   [#permalink] 06 Aug 2019, 20:15
Display posts from previous: Sort by

q is a three-digit number, in which the hundreds digit is greater than

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





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