GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 31 Mar 2020, 01:36

### 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

# A three-digit number is such that when its reverse is subtra

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

### Hide Tags

Manager
Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India
A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

Updated on: 18 Mar 2018, 09:04
10
25
00:00

Difficulty:

65% (hard)

Question Stats:

67% (02:57) correct 33% (03:14) wrong based on 372 sessions

### HideShow timer Statistics

A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?

(A) 4
(B) 5
(C) 7
(D) 8
(E) 9

Originally posted by cleetus on 10 Feb 2010, 05:42.
Last edited by pushpitkc on 18 Mar 2018, 09:04, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 62366
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

10 Feb 2010, 06:00
14
4
cleetus wrote:
Plz illustrate how to solve this equation question
1) A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?

A) 4
B) 5
C) 7
D) 8

Hi, welcome to the Gmat Club.

Solution to your question is as follows:

Three digit number $$abc$$ can be represented as $$100a+10b+c$$, its reverse number would be $$cba$$ or $$100c+10b+a$$.

Given: $$100a+10b+c-(100c+10b+a)=297$$ --> $$a-c=3$$, this gives us 7 values for $$a$$ and $$c$$: {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}.

Also given: $$3b=a-c$$, from above we know $$a-c=3$$, hence $$3b=3$$ --> $$b=1$$, only one value for $$b$$.

So total of 7 such numbers are possible: {916}{815}{714}{613}{512}{411}{310}.

_________________
##### General Discussion
Director
Joined: 03 Aug 2012
Posts: 649
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

19 Apr 2014, 07:39
1
abc - cba = 297

100a+10b+c - 100c - 10b - a = 297

99a-99c = 297

a-c = 3

also, 3b = a-c

b=1

Numbers abc

a1c

ac can take (9,6),(8,5),(7,4),(6,3),(5,2),(4,1),(3,0)

Hence 7
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10228
Location: Pune, India
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

25 May 2015, 22:06
2
1
cleetus wrote:
A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?

(A) 4
(B) 5
(C) 7
(D) 8

You can also use reasoning to solve it.

"thrice the tens digit is equal to the difference between its hundreds and units digits."

The difference between any two digits cannot be more than 9-0 = 9. So the tens digit can be 3 at most.
But if the difference between the other two digits is 9, their subtraction will give us something around 900. We need something around 300 so the tens digit must be 1 and the difference between the other two digits must be 3.

So the first such number you can have is 310. If you subtract 013 out of it, you get 297 - Correct.
Next you can have is 411. If you subtract 114 out of it, you will get 297 - Correct.
Next you can have is 512. If you subtract 215 out of it, you will get 297 - Correct.
and so on goes the pattern till you have 916.

So in all, you have 7 numbers.

_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Joined: 06 Jul 2015
Posts: 9
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

16 Aug 2015, 23:54
Bunuel wrote:
cleetus wrote:
Plz illustrate how to solve this equation question
1) A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?

A) 4
B) 5
C) 7
D) 8

Hi, welcome to the Gmat Club.

Solution to your question is as follows:

Three digit number $$abc$$ can be represented as $$100a+10b+c$$, its reverse number would be $$cba$$ or $$100c+10b+a$$.

Given: $$100a+10b+c-(100c+10b+a)=297$$ --> $$a-c=3$$, this gives us 7 values for $$a$$ and $$c$$: {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}.

Also given: $$3b=a-c$$, from above we know $$a-c=3$$, hence $$3b=3$$ --> $$b=1$$, only one value for $$b$$.

So total of 7 such numbers are possible: {916}{815}{714}{613}{512}{411}{310}.

this gives us 7 values for a and c: {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}.

Can you please write how we get 7 possible values? I understood your solution but only 7 possible probability part is unclear.
Math Expert
Joined: 02 Sep 2009
Posts: 62366
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

17 Aug 2015, 01:19
sashibagra wrote:
Bunuel wrote:
cleetus wrote:
Plz illustrate how to solve this equation question
1) A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?

A) 4
B) 5
C) 7
D) 8

Hi, welcome to the Gmat Club.

Solution to your question is as follows:

Three digit number $$abc$$ can be represented as $$100a+10b+c$$, its reverse number would be $$cba$$ or $$100c+10b+a$$.

Given: $$100a+10b+c-(100c+10b+a)=297$$ --> $$a-c=3$$, this gives us 7 values for $$a$$ and $$c$$: {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}.

Also given: $$3b=a-c$$, from above we know $$a-c=3$$, hence $$3b=3$$ --> $$b=1$$, only one value for $$b$$.

So total of 7 such numbers are possible: {916}{815}{714}{613}{512}{411}{310}.

this gives us 7 values for a and c: {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}.

Can you please write how we get 7 possible values? I understood your solution but only 7 possible probability part is unclear.

We got that a - c = 3: the positive difference between the hundreds and units digits of the number is 3. If a = 9 (max possible value of a), then c is 6, if a = 8, then c = 5, ..., if a = 3, then c = 0 (min possible value of c).

Hope it's clear.
_________________
Intern
Joined: 06 Jul 2015
Posts: 9
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

17 Aug 2015, 21:57
Quote:
Hi, welcome to the Gmat Club.

Solution to your question is as follows:

Three digit number $$abc$$ can be represented as $$100a+10b+c$$, its reverse number would be $$cba$$ or $$100c+10b+a$$.

Given: $$100a+10b+c-(100c+10b+a)=297$$ --> $$a-c=3$$, this gives us 7 values for $$a$$ and $$c$$: {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}.

Also given: $$3b=a-c$$, from above we know $$a-c=3$$, hence $$3b=3$$ --> $$b=1$$, only one value for $$b$$.

So total of 7 such numbers are possible: {916}{815}{714}{613}{512}{411}{310}.

Quote:
this gives us 7 values for a and c: {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}.

Can you please write how we get 7 possible values? I understood your solution but only 7 possible probability part is unclear.

Quote:
We got that a - c = 3: the positive difference between the hundreds and units digits of the number is 3. If a = 9 (max possible value of a), then c is 6, if a = 8, then c = 5, ..., if a = 3, then c = 0 (min possible value of c).

Hope it's clear.

I am sorry, it was really a silly question and I shouldn't asked it. It was very easy topic but I was just thinking it complicatedly so it was unclear to me. now it's clear , thanks
Intern
Joined: 10 Aug 2017
Posts: 17
GMAT 1: 720 Q48 V41
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

14 Sep 2017, 23:29
Hmm, had 6 been one of the choices, I would have fallen for it.
I basically used the same process to solve this problem -

ABC - CBA = 297, so Here I saw that A>C, A-C = 3
3B= |A-C|

Hence 1 is the only possible value for 1.

And possible values for A & C are: (9,6), (8,5), (7,4) (6,3) (5,2), (4,1) (3,0)

I was initially looking for 6, because I didn't think C could be 0 as CBA would be a two digit number..
but nowhere in the question stem say that the reverse of the three digit number ABC also has to be a three digit number.
VP
Joined: 07 Dec 2014
Posts: 1240
A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

17 Sep 2018, 17:00
1
cleetus wrote:
A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?

(A) 4
(B) 5
(C) 7
(D) 8
(E) 9

the difference between any 3-digit number xyz and it's it's reverse, zyx,
when divided by 99, gives the difference between x and z
e.g., 297/99=3
so if x=9, then z=6, and xyz=916 (we know the tens digit must be 1)
so we have:
916
815
714
613
512
411
310
7 possible values
C
Intern
Joined: 01 Jul 2018
Posts: 7
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

17 Sep 2018, 17:31
How do you say that if any 3 digit number and its reverse is divided by 99, gives the difference between hundredth and units digits? How did you arrive at that?

Posted from my mobile device
VP
Joined: 07 Dec 2014
Posts: 1240
A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

18 Sep 2018, 17:52
Achuuuuuuu wrote:
How do you say that if any 3 digit number and its reverse is divided by 99, gives the difference between hundredth and units digits? How did you arrive at that?

Posted from my mobile device

Hi Achuuuuuuu,
If you look at any two reversed 3-digit numbers,
you'll see that the difference between
them is always a multiple of 9 (in this case, 297).
When you divide this multiple by 9, you'll find
the quotient is always a multiple of 11 (in this case, 33).
When you divide that multiple by 11,
the quotient will always equal the difference between the
hundreds and units digits (in this case, 3).
Dividing the initial difference by 99 is a short cut.
I hope this helps.
gracie
VP
Joined: 24 Nov 2016
Posts: 1353
Location: United States
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

### Show Tags

08 Feb 2020, 07:48
cleetus wrote:
A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?

(A) 4
(B) 5
(C) 7
(D) 8
(E) 9

ABC-CBA=297
100A+10B+C-100C-10B-A=297…99A-99C=297…A-C=3
3B=A-C…3B=3…B=1
A-C=3: A>1>C…3≤A≤9…9-3+1=7

Ans (C)
Re: A three-digit number is such that when its reverse is subtra   [#permalink] 08 Feb 2020, 07:48
Display posts from previous: Sort by

# A three-digit number is such that when its reverse is subtra

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

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