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

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Manager
Joined: 25 Jan 2010
Posts: 104
Location: Calicut, India
A three-digit number is such that when its reverse is subtra  [#permalink]

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Updated on: 18 Mar 2018, 09:04
9
22
00:00

Difficulty:

75% (hard)

Question Stats:

65% (02:57) correct 35% (03:15) wrong based on 486 sessions

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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

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If u think this post is useful plz feed me with a kudo

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: 50627
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

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10 Feb 2010, 06:00
13
3
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}.

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Director
Joined: 03 Aug 2012
Posts: 744
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
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Re: A three-digit number is such that when its reverse is subtra  [#permalink]

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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
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Re: A three-digit number is such that when its reverse is subtra  [#permalink]

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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.

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Intern
Joined: 06 Jul 2015
Posts: 10
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

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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: 50627
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

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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.
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Joined: 06 Jul 2015
Posts: 10
Re: A three-digit number is such that when its reverse is subtra  [#permalink]

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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]

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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: 1114
A three-digit number is such that when its reverse is subtra  [#permalink]

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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]

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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: 1114
A three-digit number is such that when its reverse is subtra  [#permalink]

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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
A three-digit number is such that when its reverse is subtra &nbs [#permalink] 18 Sep 2018, 17:52
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# A three-digit number is such that when its reverse is subtra

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