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

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

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New post Updated on: 18 Mar 2018, 10:04
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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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Originally posted by cleetus on 10 Feb 2010, 06:42.
Last edited by pushpitkc on 18 Mar 2018, 10:04, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: A three-digit number is such that when its reverse is subtra [#permalink]

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New post 10 Feb 2010, 07:00
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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}.

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

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New post 19 Apr 2014, 08:39
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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New post 25 May 2015, 23:06
1
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.

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

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New post 17 Aug 2015, 00:54
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}.

Answer: C.


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

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New post 17 Aug 2015, 02:19
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}.

Answer: C.


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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 17 Aug 2015, 22:57
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}.

Answer: C.


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

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New post 15 Sep 2017, 00:29
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. :o
Re: A three-digit number is such that when its reverse is subtra   [#permalink] 15 Sep 2017, 00:29
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