Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Jan 2010
Posts: 109
Location: Calicut, India

A threedigit number is such that when its reverse is subtra [#permalink]
Show Tags
10 Feb 2010, 06:42
8
This post received KUDOS
16
This post was BOOKMARKED
Question Stats:
61% (03:41) correct
39% (02:46) wrong based on 458 sessions
HideShow timer Statistics
A threedigit 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If u think this post is useful plz feed me with a kudo
Last edited by Bunuel on 25 Feb 2014, 07:16, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Solve  Simple Equations Q#1 [#permalink]
Show Tags
10 Feb 2010, 07:00
9
This post received KUDOS
Expert's post
7
This post was BOOKMARKED
cleetus wrote: Plz illustrate how to solve this equation question 1) A threedigit 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: \(100a+10b+c(100c+10b+a)=297\) > \(ac=3\), 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: \(3b=ac\), from above we know \(ac=3\), 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.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: Solve  Simple Equations Q#1 [#permalink]
Show Tags
25 Feb 2014, 05:24
1
This post received KUDOS
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Director
Joined: 03 Aug 2012
Posts: 894
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 threedigit number is such that when its reverse is subtra [#permalink]
Show Tags
19 Apr 2014, 08:39
abc  cba = 297 100a+10b+c  100c  10b  a = 297 99a99c = 297 ac = 3 also, 3b = ac b=1 Numbers abc a1c ac can take (9,6),(8,5),(7,4),(6,3),(5,2),(4,1),(3,0) Hence 7
_________________
Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: A threedigit number is such that when its reverse is subtra [#permalink]
Show Tags
25 May 2015, 08:26
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7449
Location: Pune, India

Re: A threedigit number is such that when its reverse is subtra [#permalink]
Show Tags
25 May 2015, 23:06
cleetus wrote: A threedigit 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 90 = 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)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 07 Jul 2015
Posts: 11

Re: A threedigit number is such that when its reverse is subtra [#permalink]
Show Tags
17 Aug 2015, 00:54
Bunuel wrote: cleetus wrote: Plz illustrate how to solve this equation question 1) A threedigit 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: \(100a+10b+c(100c+10b+a)=297\) > \(ac=3\), 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: \(3b=ac\), from above we know \(ac=3\), 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.



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: A threedigit number is such that when its reverse is subtra [#permalink]
Show Tags
17 Aug 2015, 02:19
sashibagra wrote: Bunuel wrote: cleetus wrote: Plz illustrate how to solve this equation question 1) A threedigit 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: \(100a+10b+c(100c+10b+a)=297\) > \(ac=3\), 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: \(3b=ac\), from above we know \(ac=3\), 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.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 07 Jul 2015
Posts: 11

A threedigit number is such that when its reverse is subtra [#permalink]
Show Tags
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: \(100a+10b+c(100c+10b+a)=297\) > \(ac=3\), 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: \(3b=ac\), from above we know \(ac=3\), 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



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: A threedigit number is such that when its reverse is subtra [#permalink]
Show Tags
06 Oct 2016, 18:45
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A threedigit number is such that when its reverse is subtra
[#permalink]
06 Oct 2016, 18:45







