Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score. Mar 27 03:00 PM PDT  04:00 PM PDT Join a free live webinar and learn the winning strategy for a 700+ score on GMAT & the perfect application. Save your spot today! Wednesday, March 27th at 3 pm PST Mar 29 10:00 PM PDT  11:00 PM PDT Right now, their GMAT prep, GRE prep, and MBA admissions consulting services are up to $1,100 off. GMAT (Save up to $261): SPRINGEXTRAGMAT GRE Prep (Save up to $149): SPRINGEXTRAGRE MBA (Save up to $1,240): SPRINGEXTRAMBA Mar 30 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Jan 2010
Posts: 104
Location: Calicut, India

A threedigit number is such that when its reverse is subtra
[#permalink]
Show Tags
Updated on: 18 Mar 2018, 10:04
Question Stats:
66% (02:57) correct 34% (03:16) wrong based on 490 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 (E) 9
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
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.




Math Expert
Joined: 02 Sep 2009
Posts: 53795

Re: A threedigit number is such that when its reverse is subtra
[#permalink]
Show Tags
10 Feb 2010, 07:00
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: Ultimate GMAT Quantitative Megathread  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




Director
Joined: 03 Aug 2012
Posts: 703
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9007
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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 07 Jul 2015
Posts: 9

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: 53795

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: Ultimate GMAT Quantitative Megathread  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: 9

Re: 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



Intern
Joined: 10 Aug 2017
Posts: 17

Re: A threedigit number is such that when its reverse is subtra
[#permalink]
Show Tags
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, AC = 3 3B= AC 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: 1160

A threedigit number is such that when its reverse is subtra
[#permalink]
Show Tags
17 Sep 2018, 18:00
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 (E) 9 the difference between any 3digit 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 threedigit number is such that when its reverse is subtra
[#permalink]
Show Tags
17 Sep 2018, 18:31
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: 1160

A threedigit number is such that when its reverse is subtra
[#permalink]
Show Tags
18 Sep 2018, 18:52
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 3digit 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 threedigit number is such that when its reverse is subtra
[#permalink]
18 Sep 2018, 18:52






