Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43892

If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
21 Mar 2017, 03:49
Question Stats:
48% (01:41) correct 52% (02:47) wrong based on 98 sessions
HideShow timer Statistics



Director
Joined: 05 Mar 2015
Posts: 962

Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
21 Mar 2017, 10:49
Bunuel wrote: If a, b, and b represent distinct digits, what is the value of the twodigit number ab?
(1) ab*ba = aca
(2) a*b < 10 (1) b^2=c if b =2 , c= 4 if b= 3 , c=9 a could be 5 or 6 not suff (2)again same as (1) insuff combining same as above insuff Ans E



Veritas Prep GMAT Instructor
Affiliations: Veritas Prep
Joined: 21 Dec 2014
Posts: 39
Location: United States (DC)
My Company: www.parallaxprep.com
GRE 1: 1600 Q800 V800
GPA: 3.11
WE: Education (Education)

Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
21 Mar 2017, 22:00
rohit8865 wrote: Bunuel wrote: If a, b, and b represent distinct digits, what is the value of the twodigit number ab?
(1) ab*ba = aca
(2) a*b < 10 (1) b^2=c if b =2 , c= 4 if b= 3 , c=9 a could be 5 or 6 not suff (2)again same as (1) insuff combining same as above insuff Ans E I believe that you are misinterpreting the question. a, b, and c represent digits, and ab, ba, and aca represent two twodigit numbers and a threedigit number. These are not products. Like, for instance, if a = 8 and b = 3, then ab would be 83, ba would be 38, etc.



Intern
Joined: 08 Jul 2013
Posts: 13

Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
21 Mar 2017, 23:58
1
This post received KUDOS
1.suff: 21 12 only combo acceptable as digits are different 2. insuff
answer A



Senior Manager
Joined: 05 Jan 2017
Posts: 434
Location: India

Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
22 Mar 2017, 01:02
Bunuel wrote: If a, b, and b represent distinct digits, what is the value of the twodigit number ab?
(1) ab*ba = aca
(2) a*b < 10 St 1: Nothing can be predicted. INSUFFICIENT St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976.... only 12*21 = 252 hence ab can be 12 or 21. INSUFFICIENT Option E



Intern
Joined: 08 Jul 2013
Posts: 13

Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
22 Mar 2017, 05:21
1
This post received KUDOS
ByjusGMATapp wrote: Bunuel wrote: If a, b, and b represent distinct digits, what is the value of the twodigit number ab?
(1) ab*ba = aca
(2) a*b < 10 St 1: Nothing can be predicted. INSUFFICIENT St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976.... only 12*21 = 252 hence ab can be 12 or 21. INSUFFICIENT Option E ab can not be 12, only 21 because aca is 252



Intern
Joined: 25 Dec 2016
Posts: 19

Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
22 Mar 2017, 06:28
rt9 wrote: ByjusGMATapp wrote: Bunuel wrote: If a, b, and b represent distinct digits, what is the value of the twodigit number ab?
(1) ab*ba = aca
(2) a*b < 10 St 1: Nothing can be predicted. INSUFFICIENT St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976.... only 12*21 = 252 hence ab can be 12 or 21. INSUFFICIENT Option E ab can not be 12, only 21 because aca is 252 11 and 11 is another value



Math Expert
Joined: 02 Sep 2009
Posts: 43892

If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
22 Mar 2017, 07:58
vivek2k70 wrote: rt9 wrote: ByjusGMATapp wrote: St 1: Nothing can be predicted. INSUFFICIENT
St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT
St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976....
only 12*21 = 252
hence ab can be 12 or 21. INSUFFICIENT
Option E ab can not be 12, only 21 because aca is 252 11 and 11 is another value It is mentioned in the stem that a, b, and c represent distinct digits.
_________________
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



Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 308
Location: India
Concentration: Technology, Strategy
GPA: 3.7
WE: Information Technology (Consulting)

Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
22 Mar 2017, 09:25
3
This post received KUDOS
I am sure, you wanted to mention: If a, b, and C represent distinct digits Bunuel wrote: If a, b, and b represent distinct digits, what is the value of the twodigit number ab?
(1) ab*ba = aca
(2) a*b < 10 We know a,b,c are different digits. ab*ba = aca So from the 2 digit multiplication process, first we will multiply a*b. As we get the unit digit number as a itself, means b = 1. just plugging the numbers 21 & 12 gives 252, means a=2, b=1, c=5. Also there is no other integer which gives mutiplication X1 * 1X = X_X A sufficient.
_________________
Need Kudos to unlock GMAT Club tests



Math Expert
Joined: 02 Sep 2009
Posts: 43892

Re: If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
22 Mar 2017, 09:34
RMD007 wrote: I am sure, you wanted to mention: If a, b, and C represent distinct digits Bunuel wrote: If a, b, and b represent distinct digits, what is the value of the twodigit number ab?
(1) ab*ba = aca
(2) a*b < 10 We know a,b,c are different digits. ab*ba = aca So from the 2 digit multiplication process, first we will multiply a*b. As we get the unit digit number as a itself, means b = 1. just plugging the numbers 21 & 12 gives 252, means a=2, b=1, c=5. Also there is no other integer which gives mutiplication X1 * 1X = X_X A sufficient. Sure. Edited. Thank you for noticing. +1.
_________________
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: 21 Mar 2016
Posts: 551

If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
22 Mar 2017, 22:15
ByjusGMATapp wrote: Bunuel wrote: If a, b, and b represent distinct digits, what is the value of the twodigit number ab?
(1) ab*ba = aca
(2) a*b < 10 St 1: Nothing can be predicted. INSUFFICIENT St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976.... only 12*21 = 252 hence ab can be 12 or 21. INSUFFICIENT Option E ByjusGMATapp plz elaborate the stat1 ,, according to me stat 1 is suff and 12,21 is the only combo tat fits in.. thanks



Senior Manager
Joined: 02 Apr 2014
Posts: 413

If a, b, and c represent distinct digits, what is the value of the two [#permalink]
Show Tags
11 Jan 2018, 11:29
1
This post was BOOKMARKED
Statement 1: \(ab\) * \(ba\) = \(aca\) => \((10a+b)(10b+a)\) = \(100a + 10c + a\) => \(100ab + 10a^2 + 10b^2 + ab\) = \(100a + 10c + a\) => \(100ab + (a^2 + b^2)10 + ab\) = \(100a + 10c + a\)
now comparing units digit on both the sides \(ab\)= a => \(a= 0\) OR \(b = 1\) => but a cannot be 0, if it were, then aca would be 2digit number => b = 1
now comparing tens digit on both the sides \(a^2 + b^2 = c\) \(a^2 = c  b^2\) \(a^2 = c  1\) \(a\) = \(\sqrt{c  1}\) only for c = 1, 2, 5, \(\sqrt{c  1}\) yields integer if c = 1, a = 0 (which is not possible) if c = 2, a = 1 (but b is already 1) => not possible so only c = 5, a = 2, possible so number ab = 21 => sufficient
Statement 2: a * b < 10 lot of combinations ab = {14, 21, 24} not sufficient
(A)




If a, b, and c represent distinct digits, what is the value of the two
[#permalink]
11 Jan 2018, 11:29






