Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 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. Jun 23 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Read Only User
Joined: 25 Dec 2018
Posts: 148
Location: India
GPA: 2.86

N=abc, N is a three digit number with hundreds digit a, tens digit b
[#permalink]
Show Tags
06 Jan 2019, 04:33
Question Stats:
32% (02:31) correct 68% (02:40) wrong based on 93 sessions
HideShow timer Statistics
N=abc, N is a three digit number with hundreds digit a, tens digit b and units digit c. If a+b+c=20, what is the value of b? (1) The product of digits a and c is 18. (2) b/c=1 and b<a
Official Answer and Stats are available only to registered users. Register/ Login.



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936

Re: N=abc, N is a three digit number with hundreds digit a, tens digit b
[#permalink]
Show Tags
06 Jan 2019, 06:59
akurathi12 wrote: N=abc, N is a three digit number with hundreds digit a, tens digit b and units digit c. If a+b+c=20, what is the value of b?
(1) The product of digits a and c is 18.
(2) b/c=1 and b<a
\(N = \left\langle {abc} \right\rangle \,\,\,\,\,\left( {a \ne 0} \right)\) \(a + b + c = 20\,\,\,\left( * \right)\,\,\,\) \(? = b\) \(\left( 1 \right)\,\,ac = 18\,\,\,\,\mathop \Rightarrow \limits^{{\rm{all}}\,\,{\rm{possibilities}}} \,\,\,\left\{ \matrix{ \,\left( {a,b,c} \right) = \left( {2,9,9} \right)\,\,\, \Rightarrow \,\,\,? = 9 \hfill \cr \,\left( {a,b,c} \right) = \left( {9,9,2} \right)\,\,\, \Rightarrow \,\,\,? = 9 \hfill \cr \,\left( {a,b,c} \right) = \left( {3,11,6} \right)\,\,\,{\rm{impossible}} \hfill \cr \,\left( {a,b,c} \right) = \left( {6,11,3} \right)\,\,\,{\rm{impossible}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 9\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.\) \(\left( 2 \right)\,\,a > b = c\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,a\,\,{\rm{even}}\,\,{\rm{ > }}\,\,\,{\rm{6}}\,\,\,\left( {a \le 6\,\,\,\, \Rightarrow \,\,\,b = c \ge 7} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {a,b,c} \right) = \left( {8,6,6} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.\) The correct answer is therefore (D). Obs.: in official questions, when the correct alternative choice is (D), we expect the unique answers (obtained in each statement alone) to be equal. This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Manager
Joined: 01 May 2017
Posts: 82
Location: India

Re: N=abc, N is a three digit number with hundreds digit a, tens digit b
[#permalink]
Show Tags
06 Jan 2019, 07:03
N=abc, N is a three digit number with hundreds digit a, tens digit b and units digit c. If a+b+c=20, what is the value of b?
(1) The product of digits a and c is 18. a*c = 18 a,b,c are single digits 18 = 6*3 OR 9*2 if a = 6 and c= 3 then from a+b+c = 20, b = 11, which is not a single digit So (6,3) is not possible only possible solution is 9,2 for a,c We are least bothered about the value of a, c as required value is b a+b+c = 20 9+2+b = 30 b = 9 Sufficient
(2) b/c=1 and b<a Since b,c are equal, their sum will be even (even if b=c = odd OR even) As Even + even = even odd + odd = even possibilities of a is only even, as 2*a + b = 20 an even number Since 10 is 2 digit number, and b < a, lets consider a =8, let b = c = x 8 + 2(x) = 20 b = c = x = 6
Next a = 6 (only even's possible from above explanation) 6 + 2(x) = 20 b= c = x = 7 b > a which is a contradiction, So a can only take 8, and in turn b,c can only be 6 So, b = 6 Sufficient
Option D is correct



Intern
Joined: 01 Jul 2018
Posts: 6
Location: India
Concentration: Finance, General Management
WE: Science (Education)

Re: N=abc, N is a three digit number with hundreds digit a, tens digit b
[#permalink]
Show Tags
08 Jan 2019, 11:41
Dare Devil wrote: N=abc, N is a three digit number with hundreds digit a, tens digit b and units digit c. If a+b+c=20, what is the value of b?
(1) The product of digits a and c is 18. a*c = 18 a,b,c are single digits 18 = 6*3 OR 9*2 if a = 6 and c= 3 then from a+b+c = 20, b = 11, which is not a single digit So (6,3) is not possible only possible solution is 9,2 for a,c We are least bothered about the value of a, c as required value is b a+b+c = 20 9+2+b = 30 b = 9 Sufficient
(2) b/c=1 and b<a Since b,c are equal, their sum will be even (even if b=c = odd OR even) As Even + even = even odd + odd = even possibilities of a is only even, as 2*a + b = 20 an even number Since 10 is 2 digit number, and b < a, lets consider a =8, let b = c = x 8 + 2(x) = 20 b = c = x = 6
Next a = 6 (only even's possible from above explanation) 6 + 2(x) = 20 b= c = x = 7 b > a which is a contradiction, So a can only take 8, and in turn b,c can only be 6 So, b = 6 Sufficient
Option D is correct From 2 options we are getting two different values for B..is it right approach?



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936

Re: N=abc, N is a three digit number with hundreds digit a, tens digit b
[#permalink]
Show Tags
08 Jan 2019, 12:04
PKGMAT wrote: From 2 options we are getting two different values for B..is it right approach?
I have made the following observation in my previous post: Obs.: in official questions, when the correct alternative choice is (D), we expect the unique answers (obtained in each statement alone) to be equal. Reason for the observation: it was not the case here. Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Intern
Joined: 29 Jul 2018
Posts: 5
Concentration: Finance, Economics
WE: Project Management (Investment Banking)

Re: N=abc, N is a three digit number with hundreds digit a, tens digit b
[#permalink]
Show Tags
27 Mar 2019, 21:57
Give 100a+10b+c = 20 , to find 10b ?
Statement 1 : (a)*(c)=18, hence none of them is zero. Possible Values : 2*9 = 18 > B can be 9 since a + b + c = 20 9*2 = 18> B can be 9 since a + b + c = 20
Ruled out options :  (Since range of values for any figure can lie between 0 and 9 ) 3*6 = 18> B can be 11 since a + b + c = 20 6*3 = 18> B can be 11 since a + b + c = 20
Hence statement 1 is alone sufficient. (B=9)
Statement 2:  Give B/C =1 implies B=C additionally, its given b<a From the above information we can infer that, possible values of A , B , C can be A + B + C =20 9 5.5 5.5 8 6 6 7 6.5 6.5 6 7 7 abc have to be an integer and given that a > b Hence only possible option > a = 8 and B & C 6 . Alone Sufficient
Hence, answer "D"




Re: N=abc, N is a three digit number with hundreds digit a, tens digit b
[#permalink]
27 Mar 2019, 21:57






