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# N=abc, N is a three digit number with hundreds digit a, tens digit b

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Manager
Joined: 25 Dec 2018
Posts: 86
Location: India
GMAT 1: 490 Q47 V13
GPA: 2.86
N=abc, N is a three digit number with hundreds digit a, tens digit b  [#permalink]

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06 Jan 2019, 03:33
2
4
00:00

Difficulty:

95% (hard)

Question Stats:

36% (01:59) correct 64% (02:09) wrong based on 55 sessions

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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
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 616
Re: N=abc, N is a three digit number with hundreds digit a, tens digit b  [#permalink]

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06 Jan 2019, 05:59
2
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 high-level "quant" preparation starts here: https://gmath.net

Manager
Joined: 01 May 2017
Posts: 69
Location: India
Re: N=abc, N is a three digit number with hundreds digit a, tens digit b  [#permalink]

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06 Jan 2019, 06:03
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]

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08 Jan 2019, 10:41
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: 616
Re: N=abc, N is a three digit number with hundreds digit a, tens digit b  [#permalink]

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08 Jan 2019, 11:04
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 high-level "quant" preparation starts here: https://gmath.net

Re: N=abc, N is a three digit number with hundreds digit a, tens digit b &nbs [#permalink] 08 Jan 2019, 11:04
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# N=abc, N is a three digit number with hundreds digit a, tens digit b

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