My current age is two more than thrice the age of one of my

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vishwash: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Mon Feb 22, 2016 1:21 am

My current age is two more than thrice the age of one of my

by vishwash » Wed Dec 12, 2018 1:10 pm

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My current age is two more than thrice the age of one of my two sisters named Richa. After N years, I will be two more than thrice the age of my other sister named Namita. What is the minimum possible integral difference (in years) between the age of my two mentioned sisters? (N is a natural number)

options

10
6
4
2
5

source cl gmat homework book 800 level questions

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Source: Beat The GMAT — Problem Solving | Wed Dec 12, 2018 1:10 pm

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Thu Dec 13, 2018 4:28 am

vishwash wrote:My current age is two more than thrice the age of one of my two sisters named Richa. After N years, I will be two more than thrice the age of my other sister named Mamita. What is the minimum possible integral difference (in years) between the age of my two mentioned sisters? (N is a natural number)

(A) 10
(B) 6
(C) 4
(D) 2
(E) 5

source: cl gmat homework book 800 level questions

$$? = \left| {M - R} \right|\,\,{\mathop{\rm int}} \,\,{\rm{minimum}}$$
$$\left\{ \matrix{
A = 3R + 2 \hfill \cr
A + N = 3\left( {M + N} \right) + 2 \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,\,\, - N = 3\left( {R - M} \right) - 3N\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,2N = 3\left( {R - M} \right)$$
$$2N = 3\left( {R - M} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{
\,N\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,3\,\,\,\,\left[ {\,\left( {R - M} \right)\,\,{\mathop{\rm int}} \,} \right]\,\,\,\,\,\,\mathop \Rightarrow \limits^{N\,\, \ge \,1} \,\,\,\,\,\,N \ge 3 \hfill \cr
\,R - M\,\,{\rm{even}}\,\,\,\, \Rightarrow \,\,\,? = 2\,\,\,\,\,\left( {{\rm{for}}\,\,N = 3} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\left( {\rm{D}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Mar 11, 2019 7:01 am

vishwash wrote:My current age is two more than thrice the age of one of my two sisters named Richa. After N years, I will be two more than thrice the age of my other sister named Namita. What is the minimum possible integral difference (in years) between the age of my two mentioned sisters? (N is a natural number)

options

10
6
4
2
5

Let M = my current age, R = Richa's current age, and T = Namita's current age. Therefore, we have:

M = 2 + 3R

and

M + N = 2 + 3(T + N)

If we subtract the first equation from the second, we have:

N = 3(T + N) - 3R

N = 3T + 3N - 3R

3R - 3T = 2N

3(R - T) = 2N

Since N is a positive integer and 3 is not a multiple of 2, we see that R - T must be a multiple of 2. So the minimum value of R - T is 2.

Answer: D

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