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
kindly click the upvote button if my question tingled your grey cells
My current age is two more than thrice the age of one of my
This topic has expert replies
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
$$? = \left| {M - R} \right|\,\,{\mathop{\rm int}} \,\,{\rm{minimum}}$$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
$$\left\{ \matrix{
A = 3R + 2 \hfill \cr
A + N = 3\left( {M + N} \right) + 2 \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,\,\, - N = 3\left( {R - M} \right) - 3N\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,2N = 3\left( {R - M} \right)$$
$$2N = 3\left( {R - M} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{
\,N\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,3\,\,\,\,\left[ {\,\left( {R - M} \right)\,\,{\mathop{\rm int}} \,} \right]\,\,\,\,\,\,\mathop \Rightarrow \limits^{N\,\, \ge \,1} \,\,\,\,\,\,N \ge 3 \hfill \cr
\,R - M\,\,{\rm{even}}\,\,\,\, \Rightarrow \,\,\,? = 2\,\,\,\,\,\left( {{\rm{for}}\,\,N = 3} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\left( {\rm{D}} \right)$$
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
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7251
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Let M = my current age, R = Richa's current age, and T = Namita's current age. Therefore, we have: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
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews