Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?
(1) y > 3x
(2) y > x > 3
OA C
Source: Official Guide
Is the range of the integers 6, 3, y, 4, 5, and x greater
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
$$A = \left\{ {3,4,5,6} \right\} \cup \left\{ {x,y} \right\}\,\,\,\,\,\left[ {{\rm{ints}}} \right]$$BTGmoderatorDC wrote:Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?
(1) y > 3x
(2) y > x > 3
Source: Official Guide
$${R_A} = {\max _A} - {\min _A}\,\,\mathop > \limits^? \,\,9$$
$$\left( 1 \right)\,\,\,y > 3x\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,1} \right)\,\,\,\, \Rightarrow \,\,\,\,{R_A} = 6 - 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,10} \right)\,\,\,\, \Rightarrow \,\,\,\,{R_A} = 10 - 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$
$$\left( 2 \right)\,\,\,y > x > 3\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,5} \right)\,\,\,\, \Rightarrow \,\,\,\,{R_A} = 6 - 3\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,13} \right)\,\,\,\, \Rightarrow \,\,\,\,{R_A} = 13 - 3\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$
$$\left( {1 + 2} \right)\,\,\,y\mathop > \limits^{\left( 1 \right)} 3x\mathop \ge \limits^{\left( 2 \right)\,\,x \ge 4} 12\,\,\,\, \Rightarrow \,\,\,\,y \ge 13\,\,\,\,\,\, \Rightarrow \,\,\,\,{R_A} \ge 13 - 3 = 10\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
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