For any integers a, b, c, and d, sechigh(a, b, c, d) is the second highest integer when the integers are placed in an ordered list. For example sechigh(2, 5, 4, 6) = 5 and sechigh(6, 5, 3, 6) = 6 . For the integer y, what is the value of sechigh(6, 7, 11, y)?
(1) y = sechigh (7, 13, 12, x) for some integer x.
(2) y = sechigh (7, 13, 8, z) for some integer z.
OA A
Source: Manhattan Prep
For any integers a, b, c, and d, sechigh(a, b, c, d) is the
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
$$? = {\rm{sechigh}}\left( {6,7,11,y} \right)\,\,\,\,\,\,\,\,\left[ {y\,\,{\mathop{\rm int}} } \right]$$BTGmoderatorDC wrote:For any integers a, b, c, and d, sechigh(a, b, c, d) is the second highest integer when the integers are placed in an ordered list. For example sechigh(2, 5, 4, 6) = 5 and sechigh(6, 5, 3, 6) = 6 . For the integer y, what is the value of sechigh(6, 7, 11, y)?
(1) y = sechigh (7, 13, 12, x) for some integer x.
(2) y = sechigh (7, 13, 8, z) for some integer z.
Source: Manhattan Prep
$$\left( 1 \right)\,\,y = {\rm{sechigh}}\left( {7,13,12,x} \right)\,\,\,\,\left[ {x\,\,{\mathop{\rm int}} } \right]\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{
\,y = 13\,\,\,{\rm{if}}\,\,\,x \ge 13\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 11 \hfill \cr
\,y = 12\,\,\,{\rm{if}}\,\,\,x \le 12\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 11 \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,y = {\rm{sechigh}}\left( {7,13,8,z} \right)\,\,\,\,\left[ {z\,\,{\mathop{\rm int}} } \right]\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,z = 7\,\,\,\,\, \Rightarrow \,\,\,\,\,y = 8\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 8 \hfill \cr
\,\,{\rm{Take}}\,\,z = 14\,\,\,\,\, \Rightarrow \,\,\,\,\,y = 13\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 11 \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{INSUFF}}{\rm{.}}$$
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
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Given: sechigh(a, b, c, d) is the second highest integer when the integers are placed in an ordered listBTGmoderatorDC wrote:For any integers a, b, c, and d, sechigh(a, b, c, d) is the second highest integer when the integers are placed in an ordered list. For example sechigh(2, 5, 4, 6) = 5 and sechigh(6, 5, 3, 6) = 6 . For the integer y, what is the value of sechigh(6, 7, 11, y)?
(1) y = sechigh (7, 13, 12, x) for some integer x.
(2) y = sechigh (7, 13, 8, z) for some integer z.
OA A
Source: Manhattan Prep
For example
1. sechigh(2, 5, 4, 6) = sechigh(2, 4, 5, 6) = 5
2. sechigh(6, 5, 3, 6) = sechigh(3, 5, 6, 6) = 6
We have to determine the value of sechigh(6, 7, 11, y).
Question: We have to determine the value of sechigh(6, 7, 11, y).
Let's take each statement one by one.
(1) y = sechigh (7, 13, 12, x) for some integer x.
Case 1: Say y is the greatest term => y = sechigh (7, 12, 13, x) = 13.
Thus, sechigh(6, 7, 11, y) = sechigh(6, 7, 11, 13) = 11.
Case 2: Say y is the second highest term => y = sechigh (7, 12, x, 13) => y = 12 or 13
Thus, sechigh(6, 7, 11, y) = sechigh(6, 7, 11, 12/13) = 11.
Case 3: Say y is the third highest term => y = sechigh (7, x, 12, 13) => y = 12
Thus, sechigh(6, 7, 11, y) = sechigh(6, 7, 11, 12) = 11.
Case 4: Say y is the first term => y = sechigh (x, 7, 12, 13) => y = 12
Thus, sechigh(6, 7, 11, y) = sechigh(6, 7, 11, 12) = 11.
Unique answer. Sufficient.
(2) y = sechigh (7, 13, 8, z) for some integer z.
Case 1: Say y is the highest term => y = sechigh (7, 8, 13, z) => y = 13
Thus, sechigh(6, 7, 11, y) = sechigh(6, 7, 11, 13) = 11.
Case 2: Say y is the second highest term => y = sechigh (7, 8, z, 13) => 8 ≤ y ≤ 13
Thus, if 8 ≤ y ≤ 11, then sechigh(6, 7, 11, y) = sechigh(6, 7, y, 11) = y (= 8/9/10/11). No unique value of y.
Insufficient.
The correct answer: A
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: Manhattan Review Dilsukhnagar | Hyderabad GMAT Prep | Bangalore GMAT Courses | Kukatpally GRE Prep | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.