If set S consists of the numbers 1, 5, -2, 8, and n, is 0 < n < 7 ?
(1) The median of the numbers in S is less than 5.
(2) The median of the numbers in S is greater than 1.
OA C
Source: GMAT Prep
If set S consists of the numbers 1, 5, -2, 8, and n, is 0 &l
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$$S = \left\{ { - 2,1,5,8} \right\} \cup \left\{ n \right\}$$BTGmoderatorDC wrote:If set S consists of the numbers 1, 5, -2, 8, and n, is 0 < n < 7 ?
(1) The median of the numbers in S is less than 5.
(2) The median of the numbers in S is greater than 1.
Source: GMAT Prep
$$?\,\,\,:\,\,\,0 < n < 7$$
$$\left( 1 \right)\,\,\,{\rm{Med}}\left( S \right) < 5\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,n = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,0,1,5,8} \right\}} \right) = 1} \right]\,\, \hfill \cr
\,{\rm{Take}}\,\,n = 1\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,1,1,5,8} \right\}} \right) = 1} \right]\,\,\, \hfill \cr} \right.\,$$
$$\left( 2 \right)\,\,\,{\rm{Med}}\left( S \right) > 1\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,n = 7\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,1,5,7,8} \right\}} \right) = 5} \right]\,\, \hfill \cr
\,{\rm{Take}}\,\,n = 6\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,1,5,6,8} \right\}} \right) = 5} \right]\,\,\, \hfill \cr} \right.$$
$$\left( {1 + 2} \right)\,\,\,\,1 < {\rm{Med}}\left( S \right) < 5\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
$$\left( * \right)\,\,\left\{ \matrix{
\,n \le 0\,\,\, \Rightarrow \,\,\,\,Med\left( S \right) = 1\,\,,\,\,\,\,{\rm{impossible}} \hfill \cr
\,n \ge 7\,\,\, \Rightarrow \,\,\,\,Med\left( S \right) = 5\,\,,\,\,\,\,{\rm{impossible}} \hfill \cr} \right.\,\,\,\,\,\,$$
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
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Given: Set S: {-2, 1, 5, 8, n}BTGmoderatorDC wrote:If set S consists of the numbers 1, 5, -2, 8, and n, is 0 < n < 7 ?
(1) The median of the numbers in S is less than 5.
(2) The median of the numbers in S is greater than 1.
OA C
Source: GMAT Prep
Question; Is 0 < n < 7 ?
Let's take each statement one by one.
(1) The median of the numbers in S is less than 5.
Case 1: Considering n ≤ 0. Say n = -3
=> Set S: : {-3, -2, 1, 5, 8}. Median = 1 < 5. The answer is No.
Case 2: Considering 0 < n < 7. Say n = 1
=> Set S: : {-2, 1, 1, 5, 8}. Median = 1 < 5. The answer is Yes.
No unique answer. Insufficient.
(2) The median of the numbers in S is greater than 1.
Case 1: Considering 0 < n < 7. Say n = 3
=> Set S: : {-2, 1, 3, 5, 8}. Median = 3 > 1. The answer is Yes.
Case 2: Considering n > 7. Say n = 10
=> Set S: : {-2, 1, 5, 8, 10}. Median = 5 > 1. The answer is No.
No unique answer. Insufficient.
(1) and (2) together
Considering the two statements, we have 1< Median < 5. Since 1< Median < 5, in the set, excluding n, {-2, 1, 5, 8}, we must have the middle-most term, n, such that 1 < n < 5; thus, the inequality 0 < n < 7 is true. Sufficient.
The correct answer: C
Hope this helps!
-Jay
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