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If set S consists of the numbers 1, 5, -2, 8, and n, is 0 &l

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If set S consists of the numbers 1, 5, -2, 8, and n, is 0 &l

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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

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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
$$S = \left\{ { - 2,1,5,8} \right\} \cup \left\{ n \right\}$$
$$?\,\,\,:\,\,\,0 < n < 7$$

$$\left( 1 \right)\,\,\,{\rm{Med}}\left( S \right) < 5\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,n = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,0,1,5,8} \right\}} \right) = 1} \right]\,\, \hfill \cr
\,{\rm{Take}}\,\,n = 1\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,1,1,5,8} \right\}} \right) = 1} \right]\,\,\, \hfill \cr} \right.\,$$

$$\left( 2 \right)\,\,\,{\rm{Med}}\left( S \right) > 1\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,n = 7\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,1,5,7,8} \right\}} \right) = 5} \right]\,\, \hfill \cr
\,{\rm{Take}}\,\,n = 6\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\left[ {Med\left( S \right) = {\rm{Med}}\left( {\left\{ { - 2,1,5,6,8} \right\}} \right) = 5} \right]\,\,\, \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,\,\,1 < {\rm{Med}}\left( S \right) < 5\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
$$\left( * \right)\,\,\left\{ \matrix{
\,n \le 0\,\,\, \Rightarrow \,\,\,\,Med\left( S \right) = 1\,\,,\,\,\,\,{\rm{impossible}} \hfill \cr
\,n \ge 7\,\,\, \Rightarrow \,\,\,\,Med\left( S \right) = 5\,\,,\,\,\,\,{\rm{impossible}} \hfill \cr} \right.\,\,\,\,\,\,$$

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

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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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
Given: Set S: {-2, 1, 5, 8, n}
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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Manhattan Review

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