For the given set n = {3, 6, 4, 6, 5, p}, is p 2?

Question

For the given set n = {3, 6, −4, −6, 5, p}, is p > 2?

(1) The median of the set n is more than 2.

(2) The median of the set n is 0.

fskilnik · Answer

n = \left\{ { - 6, - 4,3,5,6} \right\} \cup \left\{ p \right\}

p\,\,\mathop > \limits^? \,\,2

\left( 1 \right)\,\,Me{d_n} > 2\,\,\,\,\left\{ \matrix{
 \,{\rm{Take}}\,\,p = 3\,\,\,\, \Rightarrow \,\,\,n = \left\{ { - 6, - 4,3,3,5,6} \right\}\,\,\,\,\left( {Me{d_n} = 3} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr 
 \,{\rm{Take}}\,\,p = 2\,\,\,\, \Rightarrow \,\,\,n = \left\{ { - 6, - 4,2,3,5,6} \right\}\,\,\,\,\left( {Me{d_n} = 2.5} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr} \right.

\left( 2 \right)\,\,\,Me{d_n}\,\, = \,\,\,\left\{ \matrix{
 \,{{p + 3} \over 2} > 0\,\,\,{\rm{if}}\,\,2 < p \le 5\, \hfill \cr 
 \,{{3 + 5} \over 2} > 0\,\,\,{\rm{if}}\,\,\,p > 5 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( 2 \right)\,\,{\rm{contradicted}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,p > 2\,\,{\rm{is}}\,\,{\rm{false}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,

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

Regards,
Fabio.

stne · Answer

Dear Moderator,
How can both the statements contradict each other? Hope you will look into this and do the needful. Thank you

Bunuel · Answer

This is a poor quality question, that's why it's marked as such.

On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

kiran120680 · Answer

For the given set n={3,6,-4,-6,5,p}, is p>2?

I. The median of the set n is more than 2.
II. The median of the set n is 0.

ocelot22 · Answer

IF YOU FIND MY SOLUTION TO BE HELPFUL, PLEASE GIVE ME KUDOS

We are asked if p > 2

(1) the median of set n >2. Lets write all of the elements besides p in ascending order: -6,-4,3,5,6 if p is less than -6, the median would be (-4+3)/2 = -1/2 which is not more than 2. Notice that since (-4+3)/2 = -1/2, our median must be either (3+5)/2 (placing p bertween -4 and 3 or between 5 and 6 or to the right of 6 on the number line) or our median can be (3+p)/2 (placing p between 3 and 5) Suppose p = -3 (between -3 and 3) Then our answer is NO. Suppose p = 7 (to the right of 6) then our answer is YES NS

(2) The median of n is 0. The only way for this to happen, is for the two middle numbers of the set (in ascending order) sum to 0. Since 3 is the 3rd number in ascending order, p must =-3, giving us a definite NO Sufficient

The answer is B

Bunuel · Answer

Merging topics. Please search before posting. Thank you.

For the given set n = {3, 6, 4, 6, 5, p}, is p > 2?

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