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

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Senior Manager
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If set S consists of the numbers 1, 5, -2, 8, and n, is 0 < [#permalink] New post 14 May 2012, 11:55
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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.
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Re: If set S consists of the numbers 1, 5, -2, 8, and n, is 0 < [#permalink] New post 14 May 2012, 13:09
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Stiv 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.


If set S consists of the numbers 1, 5,-2, 8 and n, is 0 < n < 7?

Note that:
If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.


So the median of our set of 5 numbers: {-2, 1, 5, 8, n} must be the middle number, so it can be:
1 if n\leq{1};
5 if n\geq{5};
n itself if 1\leq{n}\leq{5}.

(1) The median of the numbers in S is less than 5 --> so either the median=1 and in this case n\leq{1} so not necessarily in the range 0<n<7 or median=n and in this case 1\leq{n}<{5} and in this case 0<n<7 is always true. Not sufficient.

(2) The median of the numbers in S is greater than 1 --> again either the median=5 and in this case n\geq{5} so not necessarily in the range 0<n<7 or median=n and in this case 1<{n}\leq{5} and in this case 0<n<7 is always true. Not sufficient.

(1)+(2) 1<median<5 --> median=n --> 1<n<5, so 0<n<7 is true. Sufficient.

Answer: C.
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Re: If set S consists of the numbers 1, 5, -2, 8, and n, is 0 < [#permalink] New post 16 May 2012, 02:52
Thank you! It's clear now.
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Data Sufficiency - need explanation [#permalink] New post 16 Jul 2012, 04:44
If set S consist 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.

Can someone please solve it first with proper explanation and then i will ask the doubt .
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Re: Data Sufficiency - need explanation [#permalink] New post 16 Jul 2012, 04:48
Expert's post
smartmanav wrote:
If set S consist 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.

Can someone please solve it first with proper explanation and then i will ask the doubt .


Merging similar topics. Please refer to the solution above.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Data Sufficiency - need explanation   [#permalink] 16 Jul 2012, 04:48
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