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# Which of the following could be the median of the 4 integers listed ab

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Manager
Joined: 19 Nov 2007
Posts: 122
Which of the following could be the median of the 4 integers listed ab  [#permalink]

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12 Nov 2009, 02:18
4
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Difficulty:

55% (hard)

Question Stats:

61% (01:30) correct 39% (01:26) wrong based on 321 sessions

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150, 200, 250, n

Which of the following could be the median of the 4 integers listed above?

I. 175
II. 215
III. 235

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
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Re: Statistics-Median Problem  [#permalink]

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14 Sep 2010, 02:43
5
utin wrote:
soumanag wrote:
Answer is C

n< 150 -> median = 350 / 2 = 175

250>n>200 median let n = 230 median = 215

n > 250 median = (200+250)/2 = 225
median can not be greater than 225. therefore III is wrong.

I & II are correct.[/quote

Didn't understand still!!!

If n<=150
Then middle two numbers are 150 and 200, hence median is 175

If n>=250
Then middle two numbers are 200 and 250, hence median is 225

These define the max and min median possible. If n is between 150 and 250, the median will be between 175 and 225

In conclusion, median has to be between 175 & 225
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Senior Manager
Joined: 31 Aug 2009
Posts: 338
Location: Sydney, Australia
Re: Which of the following could be the median of the 4 integers listed ab  [#permalink]

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12 Nov 2009, 03:55
2
2
jade3 wrote:
150, 200, 250, n

Which of the following could be the median of the 4 integers listed above?

I. 175
II. 215
III. 235

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

1) 175. This is possible if N < 150 Implies that the two middle numbers are 150 and 200.
2) 215. This is possible if 200 < N < 250 and if (N+200)/2 = 215. i.e. N=230.
3) 235. This is not possible because again, this would require 200 < N < 250. And since 235 is closer to 250 we would require 250-235 = 235-N. N=210. However, now 235 is no longer the median of the set.

Hence C.
Manager
Joined: 04 Apr 2010
Posts: 77
Schools: UCLA Anderson
Re: Which of the following could be the median of the 4 integers listed ab  [#permalink]

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15 Apr 2010, 12:27
I. If n = 150, then the median is 175, so I works
II. If n = 230, then the median is 215, so II works
III. You cannot pick a value for n that makes the median 235

Answer is C
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Joined: 05 Mar 2010
Posts: 147
Re: Which of the following could be the median of the 4 integers listed ab  [#permalink]

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16 Apr 2010, 01:42
diacaz wrote:
hardnstrong wrote:
IMO C

Can explain if required!!!

please explain

I if n is <= 150 median is 175
II if n = 230 then median is 215
III no possible values of n because for median to be 235 n has to be greater than 250 and if n is >250 then n cannot be used to determine median

Hope it help
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Re: Which of the following could be the median of the 4 integers listed ab  [#permalink]

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16 Apr 2010, 09:55
2
chouky wrote:
hardnstrong wrote:
III no possible values of n because for median to be 235 n has to be greater than 250 and if n is >250 then n cannot be used to determine median

Hope it help

Why not ?

Median is the middle number if set of numbers are odd
or the mean of middle 2 numbers if set of numbers are even
Example - set of 1,2,3,4,5 (median is 3)
se of 1,2,3,4,5,6 (median is 3.5)

In our question here, we have a set of 4 numbers 150,200,250,n
so median is the mean of 2 middle numbers.

III option is if the median could be 235.
For a average 235 atleast one number should be greater than 235
If n is less than 250 and greater than 235, average of 2 mumbers (200 and any number between 235 and 250) can never be 235.
If the n is greater than 250 then median is average of 200 and 250 i.e. 225
Hence 235 can never be the median

Hope this help!!!!!
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Re: Which of the following could be the median of the 4 integers listed ab  [#permalink]

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10 May 2010, 04:10
ajitsah wrote:
Pls elaborate on following DS questions. Thank u.

1. 150, 200, 250, n
Which of the following could be the median of the 4 integers listed above?
I. 175
II. 215
III. 235
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Ans. (C)

2. Is ⏐mod (x)⏐< 1?
(1) ⏐mod (x + 1)⏐ = 2⏐mod (x - 1)
(2) ⏐mod (x - 3)⏐ ≠ 0
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Ans. (C)

Q1 - Answer c

As we know there are 4 numbers in the list

So the Median will be half of the sum of the two numbers

So now lets look at the options.

175 cane be the median if n is less than 150 ( (150 + 200)/2 = 175)
215 can also be the median if n is 230
235 cant be because if the median is 235 then that means ( n+ 200) / 2= 235 => n = 270 and in case n is 270 then the median should be 200 + 250 / 2 = 225

Q 2, I am not able to understand the this Q as its not properly written, could you please write this question again so that we can try to answer that one as well.
Manager
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Posts: 95
Re: Statistics-Median Problem  [#permalink]

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28 Aug 2010, 07:01
Answer is C

n< 150 -> median = 350 / 2 = 175

250>n>200 median let n = 230 median = 215

n > 250 median = (200+250)/2 = 225
median can not be greater than 225. therefore III is wrong.

I & II are correct.
Manager
Joined: 27 Mar 2010
Posts: 77
Re: Statistics-Median Problem  [#permalink]

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14 Sep 2010, 02:36
[quote="soumanag"]Answer is C

n< 150 -> median = 350 / 2 = 175

250>n>200 median let n = 230 median = 215

n > 250 median = (200+250)/2 = 225
median can not be greater than 225. therefore III is wrong.

I & II are correct.[/quote

Didn't understand still!!!
Manager
Joined: 20 Jul 2010
Posts: 176
Re: Statistics-Median Problem  [#permalink]

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14 Sep 2010, 16:18
1
Make following ordered sequence

n, 150, 200, 250
150,n,200, 250
150, 200, n, 250
and 150,200,250, n

After that same explaination as above
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Posts: 148
Location: Boston
Re: Which of the following could be the median of the 4 integers listed ab  [#permalink]

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21 Sep 2010, 11:19
jade3 wrote:
150, 200, 250, n

Which of the following could be the median of the 4 integers listed above?

I. 175
II. 215
III. 235

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Since there are four numbers in the set, the median will be the average of the two middle numbers. There are three possibilities for n we need to consider.

If n < 150, then the median is (150 + 200) / 2 = 175.
If n > 250, then the median is (200 + 250) / 2 = 225.
If 150 < n < 250, the median will be (200 + n) / 2, or 100 + (n/2). So the median will range between 175 and 225.

III is the only answer which does not fall in this range, so the answer is I and II - (C).
Manager
Joined: 18 Jan 2010
Posts: 238
Which of the following could be the median of the 4 integers listed ab  [#permalink]

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21 May 2016, 21:01
n could be placed in following positions:

1. 150, 200, 250, n
2. 150, 200, n, 250
3. 150, n, 200, 250
4. n, 150, 200, 250

Case 1

Whether n is 250 or any number more than 250, the median will always be average of 2 middle nos. (200 and 250). Median would be 225. Not one of the given options

Let us take case 4 first
Case 4

Whether n is 150 or any number less than 150, the median will always be average of 2 middle nos. (150 and 200). Median would be 175, option (1) is certainly true.

Case 2

n can be 200 or 250 or any value between 200 and 250.
If n is 200, median = 100 --> not one of given options.
If n is 250, median would be 225. Not one of the given options.

If 200<n<250, then let us check whether the median [(200+n) / 2] is equal to given options (215 & 235)

200+n = [215 *2 = 430]. Which means n = 230. This is acceptable value. Option (2) is also true.
200+n = [235 * 2 = 470]. Which means n = 270. But This value is not between 200 and 250.
We get one acceptable and one non-acceptable value.
Option 3 is Not acceptable.

Case 3

n can be 150 or 200 or any value between 150 and 200.
If n is 150, median = 175 --> option already considered .
If n is 200, Median would be 200. Not one of the given options.

If 150<n<200, then let us check whether the median [(200+n) / 2] is equal to given options (215 & 235)
we will get n=230 and 270. Both not acceptable for this case.

So (1) and (2) are correct. Option (C) is the correct answer.
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Joined: 04 Jun 2016
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GMAT 1: 750 Q49 V43
Which of the following could be the median of the 4 integers listed ab  [#permalink]

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15 Jul 2016, 01:44
jade3 wrote:
150, 200, 250, n

Which of the following could be the median of the 4 integers listed above?

I. 175
II. 215
III. 235

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

235 cannot be the median
For set with even # of elements ; Median= $$\frac{Sum of Middle 2 terms}{2}$$
$$\frac{Sum of middle 2 terms}{2}=235$$ (if we want 235 to be the median)

Sum of middle two terms = 235*2
Sum of middle two terms = 470

If we take n to be largest term then 200 and 250 will become the middle term (150,200,250,any term larger than 250)
200+ 250=450 it is not 470

If we take 250 to be the largest term then n will become a smaller term such as 249 (150,200,249,250)

then 200+249= 449

we cannot get 470 in any possible way
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Re: 150, 200, 250, n Which of the following could be the median  [#permalink]

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14 Nov 2019, 03:39
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Re: 150, 200, 250, n Which of the following could be the median   [#permalink] 14 Nov 2019, 03:39
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