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# If x is an integer, is the median of 5 numbers shown greater

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Senior Manager
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If x is an integer, is the median of 5 numbers shown greater [#permalink]

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28 Apr 2006, 00:06
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x, 3, 1, 12, 8

If x is an integer, is the median of 5 numbers shown greater than the average of 5 numbers?

(1) x>6
(2) x is greater than median of 5 numbers
[Reveal] Spoiler: OA
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Re: GMAT PREP mean and median [#permalink]

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28 Apr 2006, 00:55
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getzgetzu wrote:
x, 3, 1, 12, 8

If x is an integer, is the median of 5 numbers shown greater than the average of 5 numbers?

1) x>6
2) x is greater than median of 5 numbers

(1) insuff.
for instance x can be 7 so median is 7 itself and mean around 5 so mean < median, but x can be 1000 in that case median is 8 but mean is way larger so is not enough

(2) that means that x>8 same problem as statement (1)

together nothing

so I would go with E in this one
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Re: GMAT PREP mean and median [#permalink]

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28 Apr 2006, 11:48
getzgetzu wrote:
x, 3, 1, 12, 8

If x is an integer, is the median of 5 numbers shown greater than the average of 5 numbers?

1) x>6
2) x is greater than median of 5 numbers

I go for E.

1) x>6, so x could be lets say 9, then median is 8, and the avg is 6.6, however if x is lets say 100, the mean is greater then median, so not suff.

2) similarly since x is greater then the median, 8 is the median, from there its similar to 1). not suff

therefore, E is correct.
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Joined: 05 Jan 2006
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28 Apr 2006, 21:14
1,3,8,12 and Now we need to plug in X

1) x>6...7 to inf
X mean med
7 31/5 7
8 32/5 8
9 33/5 8
100 124/5 8

In suffi

2) x is greater than med

1,3,8,x,12
or
1,3,8,12,x

Again pluging number insufficient

Togather no furthere info

hence E
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30 Apr 2006, 04:46
Yup E it is. Had the question been what the median is then B is suff
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Re: x, 3, 1, 12, 8 If x is an integer, is the median of 5 [#permalink]

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23 May 2012, 20:44
we can arrange this question like this
1,3,x,8,12 or 1,3,8,x,12 or 1,3,8,12,x
so st 1 (24+x)/5< x,or 8 or 12 it give three different solution i.e 6<x,x<16,x<36 so seems to not sff

st 2 xis greater > median by arrange he series we get 1 3 8 x 12 or 1 3 8 12 x where 8 is median so
24+x<8 ====>x <16 so foe any value of x it gives different result.

and combining 1 n 2 x>6 and x<16 take any value so
it seems to me asn sd be E

if any err let me know plz....
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Re: If x is an integer, is the median of 5 numbers shown greater [#permalink]

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23 May 2012, 23:47
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getzgetzu wrote:
x, 3, 1, 12, 8

If x is an integer, is the median of 5 numbers shown greater than the average of 5 numbers?

(1) x>6
(2) x is greater than median of 5 numbers

Given set {1, 3, 8, 12, x}

The questions asks whether median>average, or whether median>(24+x)/5.

(1) x>6 --> if x=11 then median=8 (the middle number) and average=(24+x)/5=7, so median>average but if x=16 then median=8 and average=(24+x)/5=8, so median=average. Not sufficient.

(2) x is greater than median of 5 numbers --> median=8. Not sufficient.

(1)+(2) Examples from (1) are still valid so we still have two different answers. Not sufficient.

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Re: GMAT PREP mean and median [#permalink]

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30 May 2012, 04:30
conocieur wrote:
getzgetzu wrote:
x, 3, 1, 12, 8

If x is an integer, is the median of 5 numbers shown greater than the average of 5 numbers?

1) x>6
2) x is greater than median of 5 numbers

(1) insuff.
for instance x can be 7 so median is 7 itself and mean around 5 so mean < median, but x can be 1000 in that case median is 8 but mean is way larger so is not enough

(2) that means that x>8 same problem as statement (1)

together nothing

so I would go with E in this one

Thanks for the solution..
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Re: If x is an integer, is the median of 5 numbers shown greater [#permalink]

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15 Feb 2014, 12:37
Bunuel wrote:
getzgetzu wrote:
x, 3, 1, 12, 8

If x is an integer, is the median of 5 numbers shown greater than the average of 5 numbers?

(1) x>6
(2) x is greater than median of 5 numbers

Given set {1, 3, 8, 12, x}

The questions asks whether median>average, or whether median>(24+x)/5.

(1) x>6 --> if x=11 then median=8 (the middle number) and average=(24+x)/5=7, so median>average but if x=16 then median=8 and average=(24+x)/5=8, so median=average. Not sufficient.

(2) x is greater than median of 5 numbers --> median=8. Not sufficient.

(1)+(2) Examples from (1) are still valid so we still have two different answers. Not sufficient.

I didn't quite understand statement 2, it says that x is greater than median of 5 numbers. Shouldn't it say the same 5 numbers given in the question or something similar?

Thanks
Cheers
J
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Re: If x is an integer, is the median of 5 numbers shown greater [#permalink]

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15 Feb 2014, 23:50
jlgdr wrote:
Bunuel wrote:
getzgetzu wrote:
x, 3, 1, 12, 8

If x is an integer, is the median of 5 numbers shown greater than the average of 5 numbers?

(1) x>6
(2) x is greater than median of 5 numbers

Given set {1, 3, 8, 12, x}

The questions asks whether median>average, or whether median>(24+x)/5.

(1) x>6 --> if x=11 then median=8 (the middle number) and average=(24+x)/5=7, so median>average but if x=16 then median=8 and average=(24+x)/5=8, so median=average. Not sufficient.

(2) x is greater than median of 5 numbers --> median=8. Not sufficient.

(1)+(2) Examples from (1) are still valid so we still have two different answers. Not sufficient.

I didn't quite understand statement 2, it says that x is greater than median of 5 numbers. Shouldn't it say the same 5 numbers given in the question or something similar?

Thanks
Cheers
J

it means if we say x is 9..then median wd b 8. 1, 3 8,9,12
so x can 9 10 11 or 12 median wud b 8.
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Re: If x is an integer, is the median of 5 numbers shown greater [#permalink]

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25 Mar 2015, 14:30
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If x is an integer, is the median of 5 numbers shown greater [#permalink]

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23 Dec 2015, 09:14
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Mean has a greater flexibility in terms of how big it can get. So for the median to be greater than the mean we need to limit the upward movement of the mean by restricting the value of x. Thus we need a constraint such as x<(certain number) and since neither of the choices does so answer is E.

For instance, even if we were given x>0
then say x=1 {1 1 3 8 12} 3>25/5? NO
now say x=8 {1 3 7 8 12} 8>(24+8)/5? Yes

on the other hand, say if we were given x<6, the answer would be a definitive No

would you pls confirm if that logic looks good, Bunuel?
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Re: If x is an integer, is the median of 5 numbers shown greater [#permalink]

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17 Jul 2016, 23:28
Mean = (24 + x) / 5

Median (1,3,8,12,x) so median can be either x or 8 depending on the value of x

1) x > 6

For x = 7,
Mean = 6.2
Median = 7
Mean < Median
For x = 300

Median = 8, mean much more ( I can put x = 10000000, no limit given)

2) X > Median

So x will easily be to the right of 8. Because either x is median or 8

1,3,8,x,12 or 1,3,8,12,x

case 1 : x= 10

Mean : 34/5 = 6.8 < median

Case 2 : x = 1000000000000000000000000000000000000

Obv mean > median

Even combining, x > 8, no definite

So E
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Re: If x is an integer, is the median of 5 numbers shown greater [#permalink]

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18 Jul 2016, 00:19
tke x=10 for one case and x=1000 for other

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Re: If x is an integer, is the median of 5 numbers shown greater [#permalink]

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06 Aug 2016, 04:59
I solved it in the following way:

Is median (M) > average? Rephrase it as M > (24+X)/5 => Is X < 5M - 24.

1) X > 6, say X = 7, then M=X=7 and 5*7-24 > 7 => 11 > 7 - answer is YES
If X = 100, then M=8, then 5*8 - 24 = 16, which is less than X=100 - answer is NO

Not sufficient

2) X > M, then say X = 9, then M = 8 and 5*8 - 24 = 16 > 9 - answer is YES
If X = 100, then M=8, then 5*8 - 24 = 16, which is less than X=100 - answer is NO

Not sufficient

3) Nothing changes, both options explored previously give different results.
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Re: If x is an integer, is the median of 5 numbers shown greater [#permalink]

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04 Oct 2016, 07:25
Hi Bunuel

Just to add another dimension to this question, what if statement 1 said x<6
In this case, tmt 1 can no longer be used along with stmt too for an answer E but guess the answer will remain at E. I am assuming negative 10 and 5 as x values for stmt 1. Can I know your thought process for deciding between C and E please? Tx.

Bunuel wrote:
getzgetzu wrote:
x, 3, 1, 12, 8

If x is an integer, is the median of 5 numbers shown greater than the average of 5 numbers?

(1) x>6
(2) x is greater than median of 5 numbers

Given set {1, 3, 8, 12, x}

The questions asks whether median>average, or whether median>(24+x)/5.

(1) x>6 --> if x=11 then median=8 (the middle number) and average=(24+x)/5=7, so median>average but if x=16 then median=8 and average=(24+x)/5=8, so median=average. Not sufficient.

(2) x is greater than median of 5 numbers --> median=8. Not sufficient.

(1)+(2) Examples from (1) are still valid so we still have two different answers. Not sufficient.

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Re: If x is an integer, is the median of 5 numbers shown greater [#permalink]

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17 Dec 2016, 12:24
jlgdr wrote:
Bunuel wrote:
getzgetzu wrote:
x, 3, 1, 12, 8

If x is an integer, is the median of 5 numbers shown greater than the average of 5 numbers?

(1) x>6
(2) x is greater than median of 5 numbers

Given set {1, 3, 8, 12, x}

The questions asks whether median>average, or whether median>(24+x)/5.

(1) x>6 --> if x=11 then median=8 (the middle number) and average=(24+x)/5=7, so median>average but if x=16 then median=8 and average=(24+x)/5=8, so median=average. Not sufficient.

(2) x is greater than median of 5 numbers --> median=8. Not sufficient.

(1)+(2) Examples from (1) are still valid so we still have two different answers. Not sufficient.

I didn't quite understand statement 2, it says that x is greater than median of 5 numbers. Shouldn't it say the same 5 numbers given in the question or something similar?

Thanks
Cheers
J

I think the wording for (2) is not absolutely correct. In the original question (GMAT Prep Exam) statement (2) says "x is greater than the median of THE 5 numbers", which is different than "x is greater than the median of 5 numbers".

Hope this helps!
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Re: If x is an integer, is the median of 5 numbers shown greater [#permalink]

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12 Feb 2017, 03:12
Bunuel wrote:
getzgetzu wrote:
x, 3, 1, 12, 8

If x is an integer, is the median of 5 numbers shown greater than the average of 5 numbers?

(1) x>6
(2) x is greater than median of 5 numbers

Given set {1, 3, 8, 12, x}

The questions asks whether median>average, or whether median>(24+x)/5.

(1) x>6 --> if x=11 then median=8 (the middle number) and average=(24+x)/5=7, so median>average but if x=16 then median=8 and average=(24+x)/5=8, so median=average. Not sufficient.

(2) x is greater than median of 5 numbers --> median=8. Not sufficient.

(1)+(2) Examples from (1) are still valid so we still have two different answers. Not sufficient.

Hi bunuel,

for this qn i have took x as 7,10 & 14 and got ans as D.

plugin method is driving me crazy.
how do we get to know this type of errors while doing plugin method??
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Re: If x is an integer, is the median of 5 numbers shown greater   [#permalink] 12 Feb 2017, 03:12
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