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# What is the minimum percentage increase in the mean of set X

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Manager
Joined: 07 Nov 2009
Posts: 216
What is the minimum percentage increase in the mean of set X  [#permalink]

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26 Jan 2012, 12:32
1
4
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Difficulty:

25% (medium)

Question Stats:

73% (01:22) correct 27% (01:46) wrong based on 227 sessions

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What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A) 25%
(B) 50%
(C) 75%
(D) 100%
(E) 200%
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Posts: 60460
Re: minimum percentage increase  [#permalink]

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26 Jan 2012, 12:39
2
rohitgoel15 wrote:
What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A) 25%
(B) 50%
(C) 75%
(D) 100%
(E) 200%

Mean of X is (-4-1+0+6+9)/5=2;

In order the increase to be minimal we should replace two smallest elements of X, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.

Percent increase=(4-2)/2*100=100%.

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Re: What is the minimum percentage increase in the mean of set X  [#permalink]

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26 Mar 2012, 09:10
hi Bunuel,

request to let me if two smallest primes numbers can be negative?
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Re: What is the minimum percentage increase in the mean of set X  [#permalink]

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26 Mar 2012, 09:18
1
pappueshwar wrote:
hi Bunuel,

request to let me if two smallest primes numbers can be negative?

Only positive numbers can be primes, so the smallest prime is 2.

Hope it helps.
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Re: What is the minimum percentage increase in the mean of set X  [#permalink]

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01 Mar 2013, 03:09
1 is not a prime number, got to know it now..... was considering it & made the answer wrong
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Re: What is the minimum percentage increase in the mean of set X  [#permalink]

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23 Jul 2016, 01:08
rohitgoel15 wrote:
What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A) 25%
(B) 50%
(C) 75%
(D) 100%
(E) 200%

Current mean is =$$\frac{(-4)+(-1)+(0)+(6)+(9)}{5} = \frac{(-5+15)}{5} = \frac{10}{5} = 2$$

Since we have to find the minimum increase , we should add the smallest distinct prime 2,3
New mean is =$$\frac{(0)+(2)+(3)+(6)+(9)}{5} = \frac{20}{5} = 4$$

Percent change = $$\frac{(New -Old}{Old})* 100 = \frac{4-2}{2}*100$$

Percent change = $$\frac{2}{2}* 100 = 100$$ %

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Re: What is the minimum percentage increase in the mean of set X  [#permalink]

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17 Sep 2016, 04:45
1
Top Contributor
As others have demonstrated, the average of set X increases from 2 to 4
Many students will incorrectly conclude that we have a 200% increase, since 4 is equal to 2 times 2.
This is not the case.
Percent increase = 100(new - old)/old
So, in this case, percent increase = 100(4 - 2)/2
= 200/2
= 100

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Re: What is the minimum percentage increase in the mean of set X  [#permalink]

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17 Sep 2016, 07:48
Bunuel
answer will change if I have 5 & 2 or say 2 & 11, isn't it?
just curious...
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Re: What is the minimum percentage increase in the mean of set X  [#permalink]

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17 Sep 2016, 07:51
paidlukkha wrote:
Bunuel
answer will change if I have 5 & 2 or say 2 & 11, isn't it?
just curious...

Yes, it will change but notice that we have to determine the minimum change and for that we are taking the lowest possible values as 2 and 3.
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What is the minimum percentage increase in the mean of set X {-4, -1,  [#permalink]

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08 Dec 2016, 19:58
What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A) 25% (B) 50% (C) 75% (D) 100% (E) 200%

Stuck with above problem looking for some guidance and assistance.
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Re: What is the minimum percentage increase in the mean of set X {-4, -1,  [#permalink]

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08 Dec 2016, 20:43
1
I think D.
Mean in the initial set is 2 (-4-2+0+6+9)/5. We should replace the smallest elements -4 and -1 with prime numbers also the smallest in order to have minimum percentage increase. So we get new set (2,3,0,6,9) with mean 4. So the minimum % increase is 100%

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Re: What is the minimum percentage increase in the mean of set X  [#permalink]

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09 Dec 2016, 02:09
anairamitch1804 wrote:
What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A) 25% (B) 50% (C) 75% (D) 100% (E) 200%

Stuck with above problem looking for some guidance and assistance.

Merging topics. Please refer to the discussion above.
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Re: What is the minimum percentage increase in the mean of set X  [#permalink]

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13 Jul 2017, 15:34
rohitgoel15 wrote:
What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A) 25%
(B) 50%
(C) 75%
(D) 100%
(E) 200%

minimize set [2, 3, 0 ,6, 9] = 20/5= 4

old set [-4,-1,0,6,9] = 10/5 =2

4-2/2 = 1

D
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Re: What is the minimum percentage increase in the mean of set X  [#permalink]

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08 Dec 2019, 03:02
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Re: What is the minimum percentage increase in the mean of set X   [#permalink] 08 Dec 2019, 03:02
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