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# If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu

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If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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27 Mar 2011, 00:07
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If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by number N, by what percent will the mean M of the set increase?

(1) Z = 60
(2) N = Z/M
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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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27 Mar 2011, 01:00
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vjsharma25 wrote:
If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by number N, by what percent will the
mean M of the set increase?
(A) Z = 60
(B) N = Z / M

I don't have answer for this.But I think answer should be

.
X {-14, -12, 17, 28, 41, Z}
If all the numbers are multiplied by a constant, the mean will also increase by that constant.

1. Z=60

We get a mean of 20 here initially.
If the set is multiplied by 10, the new mean becomes 200, increasing the mean by 900%
If the set is multiplied by 2, the new mean becomes 40, increasing the mean by 100%

We must find an exact value of multiplier or mean to find the percent increase in mean.
Not Sufficient.

2. N = Z / M

(-14, -12, 17, 28, 41 + Z)/6 = M

60+Z=6M
N = Z / M; Z=NM

60+NM=6M.
Not Sufficient to find an exact mean or multiplier.
Not Sufficient.

Combining both;
60+NM=6M
NM=Z=60
60+60=6M
M = 120/6= 20
And
N = Z/M = 60/20=3

We know the multiplier.
Sufficient.

Ans: "C"

P.S.: The new mean will increase by 20% because the multiplier is 3. We wouldn't need "Z" if we knew the multiplier, however in this case; we needed Z to find the multiplier.
##### General Discussion
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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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27 Mar 2011, 03:48
Mean , M = (-14 + -12 + 17 + 28 + 41 + Z)/6

=> M = (-26 + 86 + Z)/6

=> M = (60 + Z)/6

M1 = (60N + ZN)/6

So (M1 - M)/M = ?

{60(N-1) + Z(N-1)}/(60 + Z) = ?

From (1)

Z = 60, but (N-1) does not cancel out

From (2)

N = Z/M,

Z/N = (60 + Z)/6

=> N = 6Z/(60 + Z)

not sufficient

From (1) and (2)

M= 60/N

(60 + 60)/6 = 60/N

=> N = 3

So the values can be obtained further
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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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02 Apr 2011, 19:10
M = (60+z)/6

New Mean (lets say M1) = N(60+z)/6

% increase = ((M1-M)/M)*100
= (N-1)*100

1. Z =60

=> M = 20

no info on N. So not enough to calculate % increase. Not sufficient.

2. N = Z/M

not enough to calculate % increase ( because we dont know Z or M here)

together Z=0, M = 20 , N = Z/M = 3 , enough to calculate % increase.

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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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26 Jun 2013, 07:34

If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by number N, by what percent will the
mean M of the set increase?
(A) Z = 60
(B) N = Z / M

ANS (A) : The set totals to 120 provided 60 (Z) is added to it and therefore the mean is 20. Now let's take an assumption for "N" i.e 2 and multiply it. So the the mean now is 40 which is 200 % of 20. Therefore sufficient.
Further N can be assumed as odd no. and the % can be calculated therefore sufficient.

ANS (B) : N, here can be assumed as a number but what is Z (can be any no. again) and the mean depends on Z. Therefore insufficient.
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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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26 Jun 2013, 08:01
dasikasuneel wrote:

If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by number N, by what percent will the
mean M of the set increase?
(A) Z = 60
(B) N = Z / M

ANS (A) : The set totals to 120 provided 60 (Z) is added to it and therefore the mean is 20. Now let's take an assumption for "N" i.e 2 and multiply it. So the the mean now is 40 which is 200 % of 20. Therefore sufficient.
Further N can be assumed as odd no. and the % can be calculated therefore sufficient.

ANS (B) : N, here can be assumed as a number but what is Z (can be any no. again) and the mean depends on Z. Therefore insufficient.

Please note that the OA for this question is C, not A.

When a DS question asks about the value of some variable, then the statement is sufficient ONLY if you can get the single numerical value of this variable.

Different N's will give you different numerical increase for (1).

Hope it's clear.
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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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07 Dec 2013, 06:51
If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by number N, by what percent will the mean M of the set increase?

(1) Z = 60
(2) N = Z / M

Solution: If we increase/decrease each term in a set by the same percent( multiply all the terms by a constant), mean will increase/decrease by same percent. So, to know the percent increase in the mean we have to find 'N'

(1) By knowing the value of Z, we can find the value M, but we do not know the value of 'N' : Insufficient
(2) Since Z is unknown, we cannot find 'N': Insufficient

(1)+(2)
By first we can find the values of Z and M, which are 60 and 20 respectively, and by (2) we can find 'N', which is 3
Sufficient

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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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10 Aug 2016, 14:26
Since, Z is not defined and N is not given in the question ..
We cannot get the answer if anyone of these two miss..

Option 1, can only find Z not N.
Hence insufficient.

Option 2, cannot find any of them..

However, combining both can get the value of Z and N

Hence, option C is correct

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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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18 Sep 2016, 05:21
2
A) Z=60
by knowing the value of z we can calculate mean of set
but for percent increase in mean when multiplied by N, value of N is required.
Not suff
B) N= Z/M
without value of Z, M can't be found out and without value of M and Z, N can't be found out
Not Suff
So, combining we have value of Z and further value of M and N, hence percentage increase can be calculated
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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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03 May 2018, 01:23
shringi87 wrote:
If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by number N, by what percent will the mean M of the set increase?

(1) Z = 60
(2) N = Z/M

1. We find the value of the missing element in the Set X. But without
knowing the value of the variable the set has been multiplied by, we
cannot determine the percent change in the mean (Insufficient)

2. We don't the value of the missing element(Z) and can't find the
mean of the set without Z. We cannot determine the percent change
in the mean (Insufficient)

However, on combining both the statements, we find the value of the
missing element and can calculate the mean M. Using N = Z/M, we can
determine the value of N. We can now determine the percent change
in the mean, once we have an unique value for N. (Sufficient - Option C)
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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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03 May 2018, 15:53
shringi87 wrote:
If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by number N, by what percent will the mean M of the set increase?

(1) Z = 60
(2) N = Z/M

We need to find the percent change. So we need to know the new average and old average.
To find the new average, we need: Z and N
To find the old average, we need: Z or M

Statement 1
Only Z is given. We still need N. Not sufficient.

Statement 2
Z,N,M can be anything. Not sufficient.

Combining 1&2
In Statement 1, Z is given, so we can calculate M.
In Statement 2, N is given as Z/M, so we can calculate N.
We have enough info to determine the old & new averages.

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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu  [#permalink]

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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is multiplied by nu   [#permalink] 08 Dec 2019, 07:37
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