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Manager  Joined: 10 Nov 2010
Posts: 125
If every member of set X {-14, -12, 17, 28, 41, Z} is  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 67% (02:00) correct 33% (02:02) wrong based on 488 sessions

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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
Retired Moderator Joined: 20 Dec 2010
Posts: 1643
Re: Mean after multiplying  [#permalink]

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1
4
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.
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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is  [#permalink]

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fluke wrote:
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.
What is the level of this question?

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
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Re: If every member of set X {-14, -12, 17, 28, 41, Z} is  [#permalink]

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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
Manager  Joined: 10 Nov 2010
Posts: 125
Re: Mean after multiplying  [#permalink]

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gmat1220 wrote:
I think this is loner. It is A.

But after multiplying every number by N,N will come into picture for new mean. And if you don't know N u can't calculate the % increase.
Taking statement A into effect
Old Mean = 120/6
New mean = 120N/6

You don't have N!!
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Re: Mean after multiplying  [#permalink]

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Guys,
Btw do you know where is Bunuel is these days? He is seldom online now.
Retired Moderator Joined: 20 Dec 2010
Posts: 1643
Re: Mean after multiplying  [#permalink]

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gmat1220 wrote:
Guys,
Btw do you know where is Bunuel is these days? He is seldom online now.

You know what, "I was wondering about the same". Please come back soon Legend, we are deprived of your elegant solutions/approach. Perhaps "bb" can tell us where he is these days and when will he be coming back.
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Re: Mean after multiplying  [#permalink]

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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: Mean after multiplying  [#permalink]

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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  [#permalink]

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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?
(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  [#permalink]

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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: Mean after multiplying  [#permalink]

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fluke wrote:
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.

I don't understand how you know the mean will increase by 20% by knowing that the multiplier is 3 (and not needing to know "Z")
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GMAT 1: 670 Q47 V35 Re: If every member of set X {-14, -12, 17, 28, 41, Z} is  [#permalink]

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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

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

Intern  Joined: 08 Jun 2016
Posts: 8
Re: If every member of set X {-14, -12, 17, 28, 41, Z} is  [#permalink]

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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

Sent from my AO5510 using Tapatalk Re: If every member of set X {-14, -12, 17, 28, 41, Z} is   [#permalink] 10 Aug 2016, 14:26
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