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Math Expert V
Joined: 02 Sep 2009
Posts: 59728
In a set of five consecutive integers, which of the following must cha  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 54% (01:26) correct 46% (01:19) wrong based on 57 sessions

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In a set of five consecutive integers, which of the following must change the average of the set without changing its original median ?

A. Multiplying each of the numbers in the set by 6.
B. Adding 10 to each of the numbers in the set.
C. Subtracting 3.5 from each of the numbers in the set.
D. Adding 8.2 to the 2 largest numbers and subtracting 8.2 from the 3 smallest numbers in the set.
E. Adding 5 to the 2 largest and to the 2 smallest numbers in the set.

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GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5484
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
In a set of five consecutive integers, which of the following must cha  [#permalink]

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Bunuel wrote:
In a set of five consecutive integers, which of the following must change the average of the set without changing its original median ?

A. Multiplying each of the numbers in the set by 6.
B. Adding 10 to each of the numbers in the set.
C. Subtracting 3.5 from each of the numbers in the set.
D. Adding 8.2 to the 2 largest numbers and subtracting 8.2 from the 3 smallest numbers in the set.
E. Adding 5 to the 2 largest and to the 2 smallest numbers in the set.

ONLY option e satisfies the relation IMO E
Intern  B
Joined: 12 Sep 2017
Posts: 8
Re: In a set of five consecutive integers, which of the following must cha  [#permalink]

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Archit3110 wrote:
Bunuel wrote:
In a set of five consecutive integers, which of the following must change the average of the set without changing its original median ?

A. Multiplying each of the numbers in the set by 6.
B. Adding 10 to each of the numbers in the set.
C. Subtracting 3.5 from each of the numbers in the set.
D. Adding 8.2 to the 2 largest numbers and subtracting 8.2 from the 3 smallest numbers in the set.
E. Adding 5 to the 2 largest and to the 2 smallest numbers in the set.

ONLY option e satisfies the relation IMO E

hi
can u plz expalin how E is ANS .
if we take 1,2,3,4,5 then new set will be
6,7,3,9,10
& after rearrange 3,6,7,9,10
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5484
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In a set of five consecutive integers, which of the following must cha  [#permalink]

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jafy wrote:
Archit3110 wrote:
Bunuel wrote:
In a set of five consecutive integers, which of the following must change the average of the set without changing its original median ?

A. Multiplying each of the numbers in the set by 6.
B. Adding 10 to each of the numbers in the set.
C. Subtracting 3.5 from each of the numbers in the set.
D. Adding 8.2 to the 2 largest numbers and subtracting 8.2 from the 3 smallest numbers in the set.
E. Adding 5 to the 2 largest and to the 2 smallest numbers in the set.

ONLY option e satisfies the relation IMO E

hi
can u plz expalin how E is ANS .
if we take 1,2,3,4,5 then new set will be
6,7,3,9,10
& after rearrange 3,6,7,9,10

jafy

use series (-2,-1,0,1,2)

adding 5 to two largest and smallest would make it ( -4,-3,0,6,7)

Hope this helps..
Manager  G
Joined: 12 Apr 2011
Posts: 149
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31 GMAT 2: 720 Q50 V37 WE: Marketing (Telecommunications)
Re: In a set of five consecutive integers, which of the following must cha  [#permalink]

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Hey Buddy,

if the set is -2,-1,0,1,2

Add 5 to the 2 largest numbers:
1+5 = 6
2+5 = 7

Add 5 to the 2 smallest numbers:
-2+5 = 3
-1+5 = 4

Hence the set becomes:
(0,3,4,6,7) i.e. median changes from 0 to 4.

Do we have another example which proves the correct answer is E?

Posted from my mobile device
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5484
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In a set of five consecutive integers, which of the following must cha  [#permalink]

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eabhgoy wrote:
Hey Buddy,

if the set is -2,-1,0,1,2

Add 5 to the 2 largest numbers:
1+5 = 6
2+5 = 7

Add 5 to the 2 smallest numbers:
-2+5 = 3
-1+5 = 4

Hence the set becomes:
(0,3,4,6,7) i.e. median changes from 0 to 4.

Do we have another example which proves the correct answer is E?

Posted from my mobile device

eabhgoy :
Initially solving the question I had misread the option e .. which is why i got it..

IMO It’s not possible to change the average of the set without changing its median Bunuel , i think given answer choice is wrong.. please check. if not then please provide solution..
Manager  G
Joined: 12 Apr 2011
Posts: 149
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31 GMAT 2: 720 Q50 V37 WE: Marketing (Telecommunications)
Re: In a set of five consecutive integers, which of the following must cha  [#permalink]

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1
Archit3110 wrote:
eabhgoy wrote:
Hey Buddy,

if the set is -2,-1,0,1,2

Add 5 to the 2 largest numbers:
1+5 = 6
2+5 = 7

Add 5 to the 2 smallest numbers:
-2+5 = 3
-1+5 = 4

Hence the set becomes:
(0,3,4,6,7) i.e. median changes from 0 to 4.

Do we have another example which proves the correct answer is E?

Posted from my mobile device

eabhgoy :
Initially solving the question I had misread the option e .. which is why i got it..

IMO It’s not possible to change the average of the set without changing its median Bunuel , i think given answer choice is wrong.. please check. if not then please provide solution..

Actually, my answer was A which is marked as incorrect.

Taking your set as an example: -2,-1,0,1,2
Median = 0
Average = 0

Multiple all numbers by 6: -12,-6,0,6,12
Median = 0
Average = 0

Hence, in my opinion, the correct answer is A.
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5484
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
In a set of five consecutive integers, which of the following must cha  [#permalink]

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1
eabhgoy wrote:
Archit3110 wrote:
eabhgoy wrote:
Hey Buddy,

if the set is -2,-1,0,1,2

Add 5 to the 2 largest numbers:
1+5 = 6
2+5 = 7

Add 5 to the 2 smallest numbers:
-2+5 = 3
-1+5 = 4

Hence the set becomes:
(0,3,4,6,7) i.e. median changes from 0 to 4.

Do we have another example which proves the correct answer is E?

Posted from my mobile device

eabhgoy :
Initially solving the question I had misread the option e .. which is why i got it..

IMO It’s not possible to change the average of the set without changing its median Bunuel , i think given answer choice is wrong.. please check. if not then please provide solution..

Actually, my answer was A which is marked as incorrect.

Taking your set as an example: -2,-1,0,1,2
Median = 0
Average = 0

Multiple all numbers by 6: -12,-6,0,6,12
Median = 0
Average = 0

Hence, in my opinion, the correct answer is A.

eabhgoy
which of the following must change the average of the set without changing its original median

for the eg which you have cited it does not go well with the question as the avg/mean is not changing..

found similar question. the option here given is missing from the actual question..
https://greprepclub.com/forum/in-a-set- ... -8220.html
Director  V
Joined: 27 May 2012
Posts: 947
Re: In a set of five consecutive integers, which of the following must cha  [#permalink]

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jafy wrote:
Archit3110 wrote:
Bunuel wrote:
In a set of five consecutive integers, which of the following must change the average of the set without changing its original median ?

A. Multiplying each of the numbers in the set by 6.
B. Adding 10 to each of the numbers in the set.
C. Subtracting 3.5 from each of the numbers in the set.
D. Adding 8.2 to the 2 largest numbers and subtracting 8.2 from the 3 smallest numbers in the set.
E. Adding 5 to the 2 largest and to the 2 smallest numbers in the set.

ONLY option e satisfies the relation IMO E

hi
can u plz expalin how E is ANS .
if we take 1,2,3,4,5 then new set will be
6,7,3,9,10
& after rearrange 3,6,7,9,10

yes it is not possible to change the average of the set without changing the median.
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- Stne Re: In a set of five consecutive integers, which of the following must cha   [#permalink] 18 Mar 2019, 01:27
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