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# The average weight of students in a class of 20 was 80 pounds. Five

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Manager
Joined: 07 Jun 2017
Posts: 176
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
The average weight of students in a class of 20 was 80 pounds. Five [#permalink]

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13 Nov 2017, 05:11
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Difficulty:

65% (hard)

Question Stats:

62% (01:53) correct 38% (02:17) wrong based on 45 sessions

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The average weight of students in a class of 20 was 80 pounds. Five new students joined and the weight increased to 84
pounds. If weights of the five new students are in integers, weight of no two students is same, and the lightest new student
weighs 84 pounds, what is the highest possible weight of the heaviest new student?

A. 100
B. 116
C. 158
D. 164
E. 172
[Reveal] Spoiler: OA

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Naveen
email: nkmungila@gmail.com
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Math Expert
Joined: 02 Aug 2009
Posts: 5719
The average weight of students in a class of 20 was 80 pounds. Five [#permalink]

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13 Nov 2017, 05:27
Expert's post
1
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BOOKMARKED
nkmungila wrote:
The average weight of students in a class of 20 was 80 pounds. Five new students joined and the weight increased to 84
pounds. If weights of the five new students are in integers, weight of no two students is same, and the lightest new student
weighs 84 pounds, what is the highest possible weight of the heaviest new student?

A. 100
B. 116
C. 158
D. 164
E. 172

A shortcut and logical way..

weight of these 5 has increased the average weight by 4, so overall increase $$4*(20+5)=4*25=100$$
now lowest is 84 so his role is 4 kgs in 100, others lowest possible will increase by 5,6, and 7 .. total $$= 4+5+6+7=22$$
so the largest guy will increase the weight by 100-22=78, so his weight = $$78+80=158$$
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Math Expert
Joined: 02 Aug 2009
Posts: 5719
Re: The average weight of students in a class of 20 was 80 pounds. Five [#permalink]

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13 Nov 2017, 05:33
Expert's post
1
This post was
BOOKMARKED
nkmungila wrote:
The average weight of students in a class of 20 was 80 pounds. Five new students joined and the weight increased to 84
pounds. If weights of the five new students are in integers, weight of no two students is same, and the lightest new student
weighs 84 pounds, what is the highest possible weight of the heaviest new student?

A. 100
B. 116
C. 158
D. 164
E. 172

Normal method

total weight earlier = $$20*80=1600$$
new increased weight = $$84*25=2100$$

lowest in these 5 is 84, so others should be 85,86 and 87....
total = $$84+85+86+87=342$$

so the heaviest person = $$2100-1600-342=158$$
C
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Re: The average weight of students in a class of 20 was 80 pounds. Five   [#permalink] 13 Nov 2017, 05:33
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