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Math Expert V
Joined: 02 Sep 2009
Posts: 58401
When a student Joe, weighing 41 kg, joins a group of students whose av  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 69% (02:55) correct 31% (02:56) wrong based on 107 sessions

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When a student Joe, weighing 41 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?

A. 5.5 kg
B. 11 kg
C. 30 kg
D. 36.5 kg
E. 71 kg

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Intern  Joined: 10 Nov 2014
Posts: 8
When a student Joe, weighing 41 kg, joins a group of students whose av  [#permalink]

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Bunuel wrote:
When a student Joe, weighing 41 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?

A. 5.5 kg
B. 11 kg
C. 30 kg
D. 36.5 kg
E. 71 kg

Just a series of calculations, nothing more than that. When you see problems like this, start by trying to figure out whatever new tidbits of data you can deduce using the information in the passage. Then use that new data to deduce even more data that will eventually lead to the answer.

Knowing Joe's weight and the exact influence his weight has on the average weight of the group, we should be able to figure out the number of people (n) that were originally in that group, using the formula to calculate the average of any set of numbers.

$$(30n + 41)/(n + 1) = 31$$

Doing some simple math there gives us n = 10. With Joe having thrown his weight into the group, we now have 11 people in this group, with the total weight now being 341 kgs (which we deduced from $$30n + 41$$) . Now we know that when 2 certain people in that group leave, the average weight returns back to 30. We could figure out the collective weight (w) of those two people in the group then, once again using the average formula.

$$(341 - w)/9 = 30$$

Doing some more remedial math gives us w = 71, which means the average weight of the two people that left the group is 35.5 kgs. The difference between that average and Joe's weight is 5.5 kgs (A)
Math Expert V
Joined: 02 Aug 2009
Posts: 7969
Re: When a student Joe, weighing 41 kg, joins a group of students whose av  [#permalink]

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Bunuel wrote:
When a student Joe, weighing 41 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?

A. 5.5 kg
B. 11 kg
C. 30 kg
D. 36.5 kg
E. 71 kg

Hi everyone,

It is a 700 level Q, But a bit of logic can convert this into a very easy Q..

A 10 SECONDS APPROACH..

We can solve this in under 10 seconds due to the choice available..

By removing two weights, 31 goes down to 30..
so the Quantity taken out must be greater than 31..
so the difference<41-31 or D<10..
Only 5.5 is possible in available choices
A

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7969
When a student Joe, weighing 41 kg, joins a group of students whose av  [#permalink]

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Bunuel wrote:
When a student Joe, weighing 41 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?

A. 5.5 kg
B. 11 kg
C. 30 kg
D. 36.5 kg
E. 71 kg

Hi,
One more method other than 10 secs approach..

Say the choices were not so revealing or we had to find the number of students too..

1) if adding of 41 to some quantity of 30s increases average by 1kg..
we are increasing each person by 1 kg by adding a person, who is 11 kgs higher, so NUMBER=11/1=11..

also by weighted average
say n students were already there..
$$\frac{(31-30)}{(41-30)}=\frac{1}{(n+1)}$$..
n=10..

so weight = 30*10+41=341..

with two moving out, the average weight comes down to 30..
so weight of remaining 11-2 or 9 is 9*30=270..

weight of two left= 341-270=71
average weight of these two=71/2=35.5

Difference=41-35.5=5.5

A

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Manager  Joined: 09 Jun 2015
Posts: 88
Re: When a student Joe, weighing 41 kg, joins a group of students whose av  [#permalink]

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Bunuel wrote:
When a student Joe, weighing 41 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?

A. 5.5 kg
B. 11 kg
C. 30 kg
D. 36.5 kg
E. 71 kg

After two persons leave the group the average remains the same. That means the weight of the two persons = 41+30 = 71
So, the average the two persons = 35.5
That gives the answer 41-35.5 = 5.5
Manager  B
Joined: 20 Aug 2015
Posts: 90
Location: India
GMAT 1: 710 Q50 V36 GPA: 3
Re: When a student Joe, weighing 41 kg, joins a group of students whose av  [#permalink]

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Let n be the number of students.

weight/n = 30

(weight+41)/n+1 = 31

These two equations give n = 10, weight = 300.

So, including Joe, weight is 341. When two students of weight a and b leave, we are left with 9 students.

(341-a-b)/9 = 30
=> a+b = 71.

The avg weight of these two students is 35.5

The diff between the weights of Joe and their avg is 5.5

(A)
VP  P
Joined: 07 Dec 2014
Posts: 1222
When a student Joe, weighing 41 kg, joins a group of students whose av  [#permalink]

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Bunuel wrote:
When a student Joe, weighing 41 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?

A. 5.5 kg
B. 11 kg
C. 30 kg
D. 36.5 kg
E. 71 kg

let w=total original weight of group
s=original students in group
w=30s
(30s+41)/(s+1)=31➡
s=10
w=300
let x/2=average weight of two students leaving
300/10=(341-x)/9
x=71
x/2=35.5
41-35.5=5.5 kg
A When a student Joe, weighing 41 kg, joins a group of students whose av   [#permalink] 09 Apr 2018, 18:37
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