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# Thirteen men have an average (arithmetic mean) weight of 140 pounds.

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Thirteen men have an average (arithmetic mean) weight of 140 pounds.  [#permalink]

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12 May 2017, 05:00
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5% (low)

Question Stats:

98% (01:29) correct 2% (03:04) wrong based on 60 sessions

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Thirteen men have an average (arithmetic mean) weight of 140 pounds. When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds. What is the total weight of the three men?

A. 190
B. 404
C. 440
D. 510
E. 570

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Re: Thirteen men have an average (arithmetic mean) weight of 140 pounds.  [#permalink]

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12 May 2017, 06:16
1
Bunuel wrote:
Thirteen men have an average (arithmetic mean) weight of 140 pounds. When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds. What is the total weight of the three men?

A. 190
B. 404
C. 440
D. 510
E. 570

Short Method :
13 men have an average wt. of 140 pounds. When 3 men are removed, the average wt. of the remaining 10 becomes 138 .
So we can think of it as, the 3 men took away their own weight which is equal to (average wt x 3 + 2 kg each of 10 people) = 140 x 3 + 2 x 10 = 440

Long and calculation intensive method :

13 men have an average wt. of 140 pounds. So total weight = 13 x 140 = 1820
After 3 men left the average wt. was 138 pounds. So total wt. of 10 men = 1380

Difference = 1820 - 1380 = 440

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Re: Thirteen men have an average (arithmetic mean) weight of 140 pounds.  [#permalink]

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12 May 2017, 06:24
Top Contributor
Bunuel wrote:
Thirteen men have an average (arithmetic mean) weight of 140 pounds. When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds. What is the total weight of the three men?

A. 190
B. 404
C. 440
D. 510
E. 570

Thirteen men have an average (arithmetic mean) weight of 140 pounds.
So, (SUM of all 13 men)/13 = 140
Multiply both sides by 13 to get: SUM of all 13 men = (140)(13) = 1820

When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds.
In other words, the REMAINING 10 men have an average weight of 138 pounds.
So, (SUM of REMAINING 10 men)/10 = 139
Multiply both sides by 10 to get: SUM of REMAINING 10 men = (138)(10) = 1380

Difference in TOTAL weights = 1820 - 1380 = 440
Since the TOTAL weight decreased by 440 pounds, we know that this must be the combined weight of the 3 men who were removed.

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Re: Thirteen men have an average (arithmetic mean) weight of 140 pounds.  [#permalink]

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12 May 2017, 06:31
GMATPrepNow wrote:
Bunuel wrote:
Thirteen men have an average (arithmetic mean) weight of 140 pounds. When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds. What is the total weight of the three men?

A. 190
B. 404
C. 440
D. 510
E. 570

Thirteen men have an average (arithmetic mean) weight of 140 pounds.
So, (SUM of all 13 men)/13 = 140
Multiply both sides by 13 to get: SUM of all 13 men = (140)(13) = 1820

When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds.
In other words, the REMAINING 10 men have an average weight of 138 pounds.
So, (SUM of REMAINING 10 men)/10 = 139
Multiply both sides by 10 to get: SUM of REMAINING 10 men = (138)(10) = 1380

Difference in TOTAL weights = 1820 - 1380 = 440
Since the TOTAL weight decreased by 440 pounds, we know that this must be the combined weight of the 3 men who were removed.

RELATED VIDEO

If the numbers are bigger we will have to do lots of calculations in this process. So we should learn to solve by short process also as I suggested in my solution, where we directly calculate the weights without multiplying the big numbers and substracting ..

What's your take on this GMATPrepNow...
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Re: Thirteen men have an average (arithmetic mean) weight of 140 pounds.  [#permalink]

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12 May 2017, 06:38
Top Contributor
shashankism wrote:
If the numbers are bigger we will have to do lots of calculations in this process. So we should learn to solve by short process also as I suggested in my solution, where we directly calculate the weights without multiplying the big numbers and substracting ..

What's your take on this GMATPrepNow...

If you're asking whether it's advantageous to solve questions using the fastest approach possible, then I'm going to have to say.........wait for it...................yes.
In this case, the numbers seems reasonably small enough to work with.

Cheers,
Brent
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Re: Thirteen men have an average (arithmetic mean) weight of 140 pounds.  [#permalink]

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16 May 2017, 18:23
1
Bunuel wrote:
Thirteen men have an average (arithmetic mean) weight of 140 pounds. When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds. What is the total weight of the three men?

A. 190
B. 404
C. 440
D. 510
E. 570

We are given that 13 men have an average (arithmetic mean) weight of 140 pounds. Thus, the 13 men weigh a total of 13 x 140 = 1820 pounds.

When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds. We can let n = the sum of the weights of the 3 removed men and we have:

138 = (1820 - n)/10

1380 = 1820 - n

n = 440

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Re: Thirteen men have an average (arithmetic mean) weight of 140 pounds.  [#permalink]

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12 Aug 2017, 03:27
shashankism wrote:
Bunuel wrote:
Thirteen men have an average (arithmetic mean) weight of 140 pounds. When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds. What is the total weight of the three men?

A. 190
B. 404
C. 440
D. 510
E. 570

Short Method :
13 men have an average wt. of 140 pounds. When 3 men are removed, the average wt. of the remaining 10 becomes 138 .
So we can think of it as, the 3 men took away their own weight which is equal to (average wt x 3 + 2 kg each of 10 people) = 140 x 3 + 2 x 10 = 440

Long and calculation intensive method :

13 men have an average wt. of 140 pounds. So total weight = 13 x 140 = 1820
After 3 men left the average wt. was 138 pounds. So total wt. of 10 men = 1380

Difference = 1820 - 1380 = 440

Can someone please explain this short method more? I don't understand how shashankism took 2kg of 10 people...
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Re: Thirteen men have an average (arithmetic mean) weight of 140 pounds.  [#permalink]

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12 Aug 2017, 04:41
Top Contributor
Teerex wrote:
shashankism wrote:
Bunuel wrote:
Thirteen men have an average (arithmetic mean) weight of 140 pounds. When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds. What is the total weight of the three men?

A. 190
B. 404
C. 440
D. 510
E. 570

Short Method :
13 men have an average wt. of 140 pounds. When 3 men are removed, the average wt. of the remaining 10 becomes 138 .
So we can think of it as, the 3 men took away their own weight which is equal to (average wt x 3 + 2 kg each of 10 people) = 140 x 3 + 2 x 10 = 440

Long and calculation intensive method :

13 men have an average wt. of 140 pounds. So total weight = 13 x 140 = 1820
After 3 men left the average wt. was 138 pounds. So total wt. of 10 men = 1380

Difference = 1820 - 1380 = 440

Can someone please explain this short method more? I don't understand how shashankism took 2kg of 10 people...

Total weight of the three men ,
=13*140-10*138
=(10+3)(138+2)-10*138
=10(138+2)+3(138+2)-10*138
=10*138+20+420-10*138
=20+420
=440

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Re: Thirteen men have an average (arithmetic mean) weight of 140 pounds.  [#permalink]

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12 Aug 2017, 10:52
AbdurRakib wrote:
Teerex wrote:
shashankism wrote:
Thirteen men have an average (arithmetic mean) weight of 140 pounds. When 3 of the men are removed from the group, the average weight of the remaining men becomes 138 pounds. What is the total weight of the three men?

A. 190
B. 404
C. 440
D. 510
E. 570

Short Method :
13 men have an average wt. of 140 pounds. When 3 men are removed, the average wt. of the remaining 10 becomes 138 .
So we can think of it as, the 3 men took away their own weight which is equal to (average wt x 3 + 2 kg each of 10 people) = 140 x 3 + 2 x 10 = 440

Long and calculation intensive method :

13 men have an average wt. of 140 pounds. So total weight = 13 x 140 = 1820
After 3 men left the average wt. was 138 pounds. So total wt. of 10 men = 1380

Difference = 1820 - 1380 = 440

Can someone please explain this short method more? I don't understand how shashankism took 2kg of 10 people...

Total weight of the three men ,
=13*140-10*138
=(10+3)(138+2)-10*138
=10(138+2)+3(138+2)-10*138
=10*138+20+420-10*138
=20+420
=440

I was asking for an explanation for this calculation "140 x 3 + 2 x 10 = 440 " that shashankism wrote..
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Re: Thirteen men have an average (arithmetic mean) weight of 140 pounds.   [#permalink] 12 Aug 2017, 10:52
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