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During a certain week, a seal ate 50% of the first 80 smelt

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During a certain week, a seal ate 50% of the first 80 smelt [#permalink] New post 24 May 2013, 14:44
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During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80
[Reveal] Spoiler: OA

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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink] New post 24 May 2013, 14:50
Expert's post
pikachu wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80


Total smelt = x.

Then, 0.5*80+0.3(x-80)=0.4*x --> x=160 --> 0.4*x=64.

Answer: D.
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink] New post 25 May 2013, 02:34
Bunuel wrote:
pikachu wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80


Total smelt = x.

Then, 0.5*80+0.3(x-80)=0.4*x --> x=160 --> 0.4*x=64.

Answer: D.



Bunuel why I am getting a different answer?

Let say Total number of Smelt be - 100

Seal ate - 50% of 80 I.e 40
Than.....- 30% of remaining 20(100-80) I.e 6
Which comes to total of 46(40+6)

Now its given seal ate total of 40%....

In that case 46/40*100 comes to 115 total no of spate......

Where I am going wrong ...can you explain please???
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink] New post 25 May 2013, 02:37
Expert's post
nikhilsehgal wrote:
Bunuel wrote:
pikachu wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80


Total smelt = x.

Then, 0.5*80+0.3(x-80)=0.4*x --> x=160 --> 0.4*x=64.

Answer: D.



Bunuel why I am getting a different answer?

Let say Total number of Smelt be - 100

Seal ate - 50% of 80 I.e 40
Than.....- 30% of remaining 20(100-80) I.e 6
Which comes to total of 46(40+6)

Now its given seal ate total of 40%....

In that case 46/40*100 comes to 115 total no of spate......

Where I am going wrong ...can you explain please???


The number of smelt is some particular number you cannot assume that it's 100.
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink] New post 23 May 2014, 01:45
Hi,

I am getting a different answer. My approach:
1. First Part - 80 smelts - 50% eaten = 40 ....... Statement 1
2. 2nd Part - x smelts - 30% eaten = 0.3x ....... Statement 2

Total Smelts = 1st part + 2nd part = 80+x
Seal ate 40% of total smelts => 0.4 (80+x) ....... Statement 3

Therefore , combining Statement 1,2,3
40 + 0.3x = 0.4(80+x) . This is giving x = 80 and 32 as the answer.

Kindly assist where I have gone wrong. Thanks
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink] New post 23 May 2014, 02:04
Expert's post
mayankgc wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80

Hi,

I am getting a different answer. My approach:
1. First Part - 80 smelts - 50% eaten = 40 ....... Statement 1
2. 2nd Part - x smelts - 30% eaten = 0.3x ....... Statement 2

Total Smelts = 1st part + 2nd part = 80+x
Seal ate 40% of total smelts => 0.4 (80+x) ....... Statement 3

Therefore , combining Statement 1,2,3
40 + 0.3x = 0.4(80+x) . This is giving x = 80 and 32 as the answer.

Kindly assist where I have gone wrong. Thanks


We are told that the seal ate 30% of the remaining smelt it came across. Thus x in your solution must be the number of the remaining smelt. Which makes the total number of smelt equal to 80 + x = 160. 40% of 160 is 64.

Does this make sense?
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink] New post 24 May 2014, 06:51
Yes it clears out my confusion
Thanks Bunuel... :)
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink] New post 25 May 2014, 22:25
Expert's post
pikachu wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80


Responding to a pm:

The seal ate 50% of first portion and 30% of second portion. Overall (average), it ate 40% of the entire portion.

Using scale method, Second portion/First portion = (50 - 40)/(40 - 30) = 1/1

So both portions need to be equal i.e. of 80 smelts each. So both portions together had 160 smelts and the seal ate 40% of it i.e. (40/100)*160 = 64 smelts
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink] New post 19 Sep 2015, 13:24
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Re: During a certain week, a seal ate 50% of the first 80 smelt   [#permalink] 19 Sep 2015, 13:24
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