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Six different companies are each donating a certain amount of money to

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Six different companies are each donating a certain amount of money to  [#permalink]

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New post 07 Mar 2016, 08:01
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A
B
C
D
E

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  45% (medium)

Question Stats:

68% (02:04) correct 32% (02:23) wrong based on 386 sessions

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Six different companies are each donating a certain amount of money to a specific charity. Each company is donating a different amount of money, and the total amount donated by the six companies is $58,000. Did at least one of companies donate less than $3000?

(1) The company that donated the most gave $38,000

(2) The company that donated the second least gave $4000

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Re: Six different companies are each donating a certain amount of money to  [#permalink]

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New post 08 Mar 2016, 01:46
1
Let the 6 companies be 1, 2, 3, 4, 5 and 6 in the ascending order of donations.

St1: 1 + 2 + 3 + 4 + 5 = 20000
Donations can be: 3800 + 3900 + 4000 + 4100 + 4200 --> No company donated < 3000
Donations can be: 2000 + 3000 + 4000 + 4200 + 4888 --> Yes 1 company donated < 3000
St1 is not sufficient

St2: One company paid less than 4000. Not sufficient to determine if the donation was less than 3000

Combining St1 and St2,
1 + 3 + 4 + 5 = 16000
3000 + 4100 + 4200 + 4700 = 16000 --> No company made donations < 3000
2500 + 4100 + 4200 + 5200 = 16000 --> Yes 1 company made donations < 3000
Still not sufficient

Answer: E
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Re: Six different companies are each donating a certain amount of money to  [#permalink]

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New post 08 Mar 2016, 16:35
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Six different companies are each donating a certain amount of money to a specific charity. Each company is donating a different amount of money, and the total amount donated by the six companies is $58,000. Did at least one of companies donate less than $3000?

(1) The company that donated the most gave $38,000

(2) The company that donated the second least gave $4000


In the original condition, there are 6 variables(6 different companies) and 1 equation(the total amount is $58,000), which should match with the number of equations. So you need 5 more equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
In fact, when 1) & 2), the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: Six different companies are each donating a certain amount of money to  [#permalink]

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New post 13 May 2016, 12:36
1
This is how i worked out

No. of Companies = 6
Total = 58,000
St1:- Max donation by a company is 38,000 leaving 20,000 among 5 companies. Average would be 4000/company which means there is a possibility one might be in mid 3K range while another in mid 4K range while another in mid2K range or all of them could evenly contribute 4K each. Not sufficient.
.
St2:- Second lest is 4K :- statement itself would leave 54,000 spread among 5 companies hence multiple possibilities and not sufficient.
.
Together :- 42,000 spent among 2 companies remaining 4 will a total of 16,000 which means an average of 4K again leaving possibilities.
Again not sufficient. so Answer is E

Going an extra mile a definitive answer is possible only when the average arrived at after considering st1 and st2 is either less than 3,000 or the question stem puts a constraint on amounts that can be spent by the companies.
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Re: Six different companies are each donating a certain amount of money to  [#permalink]

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New post 30 Mar 2017, 14:31
Bunuel wrote:
Six different companies are each donating a certain amount of money to a specific charity. Each company is donating a different amount of money, and the total amount donated by the six companies is $58,000. Did at least one of companies donate less than $3000?

(1) The company that donated the most gave $38,000

(2) The company that donated the second least gave $4000


1. we have 20k for 5 companies.
average, that's 4k.
we can have 1000, 2000, 3000, 4000, 4500, 5500 - answer is yes
we can have 3000, 3100, 3200, 3300, 3400, 4000 - answer is no

A & D are out.

2. second donated 4k
we can have 3000, 3100, 3200, 3300, 3400, 4000 - answer is no
or
we can have 2999, 3101, 3200, 3300, 3400, 4000 - answer is yes

1+2
we can have 3000, 3100, 3200, 3300, 3400, 4000 - answer is no
or
we can have 2999, 3101, 3200, 3300, 3400, 4000 - answer is yes


E is the answer
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Re: Six different companies are each donating a certain amount of money to  [#permalink]

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New post 13 Jul 2017, 10:56
2
Six different companies are each donating a certain amount of money to a specific charity. Each company is donating a different amount of money, and the total amount donated by the six companies is $58,000. Did at least one of companies donate less than $3000?

(1) The company that donated the most gave $38,000

Maximum donation: $38,000

This means the remaining amount of = $58,000 - $38,000 = $20,000 is paid by the remaining 5 companies.

As we do not have any further information, we can have scenarios where the amount is < $3,000 and >$3,000.

Hence, (1) ===== is NOT SUFFICIENT

(2) The company that donated the second least gave $4000

This gives us information about the second least amount as $4,000

Once again we can have scenarios where the amount is < $3,000 and >$3,000

Hence, (2) ===== is NOT SUFFICIENT

Combining (1) & (2)

Even after combining, we only know two values $38,000 & $4,000. we are now left with $16,000 which is being paid by 4 companies.

As the average amount comes down to $4,000, we can have scenarios where the amount is < $3,000 and >$3,000

Hence, (1) & (2) ===== is NOT SUFFICIENT

Hence, Answer is E

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Re: Six different companies are each donating a certain amount of money to  [#permalink]

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