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07 Mar 2016, 09:01
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:13) correct
31%
(02:19)
wrong
based on 930
sessions
History
Date
Time
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Not Attempted Yet
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) The company that donated the most gave $38,000
(2) The company that donated the second least gave $4000
08 Mar 2016, 17:35
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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.
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.
General Discussion
08 Mar 2016, 02:46
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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
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
