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GMAT 1: 760 Q51 V42
Posts: 10,057
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Difficulty:
45%
(medium)
Question Stats:
63% (02:10) correct
37%
(02:12)
wrong
based on 178
sessions
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There are 10 numbers, 70, 70, 80, 80, 80,…100. If each of the smallest 5 numbers plus x and each of the largest 5 numbers minus y, what is the difference between the average (arithmetic mean) of the original 10 numbers and the average (arithmetic mean) of the changed 10 numbers when x>y?
1) x+y=10
2) x-y=4
* A solution will be posted in two days.
1) x+y=10
2) x-y=4
* A solution will be posted in two days.
The changed numbers are 70 + x, 70 + x, 80 + x,......100 - y
Since the changed numbers are a deviation from the original numbers, the difference in average will depend on the difference between the x and y values. i.e 5(x - y)/10
St1: x+y=10 --> Clearly Not Sufficient
St2: x-y=4 --> Difference = (5*4)/10 = 2 --> Sufficient
Answer: B
Since the changed numbers are a deviation from the original numbers, the difference in average will depend on the difference between the x and y values. i.e 5(x - y)/10
St1: x+y=10 --> Clearly Not Sufficient
St2: x-y=4 --> Difference = (5*4)/10 = 2 --> Sufficient
Answer: B
GMAT 1: 760 Q51 V42
Posts: 10,057
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.
There are 10 numbers, 70, 70, 80, 80, 80,…100. If each of the smallest 5 numbers plus x and each of the largest 5 numbers minus y, what is the difference between the average (arithmetic mean) of the original 10 numbers and the average (arithmetic mean) of the changed 10 numbers when x>y?
1) x+y=10
2) x-y=4
Modify the original condition and the question, suppose sum of the first five numbers S1 and the last five numbers S2. It becomes [(S1+5x)+(S2-5y)]/10-(S1+S2)/10=5(x-y)/10 and you only need to know x-y. Therefore, the answer is B.
Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
There are 10 numbers, 70, 70, 80, 80, 80,…100. If each of the smallest 5 numbers plus x and each of the largest 5 numbers minus y, what is the difference between the average (arithmetic mean) of the original 10 numbers and the average (arithmetic mean) of the changed 10 numbers when x>y?
1) x+y=10
2) x-y=4
Modify the original condition and the question, suppose sum of the first five numbers S1 and the last five numbers S2. It becomes [(S1+5x)+(S2-5y)]/10-(S1+S2)/10=5(x-y)/10 and you only need to know x-y. Therefore, the answer is B.
Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
Let the the sum of the 4 indefinite numbers be M.
The avg of the original numbers will be (70*2 + 80*3 + M + 100)/ 10
The avg of the modified numbers will be (70*2 + 80*3 + 5x + M + 100 - 5y)/10
To retrieve the difference we should extract the first part from the second one.
(70*2 +80* 3 + 5x + M +100 - 5y - (70*2 +80*3 + M + 100))/10 = (5x - 5y) /10
We have the following choices 1. x + y = 10. 2. x-y = 4
The first one provides no opportunity for our simplified result of the difference, while the second one may help.
If we multiply each side by 5 and divide by 10 we will get the exact difference between the averages of 2 sequences.
(5x-5y)/10 = 4*5/10
(5x-5y)/10 = 2
The correct answer is B
The avg of the original numbers will be (70*2 + 80*3 + M + 100)/ 10
The avg of the modified numbers will be (70*2 + 80*3 + 5x + M + 100 - 5y)/10
To retrieve the difference we should extract the first part from the second one.
(70*2 +80* 3 + 5x + M +100 - 5y - (70*2 +80*3 + M + 100))/10 = (5x - 5y) /10
We have the following choices 1. x + y = 10. 2. x-y = 4
The first one provides no opportunity for our simplified result of the difference, while the second one may help.
If we multiply each side by 5 and divide by 10 we will get the exact difference between the averages of 2 sequences.
(5x-5y)/10 = 4*5/10
(5x-5y)/10 = 2
The correct answer is B
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