How many 5 existed in the 11 numbers?
1) The average (arithmetic mean) of the 11 numbers is 5
2) The median of the 11 numbers is 5
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How many 5 existed in the 11 numbers?
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- Max@Math Revolution
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I read the question as asking, "How many 5's are in the set of 11 numbers?"
It's the only way I could make sense of the "how many" part.
Statement 1: The average (arithmetic mean) of the 11 numbers is 5
This statement doesn't FEEL sufficient, so I'll TEST some cases.
There are several sets of numbers that satisfy statement 1. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: The median of the 11 numbers is 5
There are several sets of numbers that satisfy statement 2. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
There are several sets of numbers that satisfy BOTH statements. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
RELATED VIDEO:
Mean, Median & Mode: https://www.gmatprepnow.com/module/gmat ... /video/800
It's the only way I could make sense of the "how many" part.
Target question: How many 5's are in the set of 11 numbers?Max@Math Revolution wrote:How many 5's are in the set of 11 numbers?
1) The average (arithmetic mean) of the 11 numbers is 5
2) The median of the 11 numbers is 5
Statement 1: The average (arithmetic mean) of the 11 numbers is 5
This statement doesn't FEEL sufficient, so I'll TEST some cases.
There are several sets of numbers that satisfy statement 1. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: The median of the 11 numbers is 5
There are several sets of numbers that satisfy statement 2. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
There are several sets of numbers that satisfy BOTH statements. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
RELATED VIDEO:
Mean, Median & Mode: https://www.gmatprepnow.com/module/gmat ... /video/800
- Max@Math Revolution
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If we modify the original condition and the question, since we have 11 numbers, the median exists in these numbers. Hence, if we look at the condition 2), since the median is 5, 5 is always a part of 11 numbers. The answer is yes and the answer is B.
- 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.
- 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.
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