Asad wrote:
Walkabout wrote:
A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people?
(1) The number of people who wrote down an integer was greater than 40.
(2) The number of people who wrote down an integer was less than 70.
Hello,
What if the question has been changed a bit?
A number of people each wrote down one of the first 5 positive integers. Were any of the integers written down by more than one of the people?
(1) The number of people who wrote down an integer was greater than 2
(2) The number of people who wrote down an integer was less than 5
Is it E
Bunuel?
Thanks__
Hi Asad,
The approach that we could take with your version of the question would essentially be the same as the approach that we can take with the original form of the question (we can TEST VALUES to prove what the answer is):
We're told that an unknown number of people EACH wrote down one of the first 5 positive integers (1-5, inclusive). We're asked if ANY of the integers were written down by MORE than one person. This is a YES/NO question.
Given the 'restrictions' in this question, IF there are MORE than 5 people, then at least one of the numbers would be repeated. If there are 5 or LESS, then it's possible that a number was repeated, BUT it's also possible that NONE of the numbers were repeated.
1) The number of people who wrote down an integer was greater than 2
This information tells us that there were AT LEAST 3 people. If there were 3 people and they ALL wrote the SAME number, then the answer to the question is YES. If there were 3 people and they wrote down DIFFERENT numbers, then the answer to the question is NO.
Fact 1 is INSUFFICIENT
2) The number of people who wrote down an integer was less than 5
The examples that we used in Fact 1 can also be used in Fact 2:
This information tells us that there were NO MORE THAN 4 people. If there were 3 people and they ALL wrote the SAME number, then the answer to the question is YES. If there were 3 people and they wrote down DIFFERENT numbers, then the answer to the question is NO.
Fact 2 is INSUFFICIENT.
Combined, we know that there are either 3 people or 4 people. No additional work is required though, since we know that with 3 people, we could get a "YES" or a "NO" answer. The Final Answer would be E.
GMAT assassins aren't born, they're made,
Rich