A number of people each wrote down one

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. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient., Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient., BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient., EACH statement ALONE is sufficient., Statements (1) and (2) TOGETHER are not sufficient.

2 Explanations

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Ian Lee

This question confused me in the beginning and I realized I didn't read the question clear enough. It is asking were ANY of the first 30 integers written down by 1+ ppl (i.e. written down more than once), not asking if ALL the first 30 integers were written down.

Therefore, as long as we know there are people > 30 in the group, there is no way they can avoid having at least one number written more than once.

Dec 6, 2019 • Comment

Adam

You got it! And this does highlight the importance of reading very carefully and double checking everything, to make sure you've understood the question correctly! So long as you read it right, this one's not too tough :) But the potential for error is always there!

Dec 24, 2019 • Reply

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Mike McGarry, Magoosh Tutor