ziyuenlau wrote:At least one pencil is distributed to each of the 19 students. Did at least two students receive the same number of pencils?
1) The number of pencils distributed to each student is less than 19.
2) The total number of pencils distributed to students is 187.
Source : Math Revolution
OA=D
Statement 1: The number of pencils distributed to each student is less than 19.
The statement implies that each student gets the number of pencils between 1 and 18, inclusive.
If we wish to distribute an unequal number of pencils to each student (1, 2, 3, ..., 18), the 19th student would get the number of pencils whose count is common with one among 18 students.
The answer is YES. At least two students received the same number of pencils. Sufficient
Statement 2: The total number of pencils distributed to students is 187.
If we wish to distribute an unequal number of pencils to each student (1, 2, 3, ..., 18, 19), the sum of the number fo pencils = 1+2+3, ...18+19.
If (1+2+3, ...18+19) > 187, it implies that at least two students received the same number of pencils.
If (1+2+3, ...18+19) <= 187, it implies that two students may or may not received the same number of pencils.
Let's calculate the sum of the number fo pencils = 1+2+3, ...18+19.
1+2+3, ...18+19 = 19*(19+1)/2 = 190.
Since SUM =190 > 187, at least two students received the same number of pencils. Sufficient.
The correct answer:
D
Hope this helps!
Relevant book:
Manhattan Review GMAT Data Sufficiency Guide
-Jay
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