ziyuenlau wrote:If the sum of the 7 positive integers is smaller than 12, what is the range of the 7 integers?
1) The sum of the 7 integers is 11
2) The median of the 7 integers is 2
Source : Math Revolution
Official Answer : B
Hi ziyuenlau,
These types of questions require you to play with numbers and do some hit and trial.
We have: Sum of the 7 positive integers < 12
We have to find the range of the 7 positive integers
Let's take each statement one by one.
S1: The sum of the 7 integers is 11.
We can at least a couple of extreme cases.
Case 1: The 7 integers are: 1, 1, 1, 1, 1, 1, 5. Range = 5 - 1 = 4.
Case 2: The 7 integers are: 1, 1, 1, 2, 2, 2, 2. Range = 2 - 1 = 1. No unqiue answer. Insufficient.
There can be other cases too.
S2: The median of the 7 integers is 2.
Say the integers arranged in ascending order are: a, b, c, 2, d, e, f
Since the 4th integer is the median, the minimum value d, e, and f each can take is 2.
Thus, the integers arranged in ascending order are: a, b, c, 2, 2, 2, 2
We have to make sure that a+b+c+2+2+2+2 < 12
=> a+b+c+8 < 12
=> a+b+c < 4
Since a, b and c are positive integers, the minimum and only value each can take is 1.
Thus, the integers are: 1, 1, 1, 2, 2, 2, 2. Range = 2 - 1 = 1. Sufficient.
The correct answer:
B
Hope this helps!
Relevant book:
Manhattan Review GMAT Data Sufficiency Guide
-Jay
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