SumairaRounaq wrote:The mode of a set of 4 positive integers is 7. What is the least possible value of the sum of these 4 integers?
A) 14
B) 16
C) 17
D) 18
This comes down to the distinction between "the mode" and "a mode"
The mode of a set of 4 positive integers is 7.
This suggests that there is only 1 mode.
ASIDE: In the set {1, 2, 4, 4}, there's one mode: 4
In the set {3, 3, 4, 4}, there are two modes: 3 and 4
In the set {1, 2, 3, 4}, there are four modes: 1, 2, 3 and 4
If the mode of 4 POSITIVE INTEGERS is 7, then there must be
at least two 7's
So, our set now looks like this: {?, ?, 7, 7}
In order to MINIMIZE the sum, we must make the two remaining numbers as small as possible.
Since each number must be a POSITIVE INTEGER, one of the numbers must be 1, to get: {1, ?, 7, 7}
What about the last number?
IF that number were 1, then the set WOULD be: {1, 1, 7, 7}, in which case there would be TWO modes: 1 and 7. So, this set would break the condition that says "THE mode is 7"
So, we can't have two 1's
So, if the last number can't be 1, the next smallest number is 2 to get: {1, 2, 7, 7}
So, the smallest sum = 1 + 2 + 7 + 7 = 17
Answer: C
Cheers,
Brent
