Azizakaria wrote:Range = biggest - smallest.
Any set of 100 consecutive multiples of 7 will have the SAME RANGE.
Thus, the problem above is the same as the following:
What is the range of the first 100 positive multiples of 7?
First positive multiple of 7 = 1*7 = 7.
100th positive multiple of 7 = 100*7 = 700.
Range = biggest - smallest = 700-7 = 693.
The correct answer is A
.
Yes, but it says " that are greater than 70" how it can be the same as "the first 100 positive multiples of 7" ?
shouldn't I add 70 to the total because I'm skipping the 7 multiplies till 70 ?
ANY SET of 100 consecutive multiples of x will have the SAME RANGE.
Case 1: First 100 positive multiples of 7
smallest = 1*7 =
7.
biggest = 100*7 =
700.
range = biggest - smallest = 700-7 = 693.
Case 2: First 100 positive multiple of 7 greater than 70
To determine the smallest and the biggest, add 70 to each of the blue values in Case 1.
smallest =
7 + 70 = 77.
biggest =
700 + 70 = 770.
range = biggest - smallest = 770 - 77 = 693.
In each case, the range is 693.
The reason:
When we proceed from Case 1 to Case 2, the two values used to calculate the range -- the smallest and the biggest -- each increase by the SAME AMOUNT (70).
Since both values increase by the same amount, their difference does not change.
The result:
The range in each case is THE SAME.
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