Bunuel wrote:
Official Solution:
How many of the three-digit numbers are divisible by 7?
A. 105
B. 106
C. 127
D. 128
E. 142
Approach One: Divide all of the three-digit numbers \(999 - 100 + 1 = 900\)(Don't forget to add 1 to get the number of all the 3-digit numbers) by 7, which is 128.57, and then round it off to 128.
Approach Two: Find the first and the last multiples of 7 WITHIN the range (which is between 105 and 994). Find the positive difference, divide by 7, and add 1:
\(\frac{994-105}{7}+1=128\)
Answer: D
Hi Bunuel,
Although I solved this question using approach 2 and got it correct, I would prefer to use the Approach 1 as advised by you as it is a shorter method to solve the same.
But I have a doubt regd Approach 1:
1) In approach 1 should we ALWAYS first add 1 and then divide by 7 (or whatever number's multiple we have to find out)?
2) In approach 1 should we ALWAYS round off the resultant number to a smaller number as done in this case or does it change in certain cases?
Basically will approach one work the same way in all such type of questions no matter what range and what number's multiple we have to find out?
I have the same doubt as rohit. Approach 2 works all the time, there is no doubt on its credibility. But approach 1 is much more quicker than approach 2(since we dont need to find 1st and last terms). If the answer choices are not close we can safely use Approach 1(if 127 is not given as an option). Due to the glitches in approach 1, as explained by
in this thread, we cannot always use Approach 1.
Please mention my name in your valuable replies.