Is the sum of integers from 54 to 153,inclusive, divisible by 100?
Approach 1(explanation in mgmat guide) -
No. of terms =>153 - 54+1=100. No. of terms are even so special sums rule does not hold therefore the answer is "NO"
Special sums rule - the sum of odd no. of integers is always divisible by the no. of terms in the set but this does NOT work for even no. of terms(which is our case)
Approach 2(trying out the other way coz of which I get a different answer)
1) No. of terms is 100
2) Average of the 1st and last term is (54+153)/2= 103.5
3) 100 * 103.5 gives a multiple of 100
therefore the answer is "YES"
Can anyone explain the difference in the results?
Approach 1(explanation in mgmat guide) -
No. of terms =>153 - 54+1=100. No. of terms are even so special sums rule does not hold therefore the answer is "NO"
Special sums rule - the sum of odd no. of integers is always divisible by the no. of terms in the set but this does NOT work for even no. of terms(which is our case)
Approach 2(trying out the other way coz of which I get a different answer)
1) No. of terms is 100
2) Average of the 1st and last term is (54+153)/2= 103.5
3) 100 * 103.5 gives a multiple of 100
therefore the answer is "YES"
Can anyone explain the difference in the results?
