7/30/2019 Puzzle.txt

1/2

Example:What is the sum of the consecutive integers from 51 101, inclusive?

Step 1: Find the middle numberThe middle number in a set of consecutive numbers is also the average of that set of numbers. Interestingly, it is also the average of the first and last number.

In our example, the first number is 51 and the last is 101. The average is:

(51 + 101)/2 = 152/2 = 76

Step 2: Find the number of numbersThe number of integers is found by the following formula: Last Number First Number + 1. That "plus 1" is the part most people forget. When you just subtract twonumbers, by definition, you are finding one less than the number of total numbers between them. Adding 1 back in solves that problem.

In our example:

101 51 + 1 = 50 + 1 = 51

Step 3: MultiplyBecause the middle number is actually the average and step two finds the number

of numbers, you just multiply them together to get the sum:

76*51 = 3,876

Thus, the sum of 51 + 52 + 53 + + 99 + 100 + 101 = 3,876

Click here to road test this tip on an IL700 GMAT question.

NOTE: This works with all consecutive sets, such as consecutive even sets, consecutive odd sets, consecutive multiples of five, etc. The only difference is in Step 2. In these cases, after you subtract Last First, you must divide by the common difference between the numbers, and then add 1. Here are some examples:

Consecutive even integers from 14 24:(24 14)/2 + 1 = 6 (the difference between each number in the set is 2)

Consecutive odd integers from 23 67:(67 23)/2 + 1 = 23 (the difference between each number in the set is 2)

Consecutive multiples of five from 25 75:(75 25)/5 + 1 = 11(the difference between each number in the set is 5)

A man wanted to give 20 coconuts to the temple. He had bags which can carry a maximum of 10 coconuts. There were ten securities standing at different positionsnear the temple. Each security would take one coconut from each of the bag. (i.e. if the man carries 2 bags, and there are say 10 coconuts in each bag, the first security would take 1 from each bag i.e. total of 2. And all other securitieswould do this.) In order to give 20 coconuts to the temple, how any minimum coconuts the man should carry?

7/30/2019 Puzzle.txt

2/2

a) 20 b) 132 c) 66 d) 99Explain your answeris the answer 66?

the man would carry 7 bags at the first security at which he would be giving 7 coconuts to him.Now he would be left with 59 coconuts which could fit up in 6 bags. So he wouldcarry 6 bags to the 2nd security and give him 6 coconuts.Now he would be having 53 coconuts which would again fit into 6 bags only. so atthe 3rd security he would be giving 6 coconuts.After this he would be having 47 coconuts which would fit into 5 bags which means the 5th security will get 5 coconuts.

Similarly the process goes on till the man has 23 coconuts and he gets to the last security. He gives hin 3 coconuts acc. to the three bags which he has and gives the temple the rest 20 coconuts.