GMAT Changed on April 16th - Read about the latest changes here

 It is currently 27 May 2018, 21:57

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The sum of all integers from 43 to 107, inclusive, is divisible by whi

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 45498
The sum of all integers from 43 to 107, inclusive, is divisible by whi [#permalink]

### Show Tags

26 Nov 2017, 09:26
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

58% (01:25) correct 42% (00:59) wrong based on 45 sessions

### HideShow timer Statistics

The sum of all integers from 43 to 107, inclusive, is divisible by which of the following numbers?

A. 17
B. 18
C. 21
D. 24
E. 39

_________________
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1119
Location: India
GPA: 3.82
The sum of all integers from 43 to 107, inclusive, is divisible by whi [#permalink]

### Show Tags

26 Nov 2017, 09:44
1
This post was
BOOKMARKED
Bunuel wrote:
The sum of all integers from 43 to 107, inclusive, is divisible by which of the following numbers?

A. 17
B. 18
C. 21
D. 24
E. 39

Total numbers from 43 to 107 $$= 107-43+1=65$$

Sum of nos from 43 to 107 $$= \frac{65}{2}(43+107) = 65*75 = 3*5^3*13$$

from among the options only $$39$$ divides it.

Option E
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2587
Location: India
GPA: 3.12
The sum of all integers from 43 to 107, inclusive, is divisible by whi [#permalink]

### Show Tags

26 Nov 2017, 10:57
Bunuel wrote:
The sum of all integers from 43 to 107, inclusive, is divisible by which of the following numbers?

A. 17
B. 18
C. 21
D. 24
E. 39

Sum of n positive integers is $$\frac{n(n+1)}{2}$$

The sum of all integers between 43 and 107 can be found out as follows:

Sum of all positive integers till 107 is $$107*54$$
Similarly, the sum of all positive integers till 42 is $$43*21$$
Therefore, the sum of all integers from 43 to 107 is $$107*54 - 43*21 = 5778 - 903 = 4875$$

$$4875$$ when prime factorized is $$3*5^3*13$$ and the only number which divides this is 39(Option E)
_________________

You've got what it takes, but it will take everything you've got

The sum of all integers from 43 to 107, inclusive, is divisible by whi   [#permalink] 26 Nov 2017, 10:57
Display posts from previous: Sort by