If s is the sum of all integers from 1 to 30, inclusive, what is the sum of all the factors of s?
(A) 303
(B) 613
(C) 675
(D) 737
(E) 768
If s is the sum of all integers from 1 to 30, inclusive,
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
To calculate the sum of an integer's positive factors:
1. Prime-factorize the integer
2. Write the prime-factorization in the form (a^p)(b^q)(c^r)...
3. Sum of the factors = (1+a¹+ a²+a³+...+a^p)(1+b¹+ b²+b³+...+b^q)(1+c¹+ c²+c³+...+c^r)...
What is the sum of the positive factors of 600?
1. 600 = 2*2*2*3*5*5
2. 2*2*2*3*5*5 = 2³3¹5²
3. Sum of the factors = (1+2¹+2²+2³)(1+3¹)(1+5¹+5²) = 1860.
Average = (biggest + smallest)/2
Sum = (count)(average)
For the integers 1 through 30, inclusive:
Average = (30+1)/2 = 31/2
s = Sum = (30)(31/2) = (15)(31)
To calculate the sum of the factors of s, apply the process discussed above:
1. (15)(31) = 3*5*31
2. 3*5*31 = 3¹5¹31¹
Sum of the factors = (1+3¹)(1+5¹)(1+31¹) = 768.
The correct answer is C.
1. Prime-factorize the integer
2. Write the prime-factorization in the form (a^p)(b^q)(c^r)...
3. Sum of the factors = (1+a¹+ a²+a³+...+a^p)(1+b¹+ b²+b³+...+b^q)(1+c¹+ c²+c³+...+c^r)...
What is the sum of the positive factors of 600?
1. 600 = 2*2*2*3*5*5
2. 2*2*2*3*5*5 = 2³3¹5²
3. Sum of the factors = (1+2¹+2²+2³)(1+3¹)(1+5¹+5²) = 1860.
For any set of consecutive integers:BTGmoderatorDC wrote:If s is the sum of all integers from 1 to 30, inclusive, what is the sum of all the factors of s?
(A) 303
(B) 613
(C) 675
(D) 737
(E) 768
Average = (biggest + smallest)/2
Sum = (count)(average)
For the integers 1 through 30, inclusive:
Average = (30+1)/2 = 31/2
s = Sum = (30)(31/2) = (15)(31)
To calculate the sum of the factors of s, apply the process discussed above:
1. (15)(31) = 3*5*31
2. 3*5*31 = 3¹5¹31¹
Sum of the factors = (1+3¹)(1+5¹)(1+31¹) = 768.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
The sum of all integers from 1 to 30, inclusive, is 30(30 + 1)/2 = 15(31) = 3 x 5 x 31 = 465. So s = 3^1 x 5^1 x 31^1 has (1 + 1) x (1 + 1) x (1 + 1) = 8 factors. These 8 factors are:BTGmoderatorDC wrote:If s is the sum of all integers from 1 to 30, inclusive, what is the sum of all the factors of s?
(A) 303
(B) 613
(C) 675
(D) 737
(E) 768
1, 465
3, 155
5, 93
15, 31
Therefore, the sum of all the factors of s is 1 + 3 + 5 + 15 + 31 + 93 + 155 + 465 = 768.
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews