|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
02 Dec 2021, 07:45
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
56% (03:09) correct
44%
(03:04)
wrong
based on 139
sessions
History
Date
Time
Result
Not Attempted Yet
Find the sum of all even numbers from 10 to 300, excluding those which are multiples of 8.
A. 17014
B. 2345
C. 4562
D. 9128
E. None of the above
A. 17014
B. 2345
C. 4562
D. 9128
E. None of the above
03 Dec 2021, 05:27
Kudos
Bookmarks
\(Sum of Even Numbers Between 10 and 300 - Sum of Multiples of 8 Between 10 and 300\)
Formula for Sum of Arithmetic Sequence: \(S_n = \frac{n}{2 }(a+l)\) where n = number of terms, a = first term of sequence and l = last term in sequence
Sum of Even Numbers Between 10 and 300:
\(\frac{10}{2} = 5\)
10 is the 5th even number.
\(\frac{300}{2} = 150\)
300 is the 150th even number
\(150 - 5 + 1 = 146\)
There are 146 terms in the sequence
Plugging all of this into the arithmetic formula gives:
\(\frac{146}{2}(10+300)\)
\(=73(310)\)
\(= 22 630\)
Sum of Multiples of 8 Between 10 and 300:
First multiple of 8 between 10 and 300: `\(16\)
\(\frac{16}{8} = 2 \)
16 is the 2nd multiple of 8.
Last multiple of 8 between 10 and 300: \(296\)
\(\frac{296}{8} = 37\)
296 is the 37th multiple of 8
\(37 - 2 + 1 = 36\) There are 36 multiples of 8 between 10 and 300
Plugging this information into the sum of arithmetic sequence formula gives:
\(\frac{36}{2}(16+296)\)
\(= 18(312)\)
\(= 5616\)
Subtracting the two sums:
\(22 630 - 5616 = 17 014 \)
Answer A
Formula for Sum of Arithmetic Sequence: \(S_n = \frac{n}{2 }(a+l)\) where n = number of terms, a = first term of sequence and l = last term in sequence
Sum of Even Numbers Between 10 and 300:
\(\frac{10}{2} = 5\)
10 is the 5th even number.
\(\frac{300}{2} = 150\)
300 is the 150th even number
\(150 - 5 + 1 = 146\)
There are 146 terms in the sequence
Plugging all of this into the arithmetic formula gives:
\(\frac{146}{2}(10+300)\)
\(=73(310)\)
\(= 22 630\)
Sum of Multiples of 8 Between 10 and 300:
First multiple of 8 between 10 and 300: `\(16\)
\(\frac{16}{8} = 2 \)
16 is the 2nd multiple of 8.
Last multiple of 8 between 10 and 300: \(296\)
\(\frac{296}{8} = 37\)
296 is the 37th multiple of 8
\(37 - 2 + 1 = 36\) There are 36 multiples of 8 between 10 and 300
Plugging this information into the sum of arithmetic sequence formula gives:
\(\frac{36}{2}(16+296)\)
\(= 18(312)\)
\(= 5616\)
Subtracting the two sums:
\(22 630 - 5616 = 17 014 \)
Answer A
03 Dec 2021, 05:57
Kudos
Bookmarks
If we add all the even numbers from 10 through 300, we're adding roughly 150 numbers, and because we're adding an equally spaced list, the average number is equal to the average of the smallest and largest numbers, 10 and 300, so the average number is close to 150. So the sum of all the even numbers from 10 through 300 is very close to 150^2 = 22,500. In a long list of consecutive even numbers, roughly 1/2 will be divisible by 4, 1/4 will be divisible by 8, 1/8 will be divisible by 16, and so on, so here, we want to discard roughly 1/4 of our numbers which are multiples of 8, leaving us a sum roughly 3/4 as big, so the answer will be very close to (3/4)(22,500) and only answer A is remotely plausible.
