The sum of the digits used to write the calculation 10 + 11 + 12 + 13 is 10 (as in 1 + 0 + 1 + 1 + 1 + 2 + 1 + 3). What is the sum of the digits used to write the calculation for the sum of the integers from 1 to 110, inclusive?
A 900
B 911
C 955
D 957
E 1001
Please explain a quick solution
Calculation- pattern
This topic has expert replies
- prachi18oct
- Master | Next Rank: 500 Posts
- Posts: 269
- Joined: Sun Apr 27, 2014 10:33 pm
- Thanked: 8 times
- Followed by:5 members
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
IMPORTANT: Always check the answer choices before beginning any solution. The answer choices may hint at an approach and/or suggest that you can skip tedious calculations.The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?
A) 900
B) 911
C) 955
D) 957
E) 1001
Here, the units digits in the answer choices are all different, which suggests that I may be able to avoid some "grunt" work.
First, let's examine the numbers from 00 to 99 inclusive (i.e., 00, 01, 02, .... 97, 98, 99) [note: adding 00 to the mix doesn't change the final answer]
Notice that there are 100 digits from 00 to 99 inclusive.
Also notice that the digits in the tens and units position are equally distributed
So, in the UNITS position, there will be ten 0's, ten 1's, ten 2's . . . ten 8's and ten 9's
In the TENS position, there will be ten 0's, ten 1's, ten 2's . . . ten 8's and ten 9's
So, the sum of ALL DIGITS from 00 to 99 will equal 20(1+2+3+...7+8+9)
IMPORTANT: We don't need to calculate 20(1+2+3+...7+8+9). We need only recognize that the units digit will equal 0. That is 20(1+2+3+...7+8+9) = ??0
From here, we need to add the digits in 100 to 110 inclusive.
To do so, we can use Rich's approach, or we might even list the values and add them in our head, since there aren't many to add here.
When we add the digits in 100 to 110 inclusive, we get 57
So, the sum of the digits from 00 to 110 inclusive = ??0 + 57 = ??7
Since only D has a 7 in the units position, this is the correct answer.
Cheers,
Brent
- GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
Break the Numbers into multiple piecesprachi18oct wrote:The sum of the digits used to write the calculation 10 + 11 + 12 + 13 is 10 (as in 1 + 0 + 1 + 1 + 1 + 2 + 1 + 3). What is the sum of the digits used to write the calculation for the sum of the integers from 1 to 110, inclusive?
A 900
B 911
C 955
D 957
E 1001
Please explain a quick solution
From 0 - 9 Sum of the digits = 45
From 10 - 19 Sum of the UNIT digits = 45
From 20 - 29 Sum of the UNIT digits = 45
and so on...
i.e. There are 11 such series of 10 numbers from 1 through 110 and
Sum of the Unit digits in all 11 series = 11*45 = 495
From 0 - 9 Sum of the TENS digits = 0
From 10 - 19 Sum of the TENS digits = 1*10 = 10
From 20 - 29 Sum of the TENS digits = 2*10 = 20
From 30 - 39 Sum of the TENS digits = 3*10 = 30
and so on...
i.e. There are 11 such series of 10 numbers from 1 through 110 and
Sum of the TENS digits in all 11 series = 10+20+30+40+50+60+70+80+90+1(100 to 110)=451
Sum of HUNDREDS digit from Numbers from 1 through 110 = 11 (only 100 to 110 have Hundreds Digit)
TOTAL DIGIT SUM = 495+451+11 = 957
Answer: Option D
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour