GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jun 2019, 00:35

### 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

# find the last digit of the number 1^2+2^2+.....99^2

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 31 May 2018
Posts: 47
Location: United States
Concentration: Finance, Marketing
find the last digit of the number 1^2+2^2+.....99^2  [#permalink]

### Show Tags

20 Jul 2018, 08:10
6
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:45) correct 33% (01:37) wrong based on 110 sessions

### HideShow timer Statistics

find the last digit of the number $$1^2+2^2+..........+99^2$$.

a) 1
b) 2
c) 3
d) 4
e) 0
Senior Manager
Joined: 22 Feb 2018
Posts: 428
find the last digit of the number 1^2+2^2+.....99^2  [#permalink]

### Show Tags

20 Jul 2018, 08:33
4
2
shridhar786 wrote:
find the last digit of the number $$1^2+2^2+..........+99^2$$.

a) 1
b) 2
c) 3
d) 4
e) 0

OA:E
Sum of the Squares of First $$n$$ Positive Integers = $$\frac{{n(n+1)(2n+1)}}{{6}}$$
Putting n=99
Sum of the Squares of First $$99$$ Positive Integers = $$\frac{{99(100)(198+1)}}{{6}}={33*50*199}$$
Last Digit of the number would be $$0$$.
_________________
Good, good Let the kudos flow through you
##### General Discussion
Intern
Joined: 03 Feb 2016
Posts: 10
Re: find the last digit of the number 1^2+2^2+.....99^2  [#permalink]

### Show Tags

20 Jul 2018, 08:37
formula is 1/6N(N+1)(2N+1)
N=99
so sum=(33*199*100)/2
so last digit is '0'
Ans E
Director
Joined: 31 Jul 2017
Posts: 516
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: find the last digit of the number 1^2+2^2+.....99^2  [#permalink]

### Show Tags

20 Jul 2018, 09:23
1
shridhar786 wrote:
find the last digit of the number $$1^2+2^2+..........+99^2$$.

a) 1
b) 2
c) 3
d) 4
e) 0

Sum of the Squares of Number -

n(n+1)(2n+1)/6. Here, n = 99.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
Intern
Joined: 17 May 2018
Posts: 49
Re: find the last digit of the number 1^2+2^2+.....99^2  [#permalink]

### Show Tags

23 Jul 2018, 06:43
1
If for some reason you don't know the formula mentioned in the previous solutions, we could try to find it manually:

Last digit of the square of a number ending in 1: 1
Last digit of the square of a number ending in 2: 4
Last digit of the square of a number ending in 3: 9
Last digit of the square of a number ending in 4: 6
Last digit of the square of a number ending in 5: 5
Last digit of the square of a number ending in 6: 6
Last digit of the square of a number ending in 7: 9
Last digit of the square of a number ending in 8: 4
Last digit of the square of a number ending in 9: 1
Last digit of the square of a number ending in 0: 0

Adding these (try to group them to ease the calculation: 1 with 9, 4 with 6, etc.) we end up with a 5 for the sequence 1 to 10 (or 11 to 20, or 21 to 31... or 91 to 99). We'll need to add this 10 times or, what is the same, multiply it by 10, to find out the last digit of the sequence presented in the stem. The result is a zero as the last digit.
_________________
¿Tienes que presentar el GMAT y no sabes por dónde empezar?
¡Visita GMAT para Principiantes y recibe el curso completo gratis!
Intern
Joined: 25 Jul 2018
Posts: 11
Re: find the last digit of the number 1^2+2^2+.....99^2  [#permalink]

### Show Tags

30 Sep 2018, 06:45
Used a different approach.

So we have a series of n=99 numbers.
first + last together sum up to 1^2 + 99^2 = 100^2 , second and second last the same etc. All the combined 100^2 will have a zero at last digit.
Since the list contains 99 numbers, the middle number would be the 50, and 50^2 clearly has a zero as the last digit.

Thus, zero will be the last digit.

Pls correct me if I'm wrong.
Re: find the last digit of the number 1^2+2^2+.....99^2   [#permalink] 30 Sep 2018, 06:45
Display posts from previous: Sort by

# find the last digit of the number 1^2+2^2+.....99^2

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne