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

 It is currently 19 Aug 2018, 00:43

### 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

# If P = 1!^2 + 2!^2 + 3!^2 + ... + 10!^2. Then what is the remainder wh

Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Jul 2018
Posts: 42
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
If P = 1!^2 + 2!^2 + 3!^2 + ... + 10!^2. Then what is the remainder wh  [#permalink]

### Show Tags

05 Aug 2018, 08:04
3
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:07) correct 40% (02:03) wrong based on 25 sessions

### HideShow timer Statistics

If $$P = 1!^2 + 2!^2 + 3!^2 + ... + 10!^2$$. Then what is the remainder when $$5^{2P}$$ is divided by 13

1) 0
2) 1
3) 4
4) 8
5) 12
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 507
WE: Supply Chain Management (Energy and Utilities)
Re: If P = 1!^2 + 2!^2 + 3!^2 + ... + 10!^2. Then what is the remainder wh  [#permalink]

### Show Tags

05 Aug 2018, 08:52
1
Afc0892 wrote:
If P= $$1!^2$$ + $$2!^2$$ + $$3!^2$$ + .....+ $$10!^2$$. Then what is the remainder when $$5^{2P}$$ is divided by 13

1) 0
2) 1
3) 4
4) 8
5) 12

What is the pattern of $$Rem(\frac{5^{2p}}{13})$$?

1. If P=1, $$Rem(\frac{5^2}{13})=12$$
2. If P=2, $$Rem(\frac{5^4}{13})=1$$
3. If P=3, $$Rem(\frac{5^6}{13})=12$$
4. If P=4, $$Rem(\frac{5^8}{13})=1$$

So, when p is odd, remainder is 12 otherwise remainder is 1.

You know, factorial of any positive integer greater than or equal to 5 has unit digit '0'.

Now. P= $$1!^2$$ + $$2!^2$$ + $$3!^2$$ + .....+ $$10!^2$$
P=1+4+6+4+0..............+0=15 (Note:- only unit digits added, because unit digit of a integer decides whether it is even or odd)
Or, unit digit of P=5(odd)

Therefore, the remainder when $$5^{2*{odd}}$$ is divided by 13 is 12.

Ans. (E)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: If P = 1!^2 + 2!^2 + 3!^2 + ... + 10!^2. Then what is the remainder wh &nbs [#permalink] 05 Aug 2018, 08:52
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.