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# i know its piece of a cake......... For which n is the

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Director
Joined: 03 May 2007
Posts: 876
Schools: University of Chicago, Wharton School
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i know its piece of a cake......... For which n is the [#permalink]

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17 Aug 2007, 21:40
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i know its piece of a cake.........

For which n is the remainder largest when the number 817,380 is divided by n?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Manager
Joined: 15 Aug 2007
Posts: 70
Followers: 2

Kudos [?]: 5 [0], given: 0

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17 Aug 2007, 22:11
chiya wrote:
Fistail wrote:
i know its piece of a cake.........

For which n is the remainder largest when the number 817,380 is divided by n?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9

Answer is D... Reminder is 4..

Short cut Method...

Dividing by 2
-All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8

Dividing by 3
-If the sum is divisible by 3, so is the number

Dividing by 4
-If the last two digits in number is divisible by 4?
If so, the number is too!
for 817,380 380 is divisible by 4, reminder=0

Dividing by 5
-Numbers ending in a 5 or a 0 are always divisible by 5.
for 817,380 last digit it 0, reminder =0

Dividing by 6
-If the Number is divisible by 2 and 3 it is divisible by 6 also.
for 817,380 last digit it 2, divisible by 2
and 8+1+7+3+8+0=27, divisible by 3
Reminder=0

Dividing by 8
-if the last 3 digits are divisible by 8, so is the entire number.
for 817,380 if 380 is divisible by 8 ?, no reminder=4

Dividing by 9
- If the sum of all no's is divisible by 9, so is the number.
8+1+7+3+8+0=27, divisible by 9 reminder=0

Manager
Joined: 08 Jan 2007
Posts: 66
Location: D.C.
Followers: 1

Kudos [?]: 1 [0], given: 0

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18 Aug 2007, 10:22
[quote="chiya"][quote="chiya"][quote="Fistail"]i know its piece of a cake.........

For which n is the remainder largest when the number 817,380 is divided by n?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9[/quote]

Answer is D... Reminder is 4..[/quote]

[b]Short cut Method...[/b]

Dividing by 2
-All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8

Dividing by 3
-If the sum is divisible by 3, so is the number

Dividing by 4
-If the last two digits in number is divisible by 4?
If so, the number is too!
for 817,380 380 is divisible by 4, reminder=0

Dividing by 5
-Numbers ending in a 5 or a 0 are always divisible by 5.
for 817,380 last digit it 0, reminder =0

Dividing by 6
-If the Number is divisible by 2 and 3 it is divisible by 6 also.
for 817,380 last digit it 2, divisible by 2
and 8+1+7+3+8+0=27, divisible by 3
Reminder=0

Dividing by 8
-if the last 3 digits are divisible by 8, so is the entire number.
for 817,380 if 380 is divisible by 8 ?, no reminder=4

Dividing by 9
- If the sum of all no's is divisible by 9, so is the number.
8+1+7+3+8+0=27, divisible by 9 reminder=0

Thanks for the reminder on the rules!

D for me too!
VP
Joined: 10 Jun 2007
Posts: 1443
Followers: 7

Kudos [?]: 285 [0], given: 0

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18 Aug 2007, 11:25
Fistail wrote:
i know its piece of a cake.........

For which n is the remainder largest when the number 817,380 is divided by n?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9

Looking at the number, you already know it is divisible by 4, 5.
Divisible by 4 because 100 is divisible by 4 and 80 is divisible by 4.

You also know it is divisible by 9 if all of individual digits add up and divisible by 9. (8+1+7+3+8+0 = 27)

Choice C and D left. No need to do a whole problem. First, divide by 2. You get = 408690. From this, you know that it is divisible by 3 because the sum of digits is divisible by 3.

*Just saw previous posts, great job!
Manager
Joined: 18 Jun 2007
Posts: 87
Followers: 2

Kudos [?]: 1 [0], given: 0

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18 Aug 2007, 19:00
I come up with D as the answer

all the other options are factors of the number, the only number not a factor , hence the largest reminder is option d =8

Current Student
Joined: 28 Dec 2004
Posts: 3363
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 297 [0], given: 2

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19 Aug 2007, 11:52
I get D too..here is how i did it...

[img]For which n is the remainder largest when the number 817,380 is divided by n?

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
[/img]

well i easily elimnated 5, casue the number ends with a 0...

easily elimnated 9..casue the sum of all these integers is 27 which is not only divisible by 3, but also 9..thus remainder is 0

easily elimnated 6 cause the number is even, divisible by 3 and 2 both..

left with 4...and 8

ok.gotta pick 8 and test the number ..8 leaves a remainder 4... while 4 leaves a remainder 0...

D it is..

[/img]
19 Aug 2007, 11:52
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