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Remainder Q [#permalink] New post 05 Jan 2004, 16:21
Any idea :shock: Pls include reasoning along with all answer posts.

Find the greatest four digit number which when divided by 18, 28 and 35 leaves in each case a remainder 5.

a. 9825
b. 8820
c. 8825
d. 8815
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Re: Remainder Q [#permalink] New post 05 Jan 2004, 18:28
sunniboy007 wrote:
Any idea :shock: Pls include reasoning along with all answer posts.

Find the greatest four digit number which when divided by 18, 28 and 35 leaves in each case a remainder 5.

a. 9825
b. 8820
c. 8825
d. 8815


use prime factorization for a problem like this


18, 28, 35

3x3x2, 2x2x7, 3x5

combine uncommon primes

3x2x7x5=210

check the answer choices to see which answer is a mulitple of 210

Hark!! it's B!!!

8820 but is that the answer??? NO!!!!! Sorry Joe Bloggs! (for those who took PR for SATs)

add 5 to 8820

Thus C is your answer

verstehen Sie? Ausgezeichnet!

Last edited by Titleist on 05 Jan 2004, 18:36, edited 1 time in total.
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 [#permalink] New post 05 Jan 2004, 18:35
you mean subtract five to get (d) right?
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 [#permalink] New post 05 Jan 2004, 18:38
sunniboy007 wrote:
you mean subtract five to get (d) right?


:oops: sorry as i correctly wrote add 5 to get 8825

incorrectly wrote c instead of b - i made that correction.
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 [#permalink] New post 05 Jan 2004, 18:41
Titleist, the official answer is (D)
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 [#permalink] New post 05 Jan 2004, 18:46
sunniboy007 wrote:
Titleist, the official answer is (D)


hmmm...8825 when divided by 18,28, and 35 leaves a remainder of 5

I think i may have to disagree with that "official" answer


is that a Gmat plus question?
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 [#permalink] New post 05 Jan 2004, 18:52
your right, ...I checked on a calculator..... the official answer is incorrect...It happens
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 [#permalink] New post 05 Jan 2004, 18:57
I had three beers tonight :drinking - glad to know my brain cells are still functioning. Struggling but functioning! :out
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 [#permalink] New post 05 Jan 2004, 19:01
The way I solved it was this:
LCM of 18 , 28 and 35 = 1260
The greatest four digit number possible is 9999
Therefore, 9999/1260 leaves a remainder of 1179.
Subtract 5 from 1179 to yield 1174.
9999 - 1174 = 8825
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Last edited by sunniboy007 on 05 Jan 2004, 19:04, edited 1 time in total.
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 [#permalink] New post 05 Jan 2004, 19:04
sunniboy007 wrote:
The way I solved it was this:
LCM of 18 , 28 and 35 = 1260
The greatest four digit number possible is 9999
Therefore, 9999/1260 leaves a remainder of 1179.
Subtract 5 from 1179 to yield 1174.
9999 - 1175 = 8825


And how long did all that long division take you?
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 [#permalink] New post 05 Jan 2004, 19:10
Well - you can do it your way. But it took me less than a minute when breaking it down to prime factors. The calculation alone, the way you did it, would've taken me 2 minutes - and that's without reading and trying to figure the darn question out. I'm just lazy and like to do the least amount of calculations when it comes to these problems.

cheers!
  [#permalink] 05 Jan 2004, 19:10
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