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N = P + Q + R and P, Q, R is the consecutive integers. N = X

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N = P + Q + R and P, Q, R is the consecutive integers. N = X [#permalink] New post 11 Nov 2005, 08:16
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N = P + Q + R and P, Q, R is the consecutive integers.
N = X * Y * Z and X, Y, Z is the consecutive integers, too.
What is the remainder of N to be divided by 5 ?

(1) The remainder of P to be divided by 5 is 1
(2) The remainder of X to be divided by 5 is 1
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Re: DS - Integer [#permalink] New post 11 Nov 2005, 09:59
gamjatang wrote:
N = P + Q + R and P, Q, R is the consecutive integers.
N = X * Y * Z and X, Y, Z is the consecutive integers, too.
What is the remainder of N to be divided by 5 ?

(1) The remainder of P to be divided by 5 is 1
(2) The remainder of X to be divided by 5 is 1



It's E.
Consider two cases:
case 1: N= 1+2+3 = 1*2*3=6
in this case, P=X=1 which divided by 5 has remainder of 1. (exactly what's from the two statements)
N=6 ---> the remainder of N to be divided by 5 is 1.

case 2: N= 1+0+-1 = 1*0* (-1) = 0
in this case, P=X= 1which divided by 5 has remainder of 1 ( exactly the two statements)
N= 0 ---> the remainder of N to be divided by 5 is 0.

=> we can't find exactly what the remainder is even if we combine two statements.
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 [#permalink] New post 11 Nov 2005, 10:22
I get E too../

we dont know the oder in which the numbers appear...say if P =n, then q=n+1, r=n+2....

of q=n-1, r=n-2....we dont know....

order of the letters is important..

E it is
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 [#permalink] New post 11 Nov 2005, 14:28
i would go with D.
N = P + Q + R and P, Q, R is the consecutive integers.
N = X * Y * Z and X, Y, Z is the consecutive integers, too.
What is the remainder of N to be divided by 5 ?

(1) The remainder of P to be divided by 5 is 1
take any value of P where remainder is 1 6,16,11,21...
and multiply the each next to consicutive integer like
6+7+8/5=Remainder 1
16+17+18/5=Remainder 1
21+22+23/5=Remainder 1

Suff

(2) The remainder of X to be divided by 5 is 1

6*7*8/5=Remainder 1
16*17*18/5=Remainder 1
21*22*23/5=Remainder 1

suff..

Hence D


Suff
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 [#permalink] New post 11 Nov 2005, 15:22
how do you know P is the smallest consecutive number?
for all I know P could 6, Q=5 and R =4

?? did you read my post??


cool_jonny009 wrote:
i would go with D.
N = P + Q + R and P, Q, R is the consecutive integers.
N = X * Y * Z and X, Y, Z is the consecutive integers, too.
What is the remainder of N to be divided by 5 ?

(1) The remainder of P to be divided by 5 is 1
take any value of P where remainder is 1 6,16,11,21...
and multiply the each next to consicutive integer like
6+7+8/5=Remainder 1
16+17+18/5=Remainder 1
21+22+23/5=Remainder 1

Suff

(2) The remainder of X to be divided by 5 is 1

6*7*8/5=Remainder 1
16*17*18/5=Remainder 1
21*22*23/5=Remainder 1

suff..

Hence D


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 [#permalink] New post 11 Nov 2005, 18:43
I also got D assuming that the number are in order. In questions when they say consecutive, I think, I have always come across ordered sequence (ascending)
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 [#permalink] New post 11 Nov 2005, 19:01
as freshinha, i think the key here is the order ....those numbers are consecutive but who know which one is the largest/smallest?
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 [#permalink] New post 11 Nov 2005, 19:39
yup guys i just assumed that they are in asending order. ...... :wink: ...

is that the safe assumption to make when its stated that the numbers are in consecutive order ..... :roll: :roll:
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 [#permalink] New post 11 Nov 2005, 19:58
(1) Insuffiicent

Let P = 1, 6, 11, 16 ......

P = 1, Q = 2, R = 3 -> N = (1+2+3)/5 -> Remainder is 1
P = 6 Q = 5, R = 7 -> N = (6+5+7)/5 -> Remainder is 3

(2) Insufficient

Let X = b]1[/b], 6, 11, 16 ......

X = 1, Y = 2, Z = 3 -> N = (1*2*3)/5 -> Remainder is 1
X = 1, Y = 0, Z = -1 -> N = (1*0*-1)/5 -> Remainder is 0

I believe this question is testing whether it is correct to assume P, Q and R and X, Y and Z are in order. I don't think this is valid assumption. If the assumption was valid, then this would be an easy question.

I pick E.
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 [#permalink] New post 12 Nov 2005, 06:19
(1) Pick numbers for P:

6,7,8 and the remainder is 1
-6,-5,-4 and the remainder is 0
---->Insuff

(2) Pick numbers for X:

6,7,8 and the remainder is 1
-6,-5,-4 and the remainder is 0
---->Insuff

Together, still insuff

Straight E.
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 [#permalink] New post 13 Nov 2005, 06:20
yup got E as well..

we don't know the order, first of all, secondly even if we know the order, we don't the whether the consequtive integers are positive or negative.
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 [#permalink] New post 13 Nov 2005, 19:54
Throw my vote with D too. When it says x,y,z are consecutive integers I always think I can assume x=n-1, y=n and z=n+1. In other words, I'm assuming their orders. It's a good point to notice though. It would be nice for us to see if it is a official question and if the anwer does not confirm our assumption.
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 [#permalink] New post 13 Nov 2005, 20:13
I am bit confused, hence I am posting a basic question.

What is the reminder when -1 is divided by 5?
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 [#permalink] New post 13 Nov 2005, 20:18
Good question. I believe we normally only discuss divisors and reminders when we are dealing with positive integers.
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 [#permalink] New post 14 Nov 2005, 12:27
I believe, we need to ignore the negative sign and find out the reminder. Then add the sign to the reminder.

Eg: -6/5
-> 6/5 : remainder is 1
-> -6/5: remainder is -1

If someone has different thoughts, please post it.
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 [#permalink] New post 14 Nov 2005, 14:56
The basic requirement for remainder of a number X when divide by n is:

X = n.q + r ........ (where q is an integer quotient and r the remainder)

So, if X is negative:

-X = -n.q - r

eg. -6/5

-6 = -1(5) - 1
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 [#permalink] New post 14 Nov 2005, 15:01
tank wrote:
The basic requirement for remainder of a number X when divide by n is:

X = n.q + r ........ (where q is an integer quotient and r the remainder)

So, if X is negative:

-X = -n.q - r

eg. -6/5

-6 = -1(5) - 1

X = n.q + r

here the property of r is:

0<= r <q

in this example, -1 < 0

I guess, we should leave as out-of-scope as I did not find any problem where we need to think about this. ETS only talks about remainer in the context of positive integers.
The only think to remember is:
q <> 0
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 [#permalink] New post 14 Nov 2005, 17:25
laxieqv wrote:
as freshinha, i think the key here is the order ....those numbers are consecutive but who know which one is the largest/smallest?


OOPS! I AM TERRIBLY SORRY!

I missed to type "...consecutive integers in this order" :oops:

If you calculate this question according to "in this order", then the OA is (D).

However, without "in this order", the OA should be (E).

Again, sorry for the confusion.
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  [#permalink] 14 Nov 2005, 17:25
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