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

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Director
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N = P + Q + R and P, Q, R is the consecutive integers. N = X [#permalink]  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]  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.
Current Student
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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
Director
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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
Current Student
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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

Suff
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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)
SVP
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as freshinha, i think the key here is the order ....those numbers are consecutive but who know which one is the largest/smallest?
Director
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yup guys i just assumed that they are in asending order. ...... ...

is that the safe assumption to make when its stated that the numbers are in consecutive order .....
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(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.
Current Student
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(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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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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hey ya......

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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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keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Senior Manager
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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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Good question. I believe we normally only discuss divisors and reminders when we are dealing with positive integers.
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keep on seeking, and you will find;
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Senior Manager
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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.
Intern
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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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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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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"

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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