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Director
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n could be the sum of consecutive integers r, s, and t [#permalink]
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06 Mar 2005, 12:17
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n could be the sum of consecutive integers r, s, and t or the product of consecutive integers x, y, and z. What is the remainder when n is divided by 5? (1) When r is divided by 5, the remainder is 1 (2) When x is divided by 5, the remainder is 1[/i]



Intern
Joined: 19 Jul 2004
Posts: 43

Consider (1)
n = r + s + t = r + (r +1) + (r + 2) [since r,s,t are consecutive integers]
= 3(r+1)
When r is divided by 5, remainder is 1, hence r = 5p + 1
n = 3(5p+1 + 1) = 3(5p+2) = 15p + 6
When n will be divided by 5, it should give remainder as '1'. Hence (1) alone is sufficient
Consider (2)
n = x * y * z = x * (x+1) * (x+2) [since x,y,z are consecutive integers]
When x is divided by 5, remainder is 1, hence x = 5p + 1
x/5 > Remainder is 1
(x+1)/5 > Remainder is 2
(x+2)/5 > Remainder is 3
Hence remainder when 'n = x * (x+1) * (x+2)' is divided by 5 is
1 * 2 * 3 = 6 /5 ==> 1 remainder
Hence (2) alone is sufficient
Both are independently sufficient
Ketan



Director
Joined: 29 Oct 2004
Posts: 851

Can you assume this: r <s<t or x<y<z ?
Or can you assume this: n = rst in (1) but not n = xyz (They are all different)?



VP
Joined: 25 Nov 2004
Posts: 1483

I go with E. because,
from (1), we do not know the order of rst. r is 5k+1 but s could be 5k+2, 5k or 5k1. similarly, t could be 5k+2, 5k or 5k1.
from (2) also, we do not know the order of xyz. x is 5k+1 but y could be 5k+2, 5k or 5k1 and so does z.
from 1 and 2, we do not know. guys, correct, if any................



VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08

I admit that this is a very good question...
I naturally assumed that r <s<t or x<y<z and answered D, just because it is usually the GMAT format in this kind of problem, the smallest number first...I am curious about the OA and the feeling of the other members concerning this one



VP
Joined: 18 Nov 2004
Posts: 1433

When one says consecutive integers r,s,t....I think we r supposed to read it as r<s<t.....just my opinion....anyone with official definition.



Manager
Joined: 11 Jan 2005
Posts: 101

I will follow the similar logic as above. let s not be trickier than GMAT s writers.



Director
Joined: 29 Oct 2004
Posts: 851

Yeah, OA is (D)
But I think (E) must be correct.



SVP
Joined: 03 Jan 2005
Posts: 2233

I personally believe that in the term "consecutive integers r, s, and t" we could assume that r, s and t are in order. Anybody has any real proof from an real ETS question that would disapprove this?



Director
Joined: 21 Sep 2004
Posts: 607

it is asking for the remainder so how are we saying if 1 is sufficient or 2 is sufficient. Honghu can u please explain this one?



SVP
Joined: 03 Jan 2005
Posts: 2233

Re: DS  Divided by 5 [#permalink]
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09 Mar 2005, 10:13
ketanm already had a very nice solution to this. Basically you should try to write n out as an algebra expression using the given conditions.
n=r+s+t=r+(r+1)+(r+2) (consecutive integer)
= 3r +3 (!)
Also n=x*y*z=x*(x+1)*(x+2) (2)
(1) When r is divided by 5, the remainder is 1
r=5k+1
substite into (1)
n=3(5k+1)+3=15k+6
When 15k is divided by 5, reminder is zero. When 6 is divided by 5, reminder is 1.
Sufficient
(2) When x is divided by 5, the remainder is 1
x=5k+1
n=(5k+1)(5k+2)(5k+3) (A)
=5k((5k+2)(5k+3))+(5k+2)(5k+3)
=5k((5k+2)(5k+3))+5k*(5k+3)+2*(5k+3)
=5k((5k+2)(5k+3))+5k*(5k+3)+2*5k+6 (B)
I'm writing this out so for people who do not have a intuitive feeling about the original equation (A) can know how to access it. You don't have to multiply them all out. From (B) you can see all the items before 6 is divisible by 5. And the reminder is 1 when 6 is divide by 5.
Therefore it is also sufficient.
This is why the answer would be (D).
If we are not sure if r,s,t and x,y,z are in order, then we would not know s=r+1, t=r+2, etc, then we would not be able to arrive to our previous conclusion. In this case the answer would be (E).



Director
Joined: 21 Sep 2004
Posts: 607

great explanation. thanks...once again..



Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

D it is
I just picked numbers assuming r is the smallest and x is the smallest
for statement 1
if r divided by 5 remainder is 1, u can pick r=6 for example you
6+7+8=21=N
N/5 remainder is 1
we can check by adding 10 to each which is really like adding 30 to the above! you still get 1 as remainder
statement 2
I just foucesed on the unit digit, it truns out to be 0 and therefore the remainder is 0
sufficient
D it is..



Manager
Joined: 15 Feb 2005
Posts: 246
Location: Rockville

I agree it should be D, in the OA most examples for consecutive integers seem to be in the increase order not decreasing...on the test i would go for D



Manager
Joined: 11 Jan 2005
Posts: 57
Location: Mexico City

I used a simpler approach by using the old numbes rule for 5 saying that r and x had to be either 1 or 6 (or 11 or 16 etc) and went from their with plugging.
1+2+3 and 6+7+8 and 1*2*3 and 6*7*8 and you get the same answer
D.



Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston

It is D. Good question. And a very good explanation by KetanM



SVP
Joined: 03 Jan 2005
Posts: 2233

Caspace wrote: I used a simpler approach by using the old numbes rule for 5 saying that r and x had to be either 1 or 6 (or 11 or 16 etc) and went from their with plugging.
1+2+3 and 6+7+8 and 1*2*3 and 6*7*8 and you get the same answer
D.
Yes, very good approach. It would require you have pretty good mathematic intuition but it will save you a lot of time.



Manager
Joined: 01 Jan 2005
Posts: 166
Location: NJ

one more D. great explanations.



VP
Joined: 25 Nov 2004
Posts: 1483

Re: DS  Divided by 5 [#permalink]
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09 Mar 2005, 19:30
qhoc0010 wrote: n could be the sum of consecutive integers r, s, and t or the product of consecutive integers x, y, and z. What is the remainder when n is divided by 5? (1) When r is divided by 5, the remainder is 1 (2) When x is divided by 5, the remainder is 1[/i]
Guys, I disagree with those who have assumed the order of the integers.
In DS, we are not supposed to make an assumption because it distorts the core concept of DS. If we statrt assume, then there will be no question such as DATA SUFFICIENCY because with the assumption all DS questions are solvable. In DS question we basically deal with whether the information provided in the question is sufficient. therefore, in such questions, we must have to work arround facts and figures provided.
this is my personal opinion. Seek more opinion from you guys and moderators.




Re: DS  Divided by 5
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09 Mar 2005, 19:30






