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# If r and s are integers, is r+s divisible by 3? 1. s is

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Manager
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If r and s are integers, is r+s divisible by 3? 1. s is [#permalink]  23 Dec 2005, 10:06
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If r and s are integers, is r+s divisible by 3?

1. s is divisible by 3
2. r is divisible by 3

Kindly explain your answer. I have a specific doubt in my mind regarding the official explanation for this question. I will post my doubt tomorrow in order to give some time to those interested in taking a stab at this.

Last edited by 5elements on 23 Dec 2005, 12:52, edited 1 time in total.
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Re: DS - is r+s divisible by 3? [#permalink]  23 Dec 2005, 10:56
5elements wrote:
If r and s are integers, is r+s divisible by 3?

1. s is divisible by 3
2. r is divisible by 3

Kindly explain your answer. I have a specific doubt in my mind regarding the official explanation for this question. I will post my doubt tomorrow in order some time to give those interested in taking a stab that this.

C.

1) We don't know anything about s.... if r=3, s=6, then yes......if r=3, s=2, then no....INSUFF

2)Same reasoning as 1)....INSUFF

1) and 2) together.... we know that both are multiples of 3, therefore their sum must be divisible by 3.... SUFF
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Re: DS - is r+s divisible by 3? [#permalink]  23 Dec 2005, 11:55
5elements wrote:
If r and s are integers, is r+s divisible by 3?

1. s is divisible by 3
2. r is divisible by 3

Kindly explain your answer. I have a specific doubt in my mind regarding the official explanation for this question. I will post my doubt tomorrow in order some time to give those interested in taking a stab that this.

If r and s are integers, is r+s divisible by 3? So its asking if r/3 + s/3 an integer?

It is C.

(1) Tells us nothing about r. Insufficient.
(2) Tells us nothing about s. Insufficient.

(1) + (2) Sufficient
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Manager
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OA is C. BTW, this OG - DS question 45.

It cannot be A or B, for the reasons stated in the earlier responses by other members.

Now, regarding "C" ... here is my question/doubt

Consider r = -3 and s = 3 . Note, the question stem says that r and s are integers, so it is fair have positive value for one and negative for the other

In this case, r+s = (-3) +(3) = 0.

My understanding is "0" cannot be divided into 3, hence indivisble by 3. If this is true, then the answer should be "E"... what am I missing here?
VP
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5elements wrote:
OA is C. BTW, this OG - DS question 45.

It cannot be A or B, for the reasons stated in the earlier responses by other members.

Now, regarding "C" ... here is my question/doubt

Consider r = -3 and s = 3 . Note, the question stem says that r and s are integers, so it is fair have positive value for one and negative for the other

In this case, r+s = (-3) +(3) = 0.

My understanding is "0" cannot be divided into 3, hence indivisble by 3. If this is true, then the answer should be "E"... what am I missing here?

0 is divisible by all numbers.

However any number divided by 0 is undefined
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Manager
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As we need both the statements to determine if the sum r+s is divisible by 3
Manager
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5elements wrote:
OA is C. BTW, this OG - DS question 45.

It cannot be A or B, for the reasons stated in the earlier responses by other members.

Now, regarding "C" ... here is my question/doubt

Consider r = -3 and s = 3 . Note, the question stem says that r and s are integers, so it is fair have positive value for one and negative for the other

In this case, r+s = (-3) +(3) = 0.

My understanding is "0" cannot be divided into 3, hence indivisble by 3. If this is true, then the answer should be "E"... what am I missing here?

We can say X is divisible by Y, when the Remainder is ZERO.
When zero is divided by any number, the remainder is zero......Hence Zero is divisible by all numbers
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Re: DS - is r+s divisible by 3? [#permalink]  25 Dec 2005, 22:48
5elements wrote:
If r and s are integers, is r+s divisible by 3?

1. s is divisible by 3
2. r is divisible by 3

Kindly explain your answer. I have a specific doubt in my mind regarding the official explanation for this question. I will post my doubt tomorrow in order to give some time to those interested in taking a stab at this.

From 1, we get s = 0 mod 3. Nothing is known about r. so insuff.

From 2 we get r = 0 mod 3, nothing is known about s. So insuff.

Addding 1 +2 we get r+s = 0 mod 3. Hence C.
Re: DS - is r+s divisible by 3?   [#permalink] 25 Dec 2005, 22:48
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