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Intern  B
Joined: 10 Dec 2016
Posts: 21
If R and S are three-digit positive integers what is the quotient when  [#permalink]

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3 00:00

Difficulty:   95% (hard)

Question Stats: 31% (02:26) correct 69% (02:13) wrong based on 70 sessions

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If R and S are three-digit positive integers, what is the quotient when the sum of R and S is divided by 1000?

(1) The hundreds digit of the sum of R and S is less than the sum of the hundreds digits of R and S.

(2) When R, rounded to the nearest hundreds, is added to S, rounded to the nearest hundreds, the result is 1000.
Math Expert V
Joined: 02 Sep 2009
Posts: 58327
Re: If R and S are three-digit positive integers what is the quotient when  [#permalink]

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1
If R and S are three-digit positive integers, what is the quotient when the sum of R and S is divided by 1000?

To find the quotient when dividing by 1,000 we need to know the thousands digit of the sum. Notice that since we are adding two three-digit numbers, their sum is either a three-digit number or a four-digit number, so the quotient upon division by 1,000 is either 0 or 1. For example:

If R = 150 and y = 350, then R + S = 500 and 500 divided by 1,000 gives the quotient of 0.
If R = 750 and y = 350, then R + S = 1,100 and 1,100 divided by 1,000 gives the quotient of 1.

(1) The hundreds digit of the sum of R and S is less than the sum of the hundreds digits of R and S. The only way it could happen is if there is carry over 1 to the thousands digit after adding the hundreds digits of R and S. Thus, R + S is a four-digit number, which means that the quotient upon division by 1,000 is 1. Sufficient.

For example:
750
350
___
1,100

As you can see above, the sum of the hundreds digit of the sum (1,100) of R and S (1) is less than the sum of the hundreds digits of R and S (7 + 3 = 10): 1 < 10. Hence the carry over 1 from hundreds to thousands, making the sum a four-digit number.

(2) When R, rounded to the nearest hundreds, is added to S, rounded to the nearest hundreds, the result is 1000. If R = S = 500, then rounded to the nearest hundreds both R and S are still 500, so in this case R + S = 1,000 and the quotient upon division by 1,000 is 1. But if R = S = 499, then rounded to the nearest hundreds both R and S are 500, so in this case R + S = 998 and the quotient upon division by 1,000 is 0. Not sufficient.

Hope it's clear.
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Intern  B
Joined: 04 May 2017
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Re: If R and S are three-digit positive integers what is the quotient when  [#permalink]

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Hi Bunuel,
Could you please explain the statement two again ?
Math Expert V
Joined: 02 Sep 2009
Posts: 58327
Re: If R and S are three-digit positive integers what is the quotient when  [#permalink]

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vishuvashishth wrote:
Hi Bunuel,
Could you please explain the statement two again ?

Could you please be a little bit more specific? Which part is not clear?
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Manager  P
Joined: 01 Feb 2017
Posts: 243
If R and S are three-digit positive integers what is the quotient when  [#permalink]

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Range of Sum of Two 3-digit Integers:
Minimun: 100+100= 200
Maximum: 999+999= 1098

So, this sum, when divided by 1000, can have a quotient of either 0 or 1.

St.1 implies that sum of hundreds digit is greater than 10.
Basically, this means that sum of the two numbers is more than 1000 and hence quotient is 1. Sufficient.

St.2 implies that either number is between 450 and 549.
So, sum of two numbers can be between 900 and 1098.
That means quotient can be either 0 or 1. Insufficient.

Hence, And A If R and S are three-digit positive integers what is the quotient when   [#permalink] 13 Mar 2018, 12:43
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If R and S are three-digit positive integers what is the quotient when

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