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.

Answer: A.

Hope it's clear.

_________________

New to the Math Forum?

Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:

GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?

Extra-hard Quant Tests with Brilliant Analytics