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st 1:
sum of digits is 5 ...remainder will always be 2
Sufficient

St2: remainder will always be 2

Ans: D
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statement 1
sum of digits is 5 therefore possible combination 41,14,23,32 which yields remainder 2
statement 2
x/9 remainder 2 which means x= 11,20,29 etc
check above with 3 it gives 2 every time

therefore D
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To get the remainder when a number is divided b 3 we need the remainder when sum of the digits divided by 3 so statement 1 i sufficient
now statement 2=> x=9n+2 => 3P+2=> remainder =2
hence D is sufficient
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statement 1
As sum of digits is 5 remainder will always be 2.

Statement 2
also sufficient

Answer D
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Would you need a constraint that the digits are always positive? For example, for statement 1, could it be the case that the number is -16 (-1 + 6 = 5?) which would only have a remainder of 5?
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elizabethsmith719
What is the remainder when x is divided by 3?

(1) The sum of the digits of x is 5
(2) When x is divided by 9, the remainder is 2

Would you need a constraint that the digits are always positive? For example, for statement 1, could it be the case that the number is -16 (-1 + 6 = 5?) which would only have a remainder of 5?

The digits are always non-negative; they are 0, 1, 2, 3..., 9. However, you're right that the stem should mention that x is a positive integer, but for a different reason. If, in (1), x is a negative number, such as -14, the remainder of -14 divided by 3 is 1, and if it's 14, the remainder of 14 divided by 3 would be 2, making (1) insufficient.

P.S. Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

  • Word Problems
  • Work Problems
  • Distance Problems
  • Mixture Problems
  • Percent and Interest Problems
  • Overlapping Sets Problems
  • Statistics Problems
  • Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.­
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omg many thanks, i was just starting this morning doing exercise for DS on number properties. Thanks to you, i will not waste time on stuff that is not required :)
Bunuel
elizabethsmith719
What is the remainder when x is divided by 3?

(1) The sum of the digits of x is 5
(2) When x is divided by 9, the remainder is 2

Would you need a constraint that the digits are always positive? For example, for statement 1, could it be the case that the number is -16 (-1 + 6 = 5?) which would only have a remainder of 5?

The digits are always non-negative; they are 0, 1, 2, 3..., 9. However, you're right that the stem should mention that x is a positive integer, but for a different reason. If, in (1), x is a negative number, such as -14, the remainder of -14 divided by 3 is 1, and if it's 14, the remainder of 14 divided by 3 would be 2, making (1) insufficient.

P.S. Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

  • Word Problems
  • Work Problems
  • Distance Problems
  • Mixture Problems
  • Percent and Interest Problems
  • Overlapping Sets Problems
  • Statistics Problems
  • Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.­
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