If n, m, and p are distinct, five-digit positive integers and if p = n

Question

If n, m, and p are distinct, five-digit positive integers and if p = n + m, is the thousands digit of p equal to the sum of the thousands digits of n and m?

(1) The tens digit of p is equal to the sum of the tens digits of n and m.

(2) The hundreds digit of p is equal to the sum of the hundreds digits of n and m.

Bunuel · Answer

Similar question to practice from OG: https://gmatclub.com/forum/if-x-y-and-z ... 39138.html

Bunuel · Answer

Official Explanation To understand this question without going variable-crazy, we can draw a diagram of adding two five-digit numbers with blank spaces, like this, https://gmatclub.com/forum/download/file.php?id=50374 or whatever helps to visualize the addition. We're being asked whether the digits in the thousands position--the highlighted cells, in this figure--add up independently. Just as we learned in grade school, it boils down to whether we carried a 1 from adding the hundreds digits. If those digits add up to 10 or more, then we'll carry a one and the answer to this question will be "no"; otherwise, it will be "yes." On to the data statements, separately first. Statement (1) tells us about the wrong column. It's saying nothing about whether the hundreds column will carry over to the thousands. Insufficient. Statement (2) allows us to determine that there is no carrying of a digit to the thousands column, so we can answer the question definitively (in the affirmative). We have sufficient information. The correct answer is (B). image615.png

Bunuel · Answer

Video Explanation

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Kinshook · Answer

If n, m, and p are distinct, five-digit positive integers and if p = n + m, is the thousands digit of p equal to the sum of the thousands digits of n and m?

Let n, m & p be expressed as n1n2n3n4n5, m1m2m3m4m5 & p1p2p3p4p5 respectively.
p1p2p3p4p5 = n1n2n3n4n5 + m1m2m3m4m5

Q. Is p2 = n2 + m2 ?

(1) The tens digit of p is equal to the sum of the tens digits of n and m.
p2 = n2 + m2
Since p2 = n2 + m2; there is no carry over of sum of unit digts; p1 = n1 + m1
Since there is no carry over of sum of tens digits;
p3 = n3 + m3; or p3 +1 = n3 + m3
It is not certain whether p2 = n2 + m2
NOT SUFFICIENT

(2) The hundreds digit of p is equal to the sum of the hundreds digits of n and m.
p3 = n3 + m3
There is no carry over of sum of hundredth digit 
p2 = n2 + m2
SUFFICIENT

IMO B

sumert · Answer

30% of the people thought the way I thought so I am going to ask this- What if the thousands digits of m and n are 5 or bigger? say 7 and 6? In that case the thousands digit of P is NOT equal to the thousands digit of M + N. (6 + 7 = 13 not 3).
I know it sounds dumb but the question needs to somehow clarify this.

spawar · Answer

I thought the same way. My answer remains E!

anandjoy1022 · Answer

yeah this has to be clarified

4 7 864 m
3 7 135 n
-------
8 4 999 p
====

andreshc91 · Answer

Exactly, mi answe remains E

Usernamevisible · Answer

Fast GMAT Pattern
MAX PRODUCT under fixed total

→ make variables equal/close

MIN PRODUCT under fixed total

→ make variables uneven/extreme

AnishTrivedi99 · Answer

How is it not E? Case 1 = 11000 + 12000 = 23000; Case 2 = 18000 + 12000 = 30000?

Bunuel · Answer

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.

If n, m, and p are distinct, five-digit positive integers and if p = n

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