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If w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9?
1) w + x + y + z = 13
2) N + 5 is divisible by 9
  • a)
    Exactly one of the statements can answer the question
  • b)
    Both statements are required to answer the question
  • c)
    Each statement can answer the question individually
  • d)
    More information is required as the information provided is insufficient to answer the question
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If w, x, y, and z are the digits of the four-digit number N, a positiv...
GMAT Problem: If w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9?

Statement 1: w x y z = 13

If the sum of the digits of a number is divisible by 9, then the number itself is also divisible by 9. Here, the sum of the digits is 1+3+2=6, which is not divisible by 9. Therefore, this statement alone is not sufficient to answer the question.

Statement 2: N 5 is divisible by 9

If a number is divisible by 9, then the sum of its digits is also divisible by 9. Here, we know that N+5 is divisible by 9. Let's assume that N has digits a, b, c, and d. Then we have:

(a+b+c+d) + 5 = 9k, where k is some integer.

Simplifying, we get:

a+b+c+d = 9k-5

Since we want to find the remainder when N is divided by 9, we only need to know the value of (a+b+c+d) mod 9. From the equation above, we can see that (a+b+c+d) mod 9 is the same as (9k-5) mod 9. But 9k is always divisible by 9, so (9k-5) mod 9 is the same as (-5) mod 9, which is 4. Therefore, we know that (a+b+c+d) mod 9 is 4, and this statement alone is sufficient to answer the question.

Answer: Each statement can answer the question individually (Option C)
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Community Answer
If w, x, y, and z are the digits of the four-digit number N, a positiv...
By digit sum concept statement 1 and 2 are providing contradictory results.so either question is wrong.
I predict statement 1 may be w+x+y+z =13

if this so then option D
otherwise question is 100% wrong.
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If w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9?1) w + x + y + z = 132) N + 5 is divisible by 9a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'C'. Can you explain this answer?
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