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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
1. w + x + y + z = 13
2. N + 5 is divisible by 9
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
- d)EACH statement ALONE is sufficient to answer the question asked;
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.
Correct answer is option 'D'. Can you explain this answer?
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If w, x, y, and z are the digits of the four-digit number N, a positiv...
In order for a number, n, to be divisible by 9, its digits must add to nine. Likewise, the remainder of the sum of the digits of n divided by 9 is the remainder when n is divided by 9. In other words:
To see this, consider a few examples:
Let N = 901
901/9 = 100 + (R = 1)
(9+0+1)/9 = 10/9 = 1 + (R = 1)
Let N = 901
901/9 = 100 + (R = 1)
(9+0+1)/9 = 10/9 = 1 + (R = 1)
Let N = 85
85/9 = 9 + (R = 4)
(8+5)/9 = 1 + (R = 4)
85/9 = 9 + (R = 4)
(8+5)/9 = 1 + (R = 4)
Let N = 66
66/9 = 7 + (R = 3)
(6+6)/9 = 1 + (R = 3)
66/9 = 7 + (R = 3)
(6+6)/9 = 1 + (R = 3)
Let N = 8956
8956/9 = 995 + (R = 1)
(8+9+5+6)/9 = 28/9 = 3 + (R = 1)
Evaluate Statement (1) alone.
Based upon what was shown above, since the sum of the digits of N is always 13, we know that remainder of N/9 will always be the remainder of 13/9, which is R=4.
In case this is hard to believe, consider the following examples:
4540/9 = 504 + (R = 4)
(4+5+4+0)/9 = 13/9 = 1 + (R = 4)
8956/9 = 995 + (R = 1)
(8+9+5+6)/9 = 28/9 = 3 + (R = 1)
Evaluate Statement (1) alone.
Based upon what was shown above, since the sum of the digits of N is always 13, we know that remainder of N/9 will always be the remainder of 13/9, which is R=4.
In case this is hard to believe, consider the following examples:
4540/9 = 504 + (R = 4)
(4+5+4+0)/9 = 13/9 = 1 + (R = 4)
1390/9 = 154 + (R = 4)
(1+3+9+0)/9 = 13/9 = 1 + (R = 4)
(1+3+9+0)/9 = 13/9 = 1 + (R = 4)
7231/9 = 803 + (R = 4)
(7+2+3+1)/9 = 13/9 = 1 + (R = 4)
(7+2+3+1)/9 = 13/9 = 1 + (R = 4)
1192/9 = 132 + (R = 4)
(1+1+9+2)/9 = 13/9 = 1 + (R = 4)
Statement (1) is SUFFICIENT.
Evaluate Statement (2) alone.
If adding 5 to a number makes it divisible by 9, there are 9-5=4 left over from the last clean division. In other words, N/9 will have a remainder of 4.
To help see this, consider the following examples:
Let N = 4
N+5=9 is divisible by 9 and N/9 -> R = 4
(1+1+9+2)/9 = 13/9 = 1 + (R = 4)
Statement (1) is SUFFICIENT.
Evaluate Statement (2) alone.
If adding 5 to a number makes it divisible by 9, there are 9-5=4 left over from the last clean division. In other words, N/9 will have a remainder of 4.
To help see this, consider the following examples:
Let N = 4
N+5=9 is divisible by 9 and N/9 -> R = 4
Let N = 13
N+5=18 is divisible by 9 and N/9 -> R = 4
N+5=18 is divisible by 9 and N/9 -> R = 4
Let N = 724
N+5=729 is divisible by 9 and N/9 -> R = 4
N+5=729 is divisible by 9 and N/9 -> R = 4
Let N = 418
N+5=423 is divisible by 9 and N/9 -> R = 4
Since N + 5 is divisible by 9, we know that the remainder of N/9 will always be 4. Statement (2) is SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.
N+5=423 is divisible by 9 and N/9 -> R = 4
Since N + 5 is divisible by 9, we know that the remainder of N/9 will always be 4. Statement (2) is SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.
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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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer?
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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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer?.
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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer?.
Solutions for 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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for 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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of 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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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