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What is the remainder when the positive three-digit number 1yz is divided by 7?
(1) y + z = 7
(2) y -2 is a non-zero positive number divisible by 3
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'C'. Can you explain this answer?
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What is the remainder when the positive three-digit number 1yz is divi...
Given: A positive three-digit number 1yz is divided by 7.
To find: The remainder when the number is divided by 7.
Approach: We can use the divisibility rule of 7, which states that a number is divisible by 7 if and only if the difference between twice the units digit and the rest of the number is a multiple of 7. Using this rule, we can find the remainder when 1yz is divided by 7.
Solution:
Statement (1): yz = 7
If yz = 7, then the number 1yz could be 107, 217, 327, 437, 547, 657, 767, 877, or 987.
Checking each of these numbers using the divisibility rule of 7, we get:
- 107: 2(7) - 10 = 4, which is not divisible by 7.
- 217: 2(7) - 21 = -7, which is divisible by 7.
- 327: 2(7) - 32 = -18, which is not divisible by 7.
- 437: 2(7) - 43 = -29, which is not divisible by 7.
- 547: 2(7) - 54 = -40, which is divisible by 7.
- 657: 2(7) - 65 = -51, which is not divisible by 7.
- 767: 2(7) - 76 = -62, which is not divisible by 7.
- 877: 2(7) - 87 = -73, which is not divisible by 7.
- 987: 2(7) - 98 = -84, which is divisible by 7.
Therefore, the only possible remainders when 1yz is divided by 7 are 2 and 5. Thus, statement (1) alone is not sufficient.
Statement (2): y - 2 is a non-zero positive number divisible by 3
If y - 2 is divisible by 3, then y could be 5, 8, or 11. Checking each of these values of y, we get:
- If y = 5, then the number is 157. 2(7) - 15 = -1, which is not divisible by 7.
- If y = 8, then the number is 187. 2(7) - 18 = 2, which is not divisible by 7.
- If y = 11, then the number is 191. 2(1) - 19 = -17, which is not divisible by 7.
Thus, statement (2) alone is not sufficient.
Statements (1) and (2) together:
From statement (1), we know that yz = 7. From statement (2), we know that y - 2 is divisible by 3.
Since yz = 7, y can only be 5 or 8. If y = 5, then z = 2, and the number is 152. 2(7) - 15 = -1, which is not divisible by 7. If y = 8, then z = 9, and the number is 189
To find: The remainder when the number is divided by 7.
Approach: We can use the divisibility rule of 7, which states that a number is divisible by 7 if and only if the difference between twice the units digit and the rest of the number is a multiple of 7. Using this rule, we can find the remainder when 1yz is divided by 7.
Solution:
Statement (1): yz = 7
If yz = 7, then the number 1yz could be 107, 217, 327, 437, 547, 657, 767, 877, or 987.
Checking each of these numbers using the divisibility rule of 7, we get:
- 107: 2(7) - 10 = 4, which is not divisible by 7.
- 217: 2(7) - 21 = -7, which is divisible by 7.
- 327: 2(7) - 32 = -18, which is not divisible by 7.
- 437: 2(7) - 43 = -29, which is not divisible by 7.
- 547: 2(7) - 54 = -40, which is divisible by 7.
- 657: 2(7) - 65 = -51, which is not divisible by 7.
- 767: 2(7) - 76 = -62, which is not divisible by 7.
- 877: 2(7) - 87 = -73, which is not divisible by 7.
- 987: 2(7) - 98 = -84, which is divisible by 7.
Therefore, the only possible remainders when 1yz is divided by 7 are 2 and 5. Thus, statement (1) alone is not sufficient.
Statement (2): y - 2 is a non-zero positive number divisible by 3
If y - 2 is divisible by 3, then y could be 5, 8, or 11. Checking each of these values of y, we get:
- If y = 5, then the number is 157. 2(7) - 15 = -1, which is not divisible by 7.
- If y = 8, then the number is 187. 2(7) - 18 = 2, which is not divisible by 7.
- If y = 11, then the number is 191. 2(1) - 19 = -17, which is not divisible by 7.
Thus, statement (2) alone is not sufficient.
Statements (1) and (2) together:
From statement (1), we know that yz = 7. From statement (2), we know that y - 2 is divisible by 3.
Since yz = 7, y can only be 5 or 8. If y = 5, then z = 2, and the number is 152. 2(7) - 15 = -1, which is not divisible by 7. If y = 8, then z = 9, and the number is 189
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What is the remainder when the positive three-digit number 1yz is divi...
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What is the remainder when the positive three-digit number 1yz is divided by 7?(1) y + z = 7(2) y -2 is a non-zero positive number divisible by 3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?
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What is the remainder when the positive three-digit number 1yz is divided by 7?(1) y + z = 7(2) y -2 is a non-zero positive number divisible by 3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the remainder when the positive three-digit number 1yz is divided by 7?(1) y + z = 7(2) y -2 is a non-zero positive number divisible by 3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the remainder when the positive three-digit number 1yz is divided by 7?(1) y + z = 7(2) y -2 is a non-zero positive number divisible by 3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.
What is the remainder when the positive three-digit number 1yz is divided by 7?(1) y + z = 7(2) y -2 is a non-zero positive number divisible by 3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the remainder when the positive three-digit number 1yz is divided by 7?(1) y + z = 7(2) y -2 is a non-zero positive number divisible by 3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the remainder when the positive three-digit number 1yz is divided by 7?(1) y + z = 7(2) y -2 is a non-zero positive number divisible by 3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.
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ample number of questions to practice What is the remainder when the positive three-digit number 1yz is divided by 7?(1) y + z = 7(2) y -2 is a non-zero positive number divisible by 3a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice UPSC tests.
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