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If t is a positive integer, can t2 + 1 be evenly divided by 10?
(1) 916 × t leaves a remainder of 1 when divided by 2
(2) 916 × t leaves a remainder of 2 when divided by 5
- 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?
Verified Answer
If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916...
Steps 1 & 2: Understand Question and Draw Inferences
t2 + 1 can be evenly divided by 10 if t2 + 1 = 10 *k, where k is a positive integer
- We need to check if the last digit of t2 + 1 is 0
Step 3: Analyze Statement 1
916 × t leaves a remainder of 1 when divided by 2
- t is odd
- last digit of t can be 1, 3, 5, 7 or 9
Not Sufficient.
Step 4: Analyze Statement 2
916 × t leaves a remainder of 2 when divided by 5
- last digit of 916 × t can be 2 or 7
- last digit of t can be 2 or 7
Not Sufficient
Step 5: Analyze Both Statements Together (if needed)
Inference from statement 1: last digit of t can be 1, 3, 5, 7 or 9
Inference from statement 2: last digit of t can be 2 or 7
Inference from statement 1 and statement 2: last digit of t can be 7
--> Last digit of t2 + 1 = Last digit of (9 + 1) = 0
Hence, t2 + 1 can be evenly divided by 10
Statement 1 and Statement 2 together are sufficient to answer the question.
Answer: Option (C)
Most Upvoted Answer
If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916...
Statement (1): 916t leaves a remainder of 1 when divided by 2
If 916t leaves a remainder of 1 when divided by 2, it means that t itself must be odd. So, we can write t as t = 2k + 1, where k is an integer.
Statement (2): 916t leaves a remainder of 2 when divided by 5
If 916t leaves a remainder of 2 when divided by 5, it means that t itself must leave a remainder of 2 when divided by 5. So, we can write t as t = 5m + 2, where m is an integer.
Combining both statements:
From statement (1), we know that t = 2k + 1, and from statement (2), we know that t = 5m + 2.
Now, let's substitute the value of t from statement (1) into statement (2):
2k + 1 = 5m + 2
Simplifying the equation, we get:
2k - 5m = 1
This is a linear equation in two variables, k and m. We need to check if there are any integer solutions for this equation.
Testing the equation:
To test if there are any integer solutions for the equation 2k - 5m = 1, we can try different values of k and m:
For k = 1, m = 1, we have:
2(1) - 5(1) = 1
2 - 5 = 1 (not true)
For k = 2, m = 3, we have:
2(2) - 5(3) = 1
4 - 15 = 1 (not true)
For k = 3, m = 5, we have:
2(3) - 5(5) = 1
6 - 25 = 1 (not true)
We can continue testing different values of k and m, but we will not find any integer solutions for this equation. Therefore, we can conclude that both statements together are not sufficient to determine if t^2 - 1 can be evenly divided by 10.
Hence, the correct answer is option 'E' - Statements (1) and (2) together are not sufficient.
If 916t leaves a remainder of 1 when divided by 2, it means that t itself must be odd. So, we can write t as t = 2k + 1, where k is an integer.
Statement (2): 916t leaves a remainder of 2 when divided by 5
If 916t leaves a remainder of 2 when divided by 5, it means that t itself must leave a remainder of 2 when divided by 5. So, we can write t as t = 5m + 2, where m is an integer.
Combining both statements:
From statement (1), we know that t = 2k + 1, and from statement (2), we know that t = 5m + 2.
Now, let's substitute the value of t from statement (1) into statement (2):
2k + 1 = 5m + 2
Simplifying the equation, we get:
2k - 5m = 1
This is a linear equation in two variables, k and m. We need to check if there are any integer solutions for this equation.
Testing the equation:
To test if there are any integer solutions for the equation 2k - 5m = 1, we can try different values of k and m:
For k = 1, m = 1, we have:
2(1) - 5(1) = 1
2 - 5 = 1 (not true)
For k = 2, m = 3, we have:
2(2) - 5(3) = 1
4 - 15 = 1 (not true)
For k = 3, m = 5, we have:
2(3) - 5(5) = 1
6 - 25 = 1 (not true)
We can continue testing different values of k and m, but we will not find any integer solutions for this equation. Therefore, we can conclude that both statements together are not sufficient to determine if t^2 - 1 can be evenly divided by 10.
Hence, the correct answer is option 'E' - Statements (1) and (2) together are not sufficient.
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If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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?.
If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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?.
Solutions for If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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? in English & in Hindi are available as part of our courses for UPSC.
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If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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?, a detailed solution for If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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? has been provided alongside types of If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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? theory, EduRev gives you an
ample number of questions to practice If t is a positive integer, can t2 + 1 be evenly divided by 10?(1) 916 × t leaves a remainder of 1 when divided by 2(2) 916 × t leaves a remainder of 2 when divided by 5a)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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