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If a and b are positive integers, what is the digit at the unit's place of 18(2a + 5b)?
(1) a is even, b is a multiple of four.
(2) b = 12
(2) b = 12
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question 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 'A'. Can you explain this answer?
Verified Answer
If a and b are positive integers, what is the digit at the units place...
To determine the digit at the unit's place of 182a + 5b, we need to consider the cyclicity of the units digit of the number 18.
The units digit of any power of 18 repeats in cycles of four: 8, 4, 2, 6, 8, 4, 2, 6, and so on.
Let's analyze each statement separately:
Statement (1): a is even, b is a multiple of four.
If a is even, 2a is also even. Since the exponent of 18 is 2a + 5b, it will always be even since it contains an even number (2a) and a multiple of four (5b).
Statement (1): a is even, b is a multiple of four.
If a is even, 2a is also even. Since the exponent of 18 is 2a + 5b, it will always be even since it contains an even number (2a) and a multiple of four (5b).
In this case, the units digit of 182a + 5b will always be 4 because the exponent is always even. Therefore, statement (1) alone is sufficient to answer the question.
Statement (2): b = 12
If b = 12, we know the value of b but not the value of a. Without knowing the value of a, we cannot determine the value of 2a + 5b and, therefore, cannot determine the units digit of 182a + 5b. Thus, statement (2) alone is not sufficient to answer the question.
Since statement (1) alone is sufficient to answer the question, but statement (2) alone is not, the correct answer is (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Most Upvoted Answer
If a and b are positive integers, what is the digit at the units place...
To determine the digit at the unit's place of 182a + 5b, we need to consider the cyclicity of the units digit of the number 18.
The units digit of any power of 18 repeats in cycles of four: 8, 4, 2, 6, 8, 4, 2, 6, and so on.
Let's analyze each statement separately:
Statement (1): a is even, b is a multiple of four.
If a is even, 2a is also even. Since the exponent of 18 is 2a + 5b, it will always be even since it contains an even number (2a) and a multiple of four (5b).
Statement (1): a is even, b is a multiple of four.
If a is even, 2a is also even. Since the exponent of 18 is 2a + 5b, it will always be even since it contains an even number (2a) and a multiple of four (5b).
In this case, the units digit of 182a + 5b will always be 4 because the exponent is always even. Therefore, statement (1) alone is sufficient to answer the question.
Statement (2): b = 12
If b = 12, we know the value of b but not the value of a. Without knowing the value of a, we cannot determine the value of 2a + 5b and, therefore, cannot determine the units digit of 182a + 5b. Thus, statement (2) alone is not sufficient to answer the question.
Since statement (1) alone is sufficient to answer the question, but statement (2) alone is not, the correct answer is (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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If a and b are positive integers, what is the digit at the units place of 18(2a + 5b)?(1) a is even, b is a multiple of four.(2) b = 12a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If a and b are positive integers, what is the digit at the units place of 18(2a + 5b)?(1) a is even, b is a multiple of four.(2) b = 12a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are positive integers, what is the digit at the units place of 18(2a + 5b)?(1) a is even, b is a multiple of four.(2) b = 12a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?.
If a and b are positive integers, what is the digit at the units place of 18(2a + 5b)?(1) a is even, b is a multiple of four.(2) b = 12a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If a and b are positive integers, what is the digit at the units place of 18(2a + 5b)?(1) a is even, b is a multiple of four.(2) b = 12a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are positive integers, what is the digit at the units place of 18(2a + 5b)?(1) a is even, b is a multiple of four.(2) b = 12a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?.
Solutions for If a and b are positive integers, what is the digit at the units place of 18(2a + 5b)?(1) a is even, b is a multiple of four.(2) b = 12a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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