Consider the given number (45)y, where y is the base of the number. Some of…
2024
Consider the given number (45)y, where y is the base of the number. Some of the possible values of y are given below.
(A) 5
(B) 6
(C) 7
(D) 8
Choose the correct answer from the options given below:
Answer: B. (B), (C) and (D) Only — Answer: The given number (45)y is valid for bases 6, 7 and 8. Key rule: In base y every digit must be strictly less than y. The digits in (45)y are 4 and 5,…
- A.
(A), (B) and (C) Only
- B.
(B), (C) and (D) Only
- C.
(A), (C) and (D) Only
- D.
(A), (B), (C) and (D)
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Correct answer: B
Answer: The given number (45)y is valid for bases 6, 7 and 8.
Key rule: In base y every digit must be strictly less than y.
The digits in (45)y are 4 and 5, so the largest digit is 5. Therefore the base must be at least 6 (y ≥ 6).
Check base 5: invalid because digit 5 is not less than 5.
Check base 6: valid because digits 4 and 5 are both less than 6.
Check base 7: valid for the same reason (4 and 5 are less than 7).
Check base 8: valid because 4 and 5 are less than 8.
Conclusion: among the given choices, 6, 7 and 8 are valid bases and 5 is not. Select the choice that lists 6, 7 and 8.
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