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Updated on: 16 Aug 2025, 02:59
Originally posted by Sajjad1994 on 04 Aug 2025, 09:31.
Last edited by Sajjad1994 on 16 Aug 2025, 02:59, edited 1 time in total.
Last edited by Sajjad1994 on 16 Aug 2025, 02:59, edited 1 time in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
70% (01:08) correct
30% (01:19) wrong based on 10 sessions
History
Date
Time
Result
Not Attempted Yet
For how many integers, a, between 30 and 40 is it true that \(\frac{5}{a}\), \(\frac{8}{a}\), and \(\frac{13}{a}\) are all in lowest terms?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
16 Aug 2025, 03:03
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Official Explanation
If a is even, then 8/a is not in lowest terms, since both a and 8 are divisible by 2. Therefore, the only possibilities are 31, 33, 35, 37, and 39; but \(\frac{5}{35}=\frac{1}{7}\) and \(\frac{13}{39}=\frac{1}{3}\), so only 3 integers—31, 33, and 37—satisfy the given condition.
Answer: C
If a is even, then 8/a is not in lowest terms, since both a and 8 are divisible by 2. Therefore, the only possibilities are 31, 33, 35, 37, and 39; but \(\frac{5}{35}=\frac{1}{7}\) and \(\frac{13}{39}=\frac{1}{3}\), so only 3 integers—31, 33, and 37—satisfy the given condition.
Answer: C
