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26 May 2021, 02:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
63% (01:29) correct
37%
(01:46)
wrong
based on 97
sessions
History
Date
Time
Result
Not Attempted Yet
If a and b are integers, is 3a + 5b divisible by 26?
(1) a is divisible by 13
(2) 13 is a factor of b
(1) a is divisible by 13
(2) 13 is a factor of b
29 May 2021, 12:55
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Bunuel
Statement 1:
We don't know if 5b is a factor of 26. Insufficient.
Statement 2:
We don't know if 3a is a factor of 26. Insufficient.
Combined:
3a has a factor of 13, 5b also has a factor of 13. So we can say \(3a + 5b\) is divisible by 13 but we don't know if it is divisible by 26. Insufficient.
Ans: E
30 May 2021, 07:20
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Bunuel
Solution:
- • Given, a and b are integers.
Statement 1: a is divisible by 13
- • Then, 3a is divisible by 13 but we do not have any information about b.
Statement 2: 13 is a factor of b
- • This means that b is divisible by 13. Thus, 5b is divisible by 13 but we do not have any information about a.
Combining Statement 1 and Statement 2:
From Statement 1: 3a is divisible by 13
From Statement 2: 5b is divisible by 13
This implies, 3a + 5b is divisible by 13.
Let us consider few cases as follows:
• If 3a + 5b = 13, then 3a + 5b is not divisible by 26.
• If 3a + 5b = 26, then 3a + 5b is divisible by 26.
Thus, on combining both the statements, we get two contradictory results. Hence, the correct answer is Option E.
