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07 Feb 2024, 02:30
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C
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:
80% (01:52) correct
20%
(01:49)
wrong
based on 123
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Not Attempted Yet
If m is a positive integer, what is the remainder when m is divided by 20?
(1) When m is divided by 5, the remainder is 3.
(2) When m is divided by 8, the remainder is 3.
(1) When m is divided by 5, the remainder is 3.
(2) When m is divided by 8, the remainder is 3.
07 Feb 2024, 06:40
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I think C should be the answer
We are to find the remainder when m is divided by 20.
If we can write m as m=20k+r then r is the remainder when divided by 20.
Statement 1:
When m is divided by 5, the remainder is 3.
So we can write m= 5k+3
| k | m=5k+3 | remainder(m%20) |
|---|---|---|
| 1 | 8 | 8 |
| 2 | 13 | 13 |
| 4 | 23 | 3 |
so we can see that we don't get any conclusive remainder. Insufficient.
Statement 2:
When m is divided by 8, the remainder is 3
We can write m=8k +3
| k | m=8k+3 | remainder(m%20) |
|---|---|---|
| 1 | 11 | 11 |
| 2 | 19 | 19 |
| 3 | 27 | 7 |
Again no conclusive evidence. Insufficient
If we club both the statements together, then
We have m which gives remainder of 3 when divided by both 5 and 8. Now as we know 5 and 8 are co-prime numbers, we can write m in thios case as:
m= (5*8)k+3 = 40k +3
=> m = 2*20k +3
So, m will always produce a remainder of 3 when divided by 20.
| k | m=40k+3 | remainder(m%20) |
|---|---|---|
| 0 | 3 | 3 |
| 1 | 43 | 3 |
| 2 | 83 | 3 |
| 3 | 123 | 3 |
Hence, both of the statements together are sifficient.
Hence, correct option C
03 Jul 2025, 05:26
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