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n is a positive integer. The remainder when 5n is divided by
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27 Oct 2016, 12:40
27 Oct 2016, 12:40
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n is a positive integer.
The remainder when 5n is divided by 4 is 3.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
The remainder when 5n is divided by 4 is 3.
Quantity A |
Quantity B |
The remainder when 10n is divided by 4 |
2 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Drill 2
Question: 12
Page: 288
Question: 12
Page: 288
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Re: n is a positive integer. The remainder when 5n is divided by
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12 Nov 2016, 14:10
12 Nov 2016, 14:10
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sandy wrote:
n is a positive integer.
The remainder when 5n is divided by 4 is 3.
The remainder when 5n is divided by 4 is 3.
Quantity A |
Quantity B |
The remainder when 10n is divided by 4 |
2 |
There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
The remainder when 5n is divided by 4 is 3
Applying the above rule, we get: 5n = 4k + 3 (for some integer k)
Divide both sides by 5 to get: n = (4k + 3)/5
Quantity A: The remainder when 10n is divided by 4
Replace n with (4k + 3)/5 to get: 10n = 10((4k + 3)/5) = 8k + 6
If 10n = 8k + 6, what is the remainder when 8k + 6 is divided by 4?
Notice that 8k + 6 = 8k + 4 + 2
= 4(2k + 1) + 2
As we can see, 4(2k + 1) is a MULTIPLE OF 4
This means that 4(2k + 1) + 2 is 2 greater than a MULTIPLE OF 4
So, if we divide 4(2k + 1) + 2 by 4, the remainder will be 2
We get....
Quantity A: 2
Quantity B: 2
Answer:
Show: ::
C
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General Discussion
Re: n is a positive integer. The remainder when 5n is divided by
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27 Oct 2016, 12:42
27 Oct 2016, 12:42
1
Expert Reply
Explanation
If the remainder is 3, then 5n must be 3 more than a multiple of 4, such as 4, 8, 12, or 16. Try adding 3 to these multiples to find a possible value for 5n. 12 + 3 yields 15 as a value for 5n; n = 3. Quantity A is the remainder when 30 is divided by 4, or 2. Eliminate choices A and B.
Try a different number. If n is 7, then 5n is 35, which also has a remainder of 3 when divided by 4. In Quantity A, 70 divided by 4 has a remainder of 2. For any other numbers you try, choice C will be the answer.
If the remainder is 3, then 5n must be 3 more than a multiple of 4, such as 4, 8, 12, or 16. Try adding 3 to these multiples to find a possible value for 5n. 12 + 3 yields 15 as a value for 5n; n = 3. Quantity A is the remainder when 30 is divided by 4, or 2. Eliminate choices A and B.
Try a different number. If n is 7, then 5n is 35, which also has a remainder of 3 when divided by 4. In Quantity A, 70 divided by 4 has a remainder of 2. For any other numbers you try, choice C will be the answer.
