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Re: When divided by 5, x has a remainder of 2 [#permalink]
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06 May 2013, 11:30
3
2
For remainder questions like this, you can also think of the logic this way:
x has a remainder of 2 when divided by 5 y has a remainder of 1 when divided by 5 x+y must necessarily have a remainder of 3 when divided by 5.
Remainder of 3 when divided by 5 applies to 3, 8, 13, 18, 23, etc. Just keep adding 5's. What's the only option that's provided here that works? 8. Done.
Re: When divided by 5, x has a remainder of 2 [#permalink]
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04 May 2013, 16:38
6
2
Let x=5a+2 and y=5b+1
x+y = 5(a+b) + 3: Possible numbers for this equation are 3, 8, 13, 18, 23, 28... Therefore when (x+y) is divided by 10, the possible remainders are 3 and 8. 3 is not in the answer choices but 8 is, so answer is C.
Re: When divided by 5, x has a remainder of 2 [#permalink]
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04 May 2013, 21:51
Zarrolou wrote:
When divided by 5, x has a remainder of 2 and y has a remainder of 1. Which of the following could be the remainder when x + y is divided by 10?
A)6 B)7 C)8 D)9 E)0
Given data can be represented as \(x = 5*p + 2\) and \(y = 5*q + 1\), where p and q are non negative integers.
Hence \(x+y = 5*k + 3\), k is some non negative integer.
Now observe that the possible remainders obtained when 5*k is divided by 10 are 0 and 5, depending on the parity of k. (0 when k is even, 5 when k is odd)
Hence it follows that the possible remainders when 5*k + 3 is divided by 10 are 3 and 8. 8 is in the given options.
When divided by 5, x has a remainder of 2 and y has a [#permalink]
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14 May 2017, 12:30
Zarrolou wrote:
When divided by 5, x has a remainder of 2 and y has a remainder of 1. Which of the following could be the remainder when x + y is divided by 10?
A. 6 B. 7 C. 8 D. 9 E. 0
least possible value of x=2 least possible value of y=1 (2+1)/10 gives a remainder of 3--not listed next least value of y=6 (2+6)/10 gives a remainder of 8 C
Re: When divided by 5, x has a remainder of 2 and y has a [#permalink]
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18 May 2017, 20:06
1
Zarrolou wrote:
When divided by 5, x has a remainder of 2 and y has a remainder of 1. Which of the following could be the remainder when x + y is divided by 10?
A. 6 B. 7 C. 8 D. 9 E. 0
We should recall that when dividing by 5, we only need to know the units digit of the divisor to determine the remainder. Thus, when x is divided by 5 and the remainder is 2, the units digit of x must be either 7 or 2. Also, when y is divided by 5 and the remainder is 1, the units digit of y must be either 6 or 1.
Likewise, when dividing by 10, we only need to know the units digit of the divisor to determine the remainder. Let’s now determine some possible sums of x and y.
x + y = 7 + 6 = 13, which has a remainder of 3 when divided by 10.
x + y = 7 + 1 = 8, which has a remainder of 8 when divided by 10.
x + y = 2 + 6 = 8, which has a remainder of 8 when divided by 10.
x + y = 2 + 1 = 3, which has a remainder of 3 when divided by 10.
Thus, the possible remainders when x + y is divided by 10 are 3 and 8. Since only 8 is given in the answer choices, the correct answer is C.
Answer: C
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