When divided by 5, x has a remainder of 2 and y has a

Question

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

VeritasPrepRon · Accepted Answer

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.

Hope this helps!
-Ron

nave · Answer

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.

yezz · Answer

x = 5k+2 , y = 5t+1

x+y = 5 (k+t) + 3 thus remainder when divided by 10 depends on (k+t) if k+t are non -ve even integer r = 3 , if +ve odd remainder is 8

from choices 8 is the right choice

ppskc1989 · Answer

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. Hence correct option is C

karishmatandon · Answer

Can anybody explain how to use picking numbers strategy for such a problem?

ppskc1989 · Answer

x is of the form 5*p +2 and y is of the form 5*q + 1 Look at the options. All of them are greater than 5. So choose x and y such that their sum is greater than 5 and less than 10 (because that will simply represent the remainder we are looking for.) For instance x = 7 and y = 1 can be taken. Similarly x = 2 and y = 6 can be taken. Hope this answers your question.

karishmatandon · Answer

Oh..k..
i was just considering, 7,6 or 2,1
so i was only getting 3 as the remainder for x + y, 
thanks for the explanation

Scorpserp · Answer

hi

i used this method to solve so hope it helps u even

"x divided by 5 gives remainder 2"
=>any multiple of 5 will have units digit 0 or 5 so x would have units digit 2 or 7

and since we are to calculate for remainder when divided by 10 our main concern is the units digit only

"y divided by 5 gives remainder 1"
=> y would have units digit 1 or 6

for units digit of x+y we can take all combinations of x and y 
(2,1) units digit 3
(2,6) units digit 8
(7,1) units digit 8
(7,6) units digit 3

so x+y will have units digit either 3 or 8 
so x+y wen divided by 10 wud give either 8 or 3 as remainder

krrish · Answer

given x-2 is divisible by 5 and y-1 is also divisible by 5,
there could be either a even or odd multiple of 5, so

consider all possible varieties we get 
if both are even or if both are odd
x+y makes it even 
so remainder is 3 => 2+1

but if one is add and other is even then we get

5 +2+1 = 8,

hence solved.

please ping me if u need any further explanation .....

gracie · Answer

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

ScottTargetTestPrep · Answer

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

gracie · Answer

five least values of x=2 7 12 17 22 27
five least values of y= 1 6 11 16 21
note that all x+y values sum to a 3 or 8 units digit
C

luisdicampo · Answer

Deconstructing the Question  
We are told:
 x=5a+2 
 y=5b+1

We want the possible remainder of  x+y  when divided by  10 .

Step-by-step  
Add:
 x+y=(5a+2)+(5b+1)=5a+5b+3

x+y=5(a+b)+3

So  x+y\equiv 3 \pmod{5} .

Write:
 x+y=5k+3

Now reduce modulo 10.

If  k  is even,  5k\equiv 0 \pmod{10} .
If  k  is odd,  5k\equiv 5 \pmod{10} .

Thus the possible remainders are:
 3  or  8 .

Among the choices, only  8  appears.

Answer: C

When divided by 5, x has a remainder of 2 and y has a

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When divided by 5, x has a remainder of 2 and y has a

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