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The remainder when dividing the expression (X + Y) by 5 is 4. The rema

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The remainder when dividing the expression (X + Y) by 5 is 4. The rema  [#permalink]

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New post 05 Jul 2016, 11:26
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The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder of Y divided by 5?

A. 1.
B. 2.
C. 3.
D. 4.
E. 5.

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Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema  [#permalink]

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New post 05 Jul 2016, 12:10
1
X divided by 10 leaves 2 i.e X is either 2/ 12/ 22/ 32 etc
More over \(\frac{(X+Y)}{5}\)= Remainder 4 .. Possible values are 4/ 9/ 14/ 19 etc

Hence _2 + _? = _4
=> Ans B. 2.

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Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema  [#permalink]

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New post 05 Jul 2016, 21:48
asnwer is 2

x+y/5=4(rem)

x/10=2(rem)

so x can be 2,12,22

so y has to be 2

then only x+y=_4/5=4(rem)

hope it helps
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Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema  [#permalink]

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New post 06 Jul 2016, 05:16
Bunuel wrote:
The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder of Y divided by 5?

A. 1.
B. 2.
C. 3.
D. 4.
E. 5.


X divided by 10 gives reminder of 2. X can be 2/12/22....

X+Y divided by 5 is 4. X+Y can be 4/ 9/ 19....

If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2

Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2

Hence the answer must be 2 (B)
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Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema  [#permalink]

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New post 06 Jul 2016, 08:23
Divyadisha wrote:
Bunuel wrote:
The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder of Y divided by 5?

A. 1.
B. 2.
C. 3.
D. 4.
E. 5.


X divided by 10 gives reminder of 2. X can be 2/12/22....

X+Y divided by 5 is 4. X+Y can be 4/ 9/ 19....

If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2

Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2

Hence the answer must be 2 (B)


Also....
x+y=5m+4 and x=10K+2
hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is B
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Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema  [#permalink]

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New post 05 Dec 2016, 03:52
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1
Bunuel wrote:
The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder of Y divided by 5?

A. 1.
B. 2.
C. 3.
D. 4.
E. 5.


\(X=10*n+2\)

\(\frac{X}{5} = \frac{10*n + 2}{5} = \frac{0 + 2}{5} = \frac{2}{5}\)

\(X\) will always give remainder 2 when divided by 5, hence to obtain the sum of remainders equal to 4 \(Y\)should bring remainder 2.

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Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema  [#permalink]

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New post 05 Dec 2016, 10:01
Bunuel wrote:
The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder of Y divided by 5?

A. 1.
B. 2.
C. 3.
D. 4.
E. 5.


Lest value of x is 12

Now, \(\frac{(X + Y)}{5}\) = Remainder 4

Or, \(\frac{(12 + Y)}{5}\) = Remainder 4

So, The least value of y = 12

Remainder of \(\frac{y}{5}\) is = 2

Hence, Correct answer will be (B) 2

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Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema  [#permalink]

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New post 06 Dec 2016, 12:15
Bunuel wrote:
The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder of Y divided by 5?

A. 1.
B. 2.
C. 3.
D. 4.
E. 5.


least possible value of x=2
least possible value of y=2
2/5 gives a remainder of 2
B
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The remainder when dividing the expression (X + Y) by 5 is 4. The rema  [#permalink]

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New post 10 Dec 2017, 04:47
Hi,

Is it possible to set the two expressions X + Y = 5Q + 4 & X = 10Q + 2, minus one from the other to get Y = -5Q + 2?

The remainder is therfore 2? Can anyone confirm if this method is incorrect?

Thanks
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The remainder when dividing the expression (X + Y) by 5 is 4. The rema  [#permalink]

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New post 10 Dec 2017, 11:44
Bunuel wrote:
The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder of Y divided by 5?

A. 1.
B. 2.
C. 3.
D. 4.
E. 5.


if X+Y=4, then X<4
if X/10 leaves a remainder of 2, then X=2
Y=(X+Y)-X=(4-2)=2
2/5 leaves a remainder of 2
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The remainder when dividing the expression (X + Y) by 5 is 4. The rema &nbs [#permalink] 10 Dec 2017, 11:44
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