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

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Math Expert
Joined: 02 Sep 2009
Posts: 44636
The remainder when dividing the expression (X + Y) by 5 is 4. The rema [#permalink]

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05 Jul 2016, 12:26
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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.
[Reveal] Spoiler: OA

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Joined: 13 Sep 2015
Posts: 165
Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema [#permalink]

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05 Jul 2016, 13:10
1
KUDOS
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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Senior Manager
Joined: 02 Mar 2012
Posts: 344
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Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema [#permalink]

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05 Jul 2016, 22:48
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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Location: United States
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Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema [#permalink]

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06 Jul 2016, 06:16
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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Intern
Joined: 06 Jun 2016
Posts: 1
Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema [#permalink]

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06 Jul 2016, 09:23
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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Joined: 13 Oct 2016
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Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema [#permalink]

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05 Dec 2016, 04:52
2
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BOOKMARKED
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.

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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05 Dec 2016, 11:01
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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Director
Joined: 07 Dec 2014
Posts: 965
Re: The remainder when dividing the expression (X + Y) by 5 is 4. The rema [#permalink]

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06 Dec 2016, 13:15
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
Intern
Joined: 04 Aug 2016
Posts: 4
The remainder when dividing the expression (X + Y) by 5 is 4. The rema [#permalink]

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10 Dec 2017, 05:47
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
Director
Joined: 07 Dec 2014
Posts: 965
The remainder when dividing the expression (X + Y) by 5 is 4. The rema [#permalink]

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10 Dec 2017, 12:44
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
B
The remainder when dividing the expression (X + Y) by 5 is 4. The rema   [#permalink] 10 Dec 2017, 12:44
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