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

Question

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.

Nightfury14 · Accepted Answer

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.

Good luck
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hsbinfy · Answer

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

Divyadisha · Answer

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)

subho111 · Answer

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

vitaliyGMAT · Answer

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.

Abhishek009 · Answer

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

gracie · Answer

least possible value of x=2
least possible value of y=2
2/5 gives a remainder of 2
B

srchen · Answer

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

gracie · Answer

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

Asariol · Answer

I got the right answer. But am questioning my method. Can anyone confirm if this method is correct, if not, please explain why:

Solve for x:

x/10=k+2
x=10k+2
plug 1 in for k
x=12

Solve for y:
x+y/5=k+4
x+y=5k+4
plug in 1 for k
plug in 12 for x
12+y=9
y=-3

Plug in 3, not sure why, but I know to ignore the negative.
3/5=k+r
3=5k+r
plug in 1 for k
3=5+r
r=-2, again I know to ignore the negative

VeritasKarishma

KarishmaB · Answer

It is not correct. You cannot ignore the negative of the remainder. When the divisor is 5, a remainder of -2 is actually equal to a remainder of 3. (because 5 - 2 = 3) Check these posts first: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... unraveled/ https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/0 ... -the-gmat/ Now, think of it this way: x divided by 10 gives remainder 2. So x divided by 5 will give remainder 2 too. Since x + y give remainder 4 when divided by 5, and x gives remainder 2, when divided by 5, the other 2 must have come from y. Let me know if you need more help on divisibility and remainders concept.

MathRevolution · Answer

Remainder when dividing the expression (X + Y) by 5 is 4: (X + Y) = 5p + 4 => X + Y = 9 , 19, 29, 39, ....

Remainder of X divided by 10 is 2: X = 10q + 2 => X = 12, 22, 32, 42, ....

If X = 12 and X + Y is 19 then Y = 7.

7 divided by '5' will give the remainder '2'.

If X = 32 and X + Y is 39 then Y = 7.

7 divided by '5' will give the remainder '2'.

Answer B

Tonkotsu · Answer

I don't think you can, because the quotients (Q) are not equal to each other. However, the intuition on the remainder is the same. You're trying to make up for 4/5ths. So once you have part, you should be able to figure out the other part.

bumpbot · Answer

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

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