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When x is divided by 2, remainder is 1 and y is divided by 8, remainde

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fattty
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When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   18 Jan 2016, 22:32
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When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14
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C
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davedekoos
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   19 Jan 2016, 13:17
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fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14



When dealing with remainders and equations, it is often helpful to translate the words into formulas.

"When x is divided by 2, remainder is 1" --> This means that x is 1 more than a multiple of 2 --> \(x = 2a+1\), where \(a\) is an integer.
"y is divided by 8, remainder is 2" --> This means that y is 2 more than a multiple of 8 --> \(y = 8b+2\), where \(b\) is an integer.

Now if we plug those expressions into 2x + y we get:

\(2x + y = [2(2a+1)] + [8b+2]\)
\(= 4a+2 + 8b+2\)
\(= 4(a+2b+1)\)

So 2x + y = 4*(some integer), and is therefore a multiple of 4. The only answer choice that is a multiple of 4 is C) 12.

Answer: C
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KarishmaB
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   18 Jan 2016, 22:39
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fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10 B) 11 C) 12 D) 13 E) 14


Use some quick logic to eliminate the options:

"When x is divided by 2, remainder is 1" - means x is odd

"y is divided by 8, remainder is 2" - y is not divisible by 8. It could be 2, 10, 18... (all even numbers)

2x + y -> x is odd but 2x will be even. y is even. So 2x+y will be even. Options (B) and (E) are out.

Consider (A) 10 - y can be 2 but then x will be 4 (even); y can be 10 but then x will be 0(even) - Not possible
Consider (C) 12 - y can be 2 then x will be 5 (odd) - Works

Answer (C)
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   22 Feb 2016, 10:02
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I got it in 1 min by:
X=2a+1..i
Y=8b+2...ii

we want 2X+Y
Multiply eqi by 2
2X=4a+2 And we have Y=8b+2
add both
2X+Y=4(a+2b)+4
only c option is divisible by 4..hence the answer.
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When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   18 Jan 2016, 23:20
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fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14


Hi,

Apart from the method stated above..
lesser error prone way would be
1) if x is divided by 2, the remainder is 1, that is x is odd.
So, 2x will be a multiple of 2 but not 4, that is 2x = 2(2a+1) = 4a+2.

2) now if y divided by 8 leaves a remainder 2, y when divided by 4 will also give a remainder of 2.., that is y=8b+2=4(2b)+2=4c+2.
so if 2x+y is divided by 4, it should give us a remainder of 2+2=4, meaning 2x+y should be div by 4..
only C fits in
OR
2x+y=4a+2+4c+2=4a+4c +4 or a multiple of 4.
C
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   19 Jan 2016, 13:01
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hari1985 wrote:

Hi Karishma,

We know 2 is not divisible by 8. But it does not satisfy the condition stated in the question "y is divided by 8 remainder is 2"?
I could not connect why you have chosen y as 2. Can you please help me in understanding it?



Hi Hari,

2 is a valid choice for y because when you divide 2 by 8, the answer is 0 with remainder 2.

In general, any time you divide a smaller integer by a larger integer, the result will be 0 with the remainder equal to the smaller number. If integer \(a\) is smaller than integer \(b\), then \(\frac{a}{b}\) = 0 with remainder \(a\).

I hope that helps!

Cheers,
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   07 Sep 2018, 20:22
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Probus wrote:
chetan2u wrote:
fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14


Hi,

Apart from the method stated above..
lesser error prone way would be
1) if x is divided by 2, the remainder is 1, that is x is odd..
if the same x multiplied by 2, ( 2x), and divided by 4 will give a remainder 2..

[b]now if y divided by 8 leaves a remainder 2, y when divided by 4 will also give a remainder of 2..[/b]
so if 2x+y is divided by 4, it should give us a remainder of 2+2=4, meaning 2x+y should be div by 4..
only C fits in
C


Hi chetan2u,
Can you explain me property for the highlited portion. I get that when 18/8 reminder is 2 and 18/ 4 reminder is 2 but can you explain me logic behind the same.

Probus



1) If x is divided by 2, the remainder is 1 so X=2k+1..
Then 2x=2(2k+1)=4k+2
So when 4k+2 is divided by 4, remainder is 2

2)if y divided by 8 leaves a remainder 2.
So y = 8k+2..
Thus dividing by 4, (8k+2)/4
8k is divisible by 4, therefore remainder is 2

Thus 2x+4 will leave the same remainder as Remainder when 2x divided by 4 + Remainder when y is divided by 4...=> 2+2=4 that is it remainder is div by 4..

In choices only 12 is div by 4, hence C
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   19 Jan 2016, 12:37
VeritasPrepKarishma wrote:
fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10 B) 11 C) 12 D) 13 E) 14


Use some quick logic to eliminate the options:

"When x is divided by 2, remainder is 1" - means x is odd

"y is divided by 8, remainder is 2" - y is not divisible by 8. It could be 2, 10, 18... (all even numbers)

2x + y -> x is odd but 2x will be even. y is even. So 2x+y will be even. Options (B) and (E) are out.

Consider (A) 10 - y can be 2 but then x will be 4 (even); y can be 10 but then x will be 0(even) - Not possible
Consider (C) 12 - y can be 2 then x will be 5 (odd) - Works

Answer (C)



Hi Karishma,

We know 2 is not divisible by 8. But it does not satisfy the condition stated in the question "y is divided by 8 remainder is 2"?
I could not connect why you have chosen y as 2. Can you please help me in understanding it?
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When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   25 Feb 2016, 04:00
fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14


I had to go back to the good old number testing method for this
\(2x + y\)
pick numbers for x and y that fulfils the conditions given.
2(3) + 2
6 + 2
8. Not in the option! :(

raise x to the next level
2(5) + 2
10 + 2
12
That's in the option! :-D :-D :-D
Defnily their CANNOT be more than one possible value for \(2x + y\) in the options.
C.
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   07 Sep 2018, 12:33
chetan2u wrote:
fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14


Hi,

Apart from the method stated above..
lesser error prone way would be
1) if x is divided by 2, the remainder is 1, that is x is odd..
if the same x multiplied by 2, ( 2x), and divided by 4 will give a remainder 2..

[b]now if y divided by 8 leaves a remainder 2, y when divided by 4 will also give a remainder of 2..[/b]
so if 2x+y is divided by 4, it should give us a remainder of 2+2=4, meaning 2x+y should be div by 4..
only C fits in
C


Hi chetan2u,
Can you explain me property for the highlited portion. I get that when 18/8 reminder is 2 and 18/ 4 reminder is 2 but can you explain me logic behind the same.

Probus
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   07 Sep 2018, 12:54
fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14


next to least value of x=5
least value of y=2
2*5+2=12
C
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   12 Aug 2022, 06:46
fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14


X= 2a+1 , Y= 8b+2
now,

2X = 4a +2 if a=b=1

2X= 6 , Y=10
2X+Y= 16.
What is wrong in this approach?
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   12 Aug 2022, 07:01
Expert Reply
SolankiDas wrote:
fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14


X= 2a+1 , Y= 8b+2
now,

2X = 4a +2 if a=b=1

2X= 6 , Y=10
2X+Y= 16.
What is wrong in this approach?


There is nothing wrong. But this is COULD BE question means there can be various values.
We know that the answer will be multiple of 4, so 16 will also fit in, but in the given values only 12 will fit in.
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   05 Nov 2022, 11:41
I picked X=9 and Y= 10, which both satisfies the question. 2X+Y= 28, then I looked for answer choice which is multiple of 28, so I chose e. Would you pls explain what is my mistake?
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink] New post   20 Dec 2023, 08:16
fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)


A) 10
B) 11
C) 12
D) 13
E) 14

Minimum possible value possible value of x = 1 as 1/2 , Rem = 1
Minimum possible value possible value of y = 2 as 1/8 , Rem = 2

So, 2x + y = 2*1 + 1 => 3

Thus, the final answer must be a multiple of 3, among the options only (C) fits in perfectly, Answer must be (C)
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink]
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