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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

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

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..

now if y divided by 8 leaves a remainder 2, y when divided by 4 will also give a remainder of 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 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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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?

Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink]

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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 \(a\).

Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink]

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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:

When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink]

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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! Defnily their CANNOT be more than one possible value for \(2x + y\) in the options. C.

Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde [#permalink]

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