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When x is divided by 2, remainder is 1 and y is divided by 8, remainde
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18 Jan 2016, 21:32
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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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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde
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19 Jan 2016, 12:17
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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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde
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18 Jan 2016, 21:39
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
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18 Jan 2016, 22:20
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..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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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde
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19 Jan 2016, 11:37
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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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde
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19 Jan 2016, 12:01
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
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22 Feb 2016, 09:02
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
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25 Feb 2016, 03:00
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.



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Re: When x is divided by 2, remainder is 1 and y is divided by 8, remainde
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07 Sep 2018, 11:33
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
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07 Sep 2018, 11:54
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
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07 Sep 2018, 19:22
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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1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
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