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When the positive integer M is divided by the positive integer y, the [#permalink]

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17 Sep 2017, 09:46

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When the positive integer M is divided by the positive integer y, the quotient is 11 and the remainder is z. When you divide z by y, the remainder is 9. Which of the following could be the value of M ?

1. 108 2. 119 3. 20 4. 30

A) 1, 2 and 3 b) 1 and 2 only c) 3 only d) 1, 2, 3 and 4 e) 2 only

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we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!

My friend that's wrong. You did the logic right, but missed an important fundamental. Do you want to give it another shot? Let me know and I ll post the explanation if you need. Thanks
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we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!

Re: When the positive integer M is divided by the positive integer y, the [#permalink]

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17 Sep 2017, 10:58

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Tricky one if we miss the basics. Find below detailed explanation

When the positive integer M is divided by the positive integer y, the quotient is 11 and the remainder is z. => \(M =11y+z\) => Here \(z < y\) (That's the case only then reminder can be z)

When you divide z by y, the remainder is 9. => as \(z < y\) and when z is divided by y remainder is 9 => \(z=9\)

So our equation is \(M =11y +9\) for \(z<y\)

Which of the following could be the value of M ? So lets write all the numbers in form of above equation. If it satisfies the equation than value can be equal to M So general steps for such kind of questions : Subtract 9 from number and see if its a multiple of 11. if condition satisfies then number can be value of M

1. 108 => 108 - 9 =99 so as 99 is multiple of 11 this can be our answer. Wrong Lets write it in equation form : 108 = 11*9 +9 . So if we compare it with M=11y + z => y=z=9 not possible as z<y always So this value is not M

2. 119 => 119 - 9 =110 so as 110 is multiple of 11 this can be our answer. Lets write it in equation form : 119 = 11*10 +9 . So if we compare it with M=11y + z => y=10 and z =9 => z<y satisfies our equation So this can be value of M

3. 20 => 20 - 9 =11 so as 11 is multiple of 11 this can be our answer. Wrong Lets write it in equation form : 20 = 11*1 +9 . So if we compare it with M=11y + z => y=1 and z =9 => z>y. This can't be true as by our equation z<y always So this value is not M

4. 30 => 30 -9 =21 This cant be written in multiple of 11. So this value is not M

A) 1, 2 and 3 b) 1 and 2 only c) 3 only d) 1, 2, 3 and 4 e) 2 only

Re: When the positive integer M is divided by the positive integer y, the [#permalink]

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17 Sep 2017, 20:44

bkpolymers1617 wrote:

When the positive integer M is divided by the positive integer y, the quotient is 11 and the remainder is z. When you divide z by y, the remainder is 9. Which of the following could be the value of M ?

1. 108 2. 119 3. 20 4. 30

A) 1, 2 and 3 b) 1 and 2 only c) 3 only d) 1, 2, 3 and 4 e) 2 only

if remainder is less than divisor, then y>9 let y=10 M=10*11=110+z only option>110 is 119 E