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# When the positive integer M is divided by the positive integer y, the

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Manager
Joined: 01 Sep 2016
Posts: 189
GMAT 1: 690 Q49 V35
When the positive integer M is divided by the positive integer y, the  [#permalink]

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17 Sep 2017, 09:46
1
6
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Difficulty:

95% (hard)

Question Stats:

38% (02:40) correct 62% (02:42) wrong based on 60 sessions

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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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Intern
Joined: 29 Jun 2014
Posts: 32
Re: When the positive integer M is divided by the positive integer y, the  [#permalink]

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17 Sep 2017, 10:13
Answer is A .1 2 3 :solution...M/y= 11 +z/y...z/y =9...So m = 11y + 9...choose y =1, 9,10

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Manager
Joined: 01 Sep 2016
Posts: 189
GMAT 1: 690 Q49 V35
Re: When the positive integer M is divided by the positive integer y, the  [#permalink]

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17 Sep 2017, 10:18
vishwajeet2015 wrote:
Answer is A .1 2 3 :solution...M/y= 11 +z/y...z/y =9...So m = 11y + 9...choose y =1, 9,10

Sent from my SM-A510F using GMAT Club Forum mobile app

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!
Current Student
Joined: 02 Jul 2017
Posts: 291
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
Re: When the positive integer M is divided by the positive integer y, the  [#permalink]

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17 Sep 2017, 10:58
2
2
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

Intern
Joined: 29 Jun 2014
Posts: 32
Re: When the positive integer M is divided by the positive integer y, the  [#permalink]

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17 Sep 2017, 11:04
[SMILING FACE WITH SMILING EYES]pretty sue wnt make dat mistake ever again...thnx a ton

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VP
Joined: 07 Dec 2014
Posts: 1222
Re: When the positive integer M is divided by the positive integer y, the  [#permalink]

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17 Sep 2017, 20:44
1
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
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Re: When the positive integer M is divided by the positive integer y, the  [#permalink]

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11 Feb 2019, 20:46
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Re: When the positive integer M is divided by the positive integer y, the   [#permalink] 11 Feb 2019, 20:46
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