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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: 180
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, 08:46
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Difficulty:

95% (hard)

Question Stats:

43% (02:34) correct 57% (02:45) wrong based on 95 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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Joined: 02 Jul 2017
Posts: 268
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, 09:58
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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

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

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17 Sep 2017, 09:13
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: 180
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, 09:18
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
_________________
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!
Intern
Joined: 29 Jun 2014
Posts: 29
Re: When the positive integer M is divided by the positive integer y, the  [#permalink]

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17 Sep 2017, 10:04
[SMILING FACE WITH SMILING EYES]pretty sue wnt make dat mistake ever again...thnx a ton

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Joined: 07 Dec 2014
Posts: 1260
Re: When the positive integer M is divided by the positive integer y, the  [#permalink]

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17 Sep 2017, 19:44
1
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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20 Jun 2020, 12:29
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

Solution:

Since z is the remainder when M is divided by y, then z must be less than y. So when z is divided by y and the remainder is 9, it must mean z = 9 (because z/y = 0 R 9). Therefore, M = 11y + 9.

If M = 108, then solving 108 = 11y + 9 yields y = 9. However, 108 divided by 9 will not produce a quotient of 11 and a remainder of 9 (in fact, 108/9 = 12, so the quotient is 12 and the remainder is 0). Thus, M cannot equal 108.

If M = 119, then 119 = 11y + 9 and thus, y = 10. Dividing 9 by 10 produces a remainder of 9 (and a quotient of 0). We see that M could equal 119.

If M = 20, then 20 = 11y + 9 and thus, y = 1. However, 20 divided by 1 will not produce a quotient of 11 and a remainder of 9. Thus, M cannot equal 20.

Finally, if M = 30, then 30 = 11y + 9 does not even produce an integer value for y. Thus, M cannot equal 30 either.

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Re: When the positive integer M is divided by the positive integer y, the   [#permalink] 20 Jun 2020, 12:29