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Manager  G
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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1
6 00:00

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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we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
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Intern  B
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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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  G
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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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!
Current Student P
Joined: 02 Jul 2017
Posts: 289
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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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  B
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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[SMILING FACE WITH SMILING EYES]pretty sue wnt make dat mistake ever again...thnx a ton

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VP  P
Joined: 07 Dec 2014
Posts: 1224
Re: When the positive integer M is divided by the positive integer y, the  [#permalink]

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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
Non-Human User Joined: 09 Sep 2013
Posts: 13412
Re: When the positive integer M is divided by the positive integer y, the  [#permalink]

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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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