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Retired Moderator B
Joined: 17 Sep 2013
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If x and y are both integers such that 41y = 36x and y is not negative  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 45% (01:41) correct 55% (01:44) wrong based on 214 sessions

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If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?

(i) x is prime
(ii) y is even
(iii) xy is positive

1. ii only
2. iii only
3. i and iii only
4. ii and iii only
5. i, ii and iii
Manager  Joined: 23 Oct 2014
Posts: 84
Concentration: Marketing
Re: If x and y are both integers such that 41y = 36x and y is not negative  [#permalink]

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Quote:
If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?

(i) x is prime
(ii) y is even
(iii) xy is positive

1. ii only
2. iii only
3. i and iii only
4. ii and iii only
5. i, ii and iii

I'm kind of excited. This is my very first post. Well, here goes nothing.

So the answer is A for the following reason.

41y = 36x

i. x doesn't have to be prime. x can be a multiple of 41. We can rule out option (i).
ii. Since 36x is going to be an even number no matter what x is 41y needs to be even itself. The only way for 41y to be even is if y is even itself. Keep in mind the number zero is an even integer as well. Option (ii) is true.
iii. This option states that y is not a negative number but it doesn't say that y isn't 0. If y is 0 then x is also 0. Option (iii) doesn't hold.

So there you have it.
Manager  Joined: 14 Aug 2014
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If x and y are both integers such that 41y = 36x and y is not negative  [#permalink]

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JusTLucK04 wrote:
If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?

(i) x is prime
(ii) y is even
(iii) xy is positive

1. ii only
2. iii only
3. i and iii only
4. ii and iii only
5. i, ii and iii

First of all; make sense of the question. Effectively y = 36x/41

(i) x is prime: now if y = 36x/41 and both x and y are integers; then if x= 41, 36(41)/41 .....so the 41s cancel each other out and you get x=36. Hunky dory. But if x = 82; you get y =72 which also works. Hence x isnt necessarily prime.

(ii) y is even: y = 36(41)/41 = 36 (even). Or try 36(82)/41 = 72 (even). When you multiply even with odd, answer is even. So Y HAS TO BE EVEN.

(iii) xy is positive. Hmm. So if y is positive, then x is positive. Because if you have a -ve value of x, it leads to -ve value of y. Hence I would say iii is the answer.

So I don't think B is the right answer....I still maintain it has got to be D. I don't understand how xy wouldnt be positive.

Any ideas?

Bassanio - hat tip. Nice response. I did think re the positive answers but I forgot the question itself (or misrememered it. Nice one. Aaah.)
Intern  Joined: 22 Feb 2014
Posts: 29
Re: If x and y are both integers such that 41y = 36x and y is not negative  [#permalink]

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humboldt wrote:
JusTLucK04 wrote:
If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?

(i) x is prime
(ii) y is even
(iii) xy is positive

1. ii only
2. iii only
3. i and iii only
4. ii and iii only
5. i, ii and iii

First of all; make sense of the question. Effectively y = 36x/41

(i) x is prime: now if y = 36x/41 and both x and y are integers; then if x= 41, 36(41)/41 .....so the 41s cancel each other out and you get x=36. Hunky dory. But if x = 82; you get y =72 which also works. Hence x isnt necessarily prime.

(ii) y is even: y = 36(41)/41 = 36 (even). Or try 36(82)/41 = 72 (even). When you multiply even with odd, answer is even. So Y HAS TO BE EVEN.

(iii) xy is positive. Hmm. So if y is positive, then x is positive. Because if you have a -ve value of x, it leads to -ve value of y. Hence I would say iii is the answer.

So I don't think B is the right answer....I still maintain it has got to be D. I don't understand how xy wouldnt be positive.

Any ideas?

Bassanio - hat tip. Nice response. I did think re the positive answers but I forgot the question itself (or misrememered it. Nice one. Aaah.)

Y is not negative means - Y = 0 or Y > 0 (Positive) - If Y = 0 ==> X = 0 and XY = 0; Y>0 then X >0 and XY>0; Which means XY >= 0. So, B is the right answer. iii can't be true. (this is a must be true question)
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If x and y are both integers such that 41y = 36x and y is not negative  [#permalink]

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JusTLucK04 wrote:
If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?

(i) x is prime
(ii) y is even
(iii) xy is positive

1. ii only
2. iii only
3. i and iii only
4. ii and iii only
5. i, ii and iii

Given:
1. x and y are both integers.
2. 41y = 36x
3. y is not negative i.e. y>= 0

Statement (i) x is prime
41y = 36x : y=36x/41
Now, x has to be divisible by Y; since Y is an integer and 36 is not divisible by 41
So, X is a multiple of 41 : X = 41 is prime and X = 41*2 is not prime
Hence, Statement 1 is not always true.

Statement (ii) y is even
From statement 1 we know that y=36X/41 = 2*2*3*3*X/41
Any number that is a multiple of an Even number is an Even Number
Statement 2 is always true

Statement (iii) xy is positive
We know that Y>=0
If Y = 0; then XY = 0 and 0 is neither +ve nor -ve
If y = any +ve integer; then XY is +ve
Hence Statement 3 is not always true

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Re: If x and y are both integers such that 41y = 36x and y is not negative  [#permalink]

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41 y = 36 x

(i) x is prime :
Not necessary : x can be 41k and y can be 36k

(ii) y is even:
as 36x is even, y has to be even... SO true

(iii) xy is positive
remember Y is a NON-NEGATIVE number that means it can be 0 or +ve
and 0 does not mean +ve so

ANS is A (ii) Only
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Re: If x and y are both integers such that 41y = 36x and y is not negative  [#permalink]

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JusTLucK04 wrote:
If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?

(i) x is prime
(ii) y is even
(iii) xy is positive

1. ii only
2. iii only
3. i and iii only
4. ii and iii only
5. i, ii and iii

Its a very good and tricky question... I also made a mistake while solving it...
So here the correct solution goes..

Firstly y is non -ve .. which means y>=0
41y = 36x
-> x = 41y/36

Statement i : Since x and y are integers, Y can attain values of 0,36, 72, 108, ..... and so on.
This gives values of x as 0,41, 82, 123 ....... so on.

So x is not prime..

Statement ii : Y can attain values of 0,36, 72, 108, ..... and so on. Y will always be a multiple of 36 and hence even..
So, y is even

Statement iii : FOr +ve values of Y is surely +ve...
Y can't have -ve values as per question.
But when y = 0 , x=0. So, xy=0
So, xy is not always positive....

So, option 1. ii only is correct.....
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Posts: 10011
Location: Pune, India
Re: If x and y are both integers such that 41y = 36x and y is not negative  [#permalink]

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JusTLucK04 wrote:
If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?

(i) x is prime
(ii) y is even
(iii) xy is positive

1. ii only
2. iii only
3. i and iii only
4. ii and iii only
5. i, ii and iii

So here is one learning moment - when you read "non negative", the first thing you must do is put that variable equal to 0.
So y = 0 is possible. This means x = 0 is also possible.

41y = 36x
Now since 41 is a prime number, x would be a multiple of 41.
Also, all factors of 36 would be in y so y would be a multiple of 36.

(i) x is prime
x could be 41 or 82 or 0 etc. This may not be true.

(ii) y is even
y is a multiple of 36. It must be even. This must be true.

(iii) xy is positive
x and y could be 0. So this may not be true.

_________________
Karishma
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Re: If x and y are both integers such that 41y = 36x and y is not negative  [#permalink]

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VeritasPrepKarishma wrote:
JusTLucK04 wrote:
If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?

(i) x is prime
(ii) y is even
(iii) xy is positive

1. ii only
2. iii only
3. i and iii only
4. ii and iii only
5. i, ii and iii

So here is one learning moment - when you read "non negative", the first thing you must do is put that variable equal to 0.
So y = 0 is possible. This means x = 0 is also possible.

41y = 36x
Now since 41 is a prime number, x would be a multiple of 41.
Also, all factors of 36 would be in y so y would be a multiple of 36.

(i) x is prime
x could be 41 or 82 or 0 etc. This may not be true.

(ii) y is even
y is a multiple of 36. It must be even. This must be true.

(iii) xy is positive
x and y could be 0. So this may not be true.

Yes Karishma, You are correct .. First we should put value 0 and then proceed for other solutions, So that we don't forget about 0. After all we are humans and we do mistakes . Mostly people do same mistakes. So to ace in GMAT, we must change our approach in solving problem and bring such process into practice..

Thanks for pointing this out.. VP  P
Joined: 24 Nov 2016
Posts: 1110
Location: United States
Re: If x and y are both integers such that 41y = 36x and y is not negative  [#permalink]

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JusTLucK04 wrote:
If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?

(i) x is prime
(ii) y is even
(iii) xy is positive

1. ii only
2. iii only
3. i and iii only
4. ii and iii only
5. i, ii and iii

y≠<0
41y=36x
y=36x/41

(i) x is prime: y=0=36x/41 x=0≠prime
(ii) y is even: y=even/odd=(even,fraction)=integer=even
(iii) xy is positive: (x,y)=0 xy=0≠positive

Ans (A) Re: If x and y are both integers such that 41y = 36x and y is not negative   [#permalink] 04 Dec 2019, 06:11
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