If x and y are both integers such that 41y = 36x and y is not negative

Question

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

BassanioGratiano · Accepted Answer

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.

humboldt · Answer

How interesting. Ok. So here's why the answer is the answer.

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.)

harshaiit · Answer

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)

Ashishmathew01081987 · Answer

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

Answer is A

sanket1991 · Answer

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

shashankism · Answer

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.....

KarishmaB · Answer

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.

Answer (A)

shashankism · Answer

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..

exc4libur · Answer

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)

MathRevolution · Answer

The relation holds when 41y = 36x

Case I: x = y = 0
Case II: x = 41 and y = 36 (41 * 36 = 36 * 41)

From Case I: 'x' is not prime, 'y' is even and xy is 0.
From Case II: 'x' is prime and 'y' is even and also xy is positive.

Therefore, in both cases, 'y' is even.

Only Option (ii) is true always.

Answer A

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If x and y are both integers such that 41y = 36x and y is not negative

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If x and y are both integers such that 41y = 36x and y is not negative

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