Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 17 Sep 2013
Posts: 316
Concentration: Strategy, General Management
WE: Analyst (Consulting)

If x and y are both integers such that 41y = 36x and y is not negative
[#permalink]
Show Tags
31 Oct 2014, 14:29
Question Stats:
45% (01:41) correct 55% (01:44) wrong based on 214 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.



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]
Show Tags
31 Oct 2014, 15:44
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
Posts: 75

If x and y are both integers such that 41y = 36x and y is not negative
[#permalink]
Show Tags
31 Oct 2014, 15:51
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 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.)



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]
Show Tags
31 Oct 2014, 17:42
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 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.) 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)



Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 105
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)

If x and y are both integers such that 41y = 36x and y is not negative
[#permalink]
Show Tags
31 Oct 2014, 21:46
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 trueAnswer is A



Manager
Joined: 14 Sep 2014
Posts: 86
WE: Engineering (Consulting)

Re: If x and y are both integers such that 41y = 36x and y is not negative
[#permalink]
Show Tags
06 Dec 2014, 06:51
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 NONNEGATIVE number that means it can be 0 or +ve and 0 does not mean +ve so
ANS is A (ii) Only



Director
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 725
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: If x and y are both integers such that 41y = 36x and y is not negative
[#permalink]
Show Tags
12 May 2017, 03:45
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 evenStatement 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.....



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10027
Location: Pune, India

Re: If x and y are both integers such that 41y = 36x and y is not negative
[#permalink]
Show Tags
12 May 2017, 05:13
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. Answer (A)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Director
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 725
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: If x and y are both integers such that 41y = 36x and y is not negative
[#permalink]
Show Tags
12 May 2017, 06:26
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. Answer (A) 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
Joined: 24 Nov 2016
Posts: 1139
Location: United States

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






