Author 
Message 
TAGS:

Hide Tags

VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1083
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
09 Mar 2013, 13:06
1
This post received KUDOS
7
This post was BOOKMARKED
Question Stats:
52% (02:11) correct
48% (01:39) wrong based on 254 sessions
HideShow timer Statistics
If x and y are integers and 2 < x < y, does y = 16 ? (1) The GCF of X and Y is 2. (2) The LCM of X and Y is 48.
Official Answer and Stats are available only to registered users. Register/ Login.



VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1083
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: if x and y are integers and 2<x<y, does y =16 [#permalink]
Show Tags
09 Mar 2013, 13:09
I know that each statements are insufficient by itself. But i think Even taken together they are insufficient. We know that GCF*LCM = X*Y So X*Y = 96 Hence , when y = 24 , x =4 Similarly when y = 16 , x = 6 So i think both statements are insufficient taken together.
Archit



Math Expert
Joined: 02 Sep 2009
Posts: 39738

Re: if x and y are integers and 2<x<y, does y =16 [#permalink]
Show Tags
09 Mar 2013, 13:26



Manager
Joined: 29 Sep 2013
Posts: 52

Re: if x and y are integers and 2<x<y, does y =16 [#permalink]
Show Tags
19 Oct 2013, 20:07
Archit143 wrote: I know that each statements are insufficient by itself. But i think Even taken together they are insufficient. We know that GCF*LCM = X*Y So X*Y = 96 Hence , when y = 24 , x =4 Similarly when y = 16 , x = 6 So i think both statements are insufficient taken together.
Archit If GCF is 2 and LCM is 48, than the Pair of X and Y can be: X=2,Y=48 and X=6,Y=16 and X=16, Y=6 and X=48, Y=2 I think the answer is



Math Expert
Joined: 02 Sep 2009
Posts: 39738

Re: if x and y are integers and 2<x<y, does y =16 [#permalink]
Show Tags
20 Oct 2013, 04:36
suk1234 wrote: Archit143 wrote: I know that each statements are insufficient by itself. But i think Even taken together they are insufficient. We know that GCF*LCM = X*Y So X*Y = 96 Hence , when y = 24 , x =4 Similarly when y = 16 , x = 6 So i think both statements are insufficient taken together.
Archit If GCF is 2 and LCM is 48, than the Pair of X and Y can be: X=2,Y=48 and X=6,Y=16 and X=16, Y=6 and X=48, Y=2I think the answer is Please read the stem carefully. It's given that 2<x<y.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 31 Mar 2013
Posts: 72
Location: India
GPA: 3.02

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
05 Nov 2013, 03:15
I am not getting the right answer for some reason. Can you please tell me the set of numbers for which both the statements are satisfied?
thank you.



Math Expert
Joined: 02 Sep 2009
Posts: 39738

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
05 Nov 2013, 07:00



Manager
Joined: 31 Mar 2013
Posts: 72
Location: India
GPA: 3.02

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
05 Nov 2013, 07:13
Thanks Bunuel. But I am a but unclear still. Is there another set of numbers that satisfy both statements? Else answer should be C, no?



Math Expert
Joined: 02 Sep 2009
Posts: 39738

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
05 Nov 2013, 07:15



Manager
Joined: 31 Mar 2013
Posts: 72
Location: India
GPA: 3.02

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
05 Nov 2013, 07:18
My goodness. Thank you so much! I thought the answer was E and I was very confused. I saw the answer of some post and assumed it to be OA.



Intern
Joined: 29 May 2012
Posts: 12
Concentration: General Management, Finance
GPA: 3.49

If x and y are integers and 2 < x < y, does y = 16? [#permalink]
Show Tags
06 Nov 2013, 10:59
If x and y are integers and 2 < x < y, does y = 16? (1) The GCF of x and y is 2 (2) The LCM of x and y is 48
_________________
"When ideas get really complicated and the world gets complicated, its foolish to think that the person who's first can figure it all out"



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4132

Re: If x and y are integers and 2 < x < y, does y = 16? [#permalink]
Show Tags
06 Nov 2013, 19:05
3
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
accincognito wrote: If x and y are integers and 2 < x < y, does y = 16?
(1) The GCF of x and y is 2 (2) The LCM of x and y is 48 Dear accincognito, I'm happy to help. This is a hard problem! See this post for some insight: http://magoosh.com/gmat/2012/gmatmathfactors/Statement #1: The GCF of x and y is 2This leave open a wide array of possibilities. All we know is that x and y are two even numbers, both bigger than 2, with no common factors other than two: they could be x = 4, y = 6 x = 6, y = 8 x = 6, y = 10 x = 6, y = 16 So, it's possible for y to equal 16 or equal something else. This statement, alone and by itself, does not give us sufficient information, so it is insufficient. Statement #2: The LCM of x and y is 48Without any other information, we could have x = 3, y = 16 x = 4, y = 48 So, it's possible for y to equal 16 or equal something else. This statement, alone and by itself, does not give us sufficient information, so it is insufficient. Combined: this is where it gets interesting. The GCF of x and y is 2The LCM of x and y is 48This is a tricky combination. First, let's list all the factors of 48  in order to have a LCM of 48 with another number, each number must be a factor of 48. factors of 48 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48} Those are the possible candidates for x & y. We can eliminate 1 & 2, because x > 2, and we can eliminate 3, because that cannot have a GCF of 2 with anything else. Possibilities for x & y = {4, 6, 8, 12, 16, 24, 48} If y = 48, then every other number in the set is factor of 48, so the GCF would be the smaller number  e.g. the GCF of 6 and 48 is 6. Therefore, we can't use 48. If y = 24, then the first four numbers are factors of 24, so they don't work, and the GCF of 16 & 24 is 8. Therefore, we can't use 24. Possibilities for x & y = {4, 6, 8, 12, 16} Suppose y = 16 x = 4, y = 16 ===> GCF = 4, doesn't work x = 6, y = 16 ===> GCF = 2  this is one possible pair!! x = 8, y = 16 ===> GCF = 8, doesn't work x = 12, y = 16 ===> GCF = 4, doesn't work Suppose y = 8 x = 4, y = 8 ===> GCF = 4, doesn't work x = 6, y = 8 ===> GCF = 2, but LCM = 24, doesn't work Suppose y = 6 x = 4, y = 6 ===> GCF = 2, but LCM = 12, doesn't work So, after all that, the only pair that satisfies both statements is x = 6, y = 16, so it turns out, y does in fact equal 16. We are able to give a definitive answer to the prompt question, so the combined statements are sufficient. Answer = (C)Does all this make sense? Mike
_________________
Mike McGarry Magoosh Test Prep



Current Student
Joined: 06 Sep 2013
Posts: 1997
Concentration: Finance

Re: If x and y are integers and 2 < x < y, does y = 16? [#permalink]
Show Tags
31 Mar 2014, 08:20
1
This post received KUDOS
mikemcgarry wrote: accincognito wrote: If x and y are integers and 2 < x < y, does y = 16?
(1) The GCF of x and y is 2 (2) The LCM of x and y is 48 Dear accincognito, I'm happy to help. This is a hard problem! See this post for some insight: http://magoosh.com/gmat/2012/gmatmathfactors/Statement #1: The GCF of x and y is 2This leave open a wide array of possibilities. All we know is that x and y are two even numbers, both bigger than 2, with no common factors other than two: they could be x = 4, y = 6 x = 6, y = 8 x = 6, y = 10 x = 6, y = 16 So, it's possible for y to equal 16 or equal something else. This statement, alone and by itself, does not give us sufficient information, so it is insufficient. Statement #2: The LCM of x and y is 48Without any other information, we could have x = 3, y = 16 x = 4, y = 48 So, it's possible for y to equal 16 or equal something else. This statement, alone and by itself, does not give us sufficient information, so it is insufficient. Combined: this is where it gets interesting. The GCF of x and y is 2The LCM of x and y is 48This is a tricky combination. First, let's list all the factors of 48  in order to have a LCM of 48 with another number, each number must be a factor of 48. factors of 48 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48} Those are the possible candidates for x & y. We can eliminate 1 & 2, because x > 2, and we can eliminate 3, because that cannot have a GCF of 2 with anything else. Possibilities for x & y = {4, 6, 8, 12, 16, 24, 48} If y = 48, then every other number in the set is factor of 48, so the GCF would be the smaller number  e.g. the GCF of 6 and 48 is 6. Therefore, we can't use 48. If y = 24, then the first four numbers are factors of 24, so they don't work, and the GCF of 16 & 24 is 8. Therefore, we can't use 24. Possibilities for x & y = {4, 6, 8, 12, 16} Suppose y = 16 x = 4, y = 16 ===> GCF = 4, doesn't work x = 6, y = 16 ===> GCF = 2  this is one possible pair!! x = 8, y = 16 ===> GCF = 8, doesn't work x = 12, y = 16 ===> GCF = 4, doesn't work Suppose y = 8 x = 4, y = 8 ===> GCF = 4, doesn't work x = 6, y = 8 ===> GCF = 2, but LCM = 24, doesn't work Suppose y = 6 x = 4, y = 6 ===> GCF = 2, but LCM = 12, doesn't work So, after all that, the only pair that satisfies both statements is x = 6, y = 16, so it turns out, y does in fact equal 16. We are able to give a definitive answer to the prompt question, so the combined statements are sufficient. Answer = (C)Does all this make sense? Mike No need to test that many cases, let's see x,y are positive integers and 2<x<y. Is y=16? First statement GCF (x,y) is 2 Well we could have: x=4, y=6 answer is NO or x=6, y=16 answer is YES Hence insufficient Second Statement LCM (x,y) is 48 48 = 2^4 * 3 Now we can test cases here too: Either x=3 and y=2^4 when answer is YES OR x=7 y = 48 answer is NO Both together Since GCF =2 and LCM = 48 and since 2<x<y we can only have x=6, y=16 Hence C is the correct answer Please ask if anything remains unclear Cheers J



Current Student
Joined: 06 Sep 2013
Posts: 1997
Concentration: Finance

Re: If x and y are integers and 2 < x < y, does y = 16? [#permalink]
Show Tags
31 Mar 2014, 08:20
1
This post received KUDOS
Again @Mike, No need for all the fuzz, let's see x,y are positive integers and 2<x<y. Is y=16? First statement GCF (x,y) is 2 Well we could have: x=4, y=6 answer is NO or x=6, y=16 answer is YES Hence insufficient Second Statement LCM (x,y) is 48 48 = 2^4 * 3 Now we can test cases here too: Either x=3 and y=2^4 when answer is YES OR x=7 y = 48 answer is NO Both together Since GCF =2 and LCM = 48 and since 2<x<y we can only have x=6, y=16 Hence C is the correct answer Please ask if anything remains unclear Cheers J
Last edited by jlgdr on 29 May 2014, 07:18, edited 1 time in total.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7448
Location: Pune, India

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
01 Apr 2014, 20:57
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Archit143 wrote: If x and y are integers and 2 < x < y, does y = 16 ?
(1) The GCF of X and Y is 2. (2) The LCM of X and Y is 48. Given: 2 < X < Y Question: Does Y = 16? (1) The GCF of X and Y is 2. X = 2a; Y = 2b (a and b are co prime integers) Y may or may not be 16 e.g. X = 6, Y = 16 OR X = 6, Y = 8 etc (2) The LCM of X and Y is 48. \(48 = 2^4 * 3\) One of X and Y must have 2^4 = 16 as a factor and one must have 3 as a factor. Again, Y may or may not be 16 e.g. X = 6, Y = 16 OR X = 1, Y = 48 etc Using both together, X = 2a, Y = 2b. Since a and b need to be coprime and both X and Y need to be greater than 2, one of a and b must be 3 and the other must be 8 (since X and Y already have a 2 to make 16). X = 6, Y = 16 (since X is less than Y). Y must be 16. Answer (C)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



VP
Joined: 18 Sep 2014
Posts: 1205
Location: India

If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
10 Jan 2016, 09:24
If x and y are integers and \(2 < x < y\), does \(y = 16\) ? (1) The GCF of X and Y is 2. since we have many solutions such as \((6, 8)\), \((6,16)\), etc. we cannot say whether \(y=16\) or not. Statement 1 is insufficient. (2) The LCM of X and Y is 48.since we have many solutions such as \((16, 24)\), \((3,16)\), etc. we cannot say whether \(y=16\) or not. Statement 2 is insufficient.Combining 1 and 2, we know that \(LCM * GCF\)= product of the integers \(x * y\) so \(xy=96=2^5*3\) since GCF is 2, we know that both are even numbers indicating a single 2 in both x and y. Thereby we get values of \((x,y)\) as \((6, 16)\), \((8, 12)\) and \((4, 24).\) out of these 3 pairs only \((6,16)\) has \(LCM\) of \(48\). So \(y=16\) and thus \(C\) is the correct answer.
_________________
The only time you can lose is when you give up. Try hard and you will suceed. Thanks = Kudos. Kudos are appreciated
http://gmatclub.com/forum/rulesforpostinginverbalgmatforum134642.html When you post a question Pls. Provide its source & TAG your questions Avoid posting from unreliable sources.
My posts http://gmatclub.com/forum/beautyofcoordinategeometry213760.html#p1649924 http://gmatclub.com/forum/callingallmarchaprilgmattakerswhowanttocross213154.html http://gmatclub.com/forum/possessivepronouns200496.html http://gmatclub.com/forum/doublenegatives206717.html http://gmatclub.com/forum/thegreatestintegerfunction223595.html#p1721773 https://gmatclub.com/forum/improvereadinghabit233410.html#p1802265



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 3472
GPA: 3.82

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
11 Jan 2016, 17:52
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. If x and y are integers and 2 < x < y, does y = 16 ? (1) The GCF of X and Y is 2. (2) The LCM of X and Y is 48. In the original condition, there are 2 variables(x,y) and 1 equation(2<x<y), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1equation, which is likely to make D the answer. For 1), (x,y)=(4,6) > no, (x,y)=(6,16) > yes, which is not sufficient. For 2), (x,y)=(3,48) > no, (x,y)=(6,16) > yes, which is not sufficient. When 1) & 2), (x,y)=(6,16) > yes, which is sufficient. Therefore, the answer is C. For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Find a 10% off coupon code for GMAT Club members. “Receive 5 Math Questions & Solutions Daily” Unlimited Access to over 120 free video lessons  try it yourself See our Youtube demo



Intern
Joined: 06 Jul 2014
Posts: 3

LCM, GCF [#permalink]
Show Tags
11 Oct 2016, 05:36
If x and y are integers and 2<x<y, does y=16?
(1) The greatest common factor of x and y is 2. (2) The lowest common multiple of x and y is 48.



Math Expert
Joined: 02 Sep 2009
Posts: 39738

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
11 Oct 2016, 05:39



SVP
Joined: 05 Jul 2006
Posts: 1747

Re: If x and y are integers and 2 < x < y, does y = 16 ? [#permalink]
Show Tags
12 Oct 2016, 12:40
Archit143 wrote: If x and y are integers and 2 < x < y, does y = 16 ?
(1) The GCF of X and Y is 2. (2) The LCM of X and Y is 48. FROM 1 GCF is 2 ( common prime factor with the lowest power ) (x,y) could be (4, 28) , (6,10) (14,16) ... insuff from 2 LCM = (2^4 *3) ( factors unique to each integer * common prime factor to the largest power) ... insuff both since 2 is the GCF then one one of the 2 numbers has 2^1 and the other 2^4 and we need to know where the 3 factor belongs ( it only belongs to one of the two numbers since GCF is 2) . from stem 2<x<y , thus the smallest of x and y has to be bigger than 2^1 by the 3 factor , thus (x,y) = (6,16)




Re: If x and y are integers and 2 < x < y, does y = 16 ?
[#permalink]
12 Oct 2016, 12:40







