November 18, 2018 November 18, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 04 Jan 2012
Posts: 5
GPA: 3.97
WE: Analyst (Mutual Funds and Brokerage)

Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
22 Feb 2012, 06:33
Question Stats:
44% (02:16) correct 56% (01:54) wrong based on 259 sessions
HideShow timer Statistics
Is product 2*x*5*y an even integer? (1) 2 + x + 5 + y is an even integer (2) x  y is an odd integer I have a solution for this question but can't figure out how it was determined that y is an integer. Thanks!!
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 50623

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
22 Feb 2012, 07:26
omerrauf wrote: I dont get it. \(2\) is already being multiplied to the original number. so unless \(x\) and \(y\) is a fraction, let's say \(\frac{1}{2}\) then it could be odd, but as long as \(x\) and \(y\) are integers, there is no way this could be an odd number since it is being multiplied by \(2\). Now if we look at Statement A, it still does not tell us that \(x\) and \(y\) are integers or not. Since \(x\) could be \(\frac{1}{2}\) and \(y\) again could be \(\frac{1}{2}\) so A is obviously Insufficient. We cannot even establish if \(2*x*5*y\) is an integer, let alone it is even or not. And the presence of \(2\) is extremely misleading.
Now B says that \((x  y)\) is an odd integer. Let's suppose \(x=\frac{4}{3}\) and \(y=\frac{1}{3}\), then \((xy)=1\) which is an odd integer as it is supposed to be but that does not make \(2*x*5*y\) an even integer an integer at all. On the other hand let x=4 and y=3 than \((xy)=1\) which is again an odd integer so yes \(2*x*5*y\) is an even integer. Two different answers, Hence Insufficient.
Now if we combine A & B:
Statement A: \(2+x+5+y\)is \(even\) so \((x+y)+7\) is \(even\) so \((x+y)\) has to be odd Statement B: \(xy=odd\) which is basically just restating Statement A.
There is something wrong with the question. Do you have a source for this one? Is product 2*x*5*y an even integer?Notice that we are not told that x and y are integers. Question: \(2*x*5*y=even\). As there is 2 as a multiple, then this expression will be even if \(5xy=integer\). Basically we are asked is \(5xy=integer\) true? Note that \(x\) and \(y\) may not be integers for \(2*x*5*y\) to be even (example \(x=\frac{7}{9}\) and \(y=\frac{9}{7}\)) BUT if they are integers then \(2*x*5*y\) is even. (1) \(2+x+5+y=even\) > \(7+x+y=even\) > \(x+y=odd\). Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=1.7 answer NO) (2) \(xy=odd\). Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=0.3 answer NO) (1)+(2) Sum (1) and (2) \((x+y)+(xy)=odd_1+odd_2\) > \(2x=even\) > \(x=integer\) > \(y=integer\) > Both \(x\) and \(y\) are integers. Hence sufficient. Answer: C. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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
Status: Employed
Joined: 17 Nov 2011
Posts: 80
Location: Pakistan
Concentration: International Business, Marketing
GPA: 3.2
WE: Business Development (Internet and New Media)

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
22 Feb 2012, 07:04
I dont get it. \(2\) is already being multiplied to the original number. so unless \(x\) and \(y\) is a fraction, let's say \(\frac{1}{2}\) then it could be odd, but as long as \(x\) and \(y\) are integers, there is no way this could be an odd number since it is being multiplied by \(2\). Now if we look at Statement A, it still does not tell us that \(x\) and \(y\) are integers or not. Since \(x\) could be \(\frac{1}{2}\) and \(y\) again could be \(\frac{1}{2}\) so A is obviously Insufficient. We cannot even establish if \(2*x*5*y\) is an integer, let alone it is even or not. And the presence of \(2\) is extremely misleading. Now B says that \((x  y)\) is an odd integer. Let's suppose \(x=\frac{4}{3}\) and \(y=\frac{1}{3}\), then \((xy)=1\) which is an odd integer as it is supposed to be but that does not make \(2*x*5*y\) an even integer an integer at all. On the other hand let x=4 and y=3 than \((xy)=1\) which is again an odd integer so yes \(2*x*5*y\) is an even integer. Two different answers, Hence Insufficient. Now if we combine A & B: Statement A: \(2+x+5+y\)is \(even\) so \((x+y)+7\) is \(even\) so \((x+y)\) has to be oddStatement B: \(xy=odd\) which is basically just restating Statement A. There is something wrong with the question. Do you have a source for this one?
_________________
"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde



Manager
Status: Employed
Joined: 17 Nov 2011
Posts: 80
Location: Pakistan
Concentration: International Business, Marketing
GPA: 3.2
WE: Business Development (Internet and New Media)

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
22 Feb 2012, 07:30
Many thanks Bunuel. Had a hard time with this one !
_________________
"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde



Manager
Joined: 10 Jan 2010
Posts: 158
Location: Germany
Concentration: Strategy, General Management
GPA: 3
WE: Consulting (Telecommunications)

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
22 Feb 2012, 07:48
Is product 2*x*5*y an even integer?
1. 2 + x + 5 + y is an even integer 2. x  y is an odd integer
1. 7 + x + y = even (7+1+2 satisfy the statement, 7+2.5+0.5 satisfy the statement as well > not sufficient) 2. x  y = odd (52 = odd and 5.52.5 = odd > not sufficient)
Together: (x+y)+(xy) = odd + odd > 2x = even 2x can only be even if x is an integer, thus y must be an integer too
"C"



Intern
Joined: 17 Jan 2012
Posts: 41

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
24 Feb 2012, 10:18
Bunuel wrote: omerrauf wrote: I dont get it. \(2\) is already being multiplied to the original number. so unless \(x\) and \(y\) is a fraction, let's say \(\frac{1}{2}\) then it could be odd, but as long as \(x\) and \(y\) are integers, there is no way this could be an odd number since it is being multiplied by \(2\). Now if we look at Statement A, it still does not tell us that \(x\) and \(y\) are integers or not. Since \(x\) could be \(\frac{1}{2}\) and \(y\) again could be \(\frac{1}{2}\) so A is obviously Insufficient. We cannot even establish if \(2*x*5*y\) is an integer, let alone it is even or not. And the presence of \(2\) is extremely misleading.
Now B says that \((x  y)\) is an odd integer. Let's suppose \(x=\frac{4}{3}\) and \(y=\frac{1}{3}\), then \((xy)=1\) which is an odd integer as it is supposed to be but that does not make \(2*x*5*y\) an even integer an integer at all. On the other hand let x=4 and y=3 than \((xy)=1\) which is again an odd integer so yes \(2*x*5*y\) is an even integer. Two different answers, Hence Insufficient.
Now if we combine A & B:
Statement A: \(2+x+5+y\)is \(even\) so \((x+y)+7\) is \(even\) so \((x+y)\) has to be odd Statement B: \(xy=odd\) which is basically just restating Statement A.
There is something wrong with the question. Do you have a source for this one? Is product 2*x*5*y an even integer?Notice that we are not told that x and y are integers. Question: \(2*x*5*y=even\). As there is 2 as a multiple, then this expression will be even if \(5xy=integer\). Basically we are asked is \(5xy=integer\) true? Note that \(x\) and \(y\) may not be integers for \(2*x*5*y\) to be even (example \(x=\frac{7}{9}\) and \(y=\frac{9}{7}\)) BUT if they are integers then \(2*x*5*y\) is even. (1) \(2+x+5+y=even\) > \(7+x+y=even\) > \(x+y=odd\). Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=1.7 answer NO) (2) \(xy=odd\). Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=0.3 answer NO) (1)+(2) Sum (1) and (2) \((x+y)+(xy)=odd_1+odd_2\) > \(2x=even\) > \(x=integer\) > \(y=integer\) > Both \(x\) and \(y\) are integers. Hence sufficient. Answer: C. Hope it's clear. A real tricky question and an awesome explanation. Thanks



Intern
Joined: 11 Feb 2012
Posts: 2

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
20 Mar 2012, 07:24
What if x or y=0. Zero is not an even or an odd integer, then what? I suspect the answer should be E. Can anybody comment on this?



Math Expert
Joined: 02 Sep 2009
Posts: 50623

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
20 Mar 2012, 07:31



Intern
Joined: 11 Feb 2012
Posts: 2

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
20 Mar 2012, 07:35
Bunuel wrote: liyasecret wrote: What if x or y=0. Zero is not an even or an odd integer, then what? I suspect the answer should be E. Can anybody comment on this? Welcome to GMAT Club. Below is an answer to your question. Zero is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder, so since 0/2=0=integer then zero is even. Hope it helps. Thanks a lot, Bunuel. It is clear now.



Intern
Joined: 17 Jan 2013
Posts: 45
Location: India

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
26 Feb 2013, 23:18
i knw its a silly question to ask but can anybody pls explain: 2x can only be even if x is an integer,?? what if x is a value like .7.. then 2x is 1.4.. which is even i assume.. or is it not?? any help would be highly appreciated!!!



Math Expert
Joined: 02 Sep 2009
Posts: 50623

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
27 Feb 2013, 01:01



Intern
Joined: 17 Jan 2013
Posts: 45
Location: India

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
27 Feb 2013, 02:46
Ohhhh yeaahh Bunuel! ****.. what a silly question that was in real .. damn! yet did anyone tell u, you rock?!!! thanks alot



Senior Manager
Joined: 03 Sep 2012
Posts: 382
Location: United States
Concentration: Healthcare, Strategy
GPA: 3.88
WE: Medicine and Health (Health Care)

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
16 Mar 2013, 23:05
No matter what the value of x and y is (as long as it is an integer) the product will always be an Even number , therefore what this question is asking essentially is whether x and y are integers.. Statement (1) : Simplified we get, x+y = Odd Integer... This is satisfied by x being 2.5 and y being 0.5 , therefore we are not certain whether x and y are integers .. Not Suff. Statement (2) : x  y = odd integer, this again is satisfied with 3.5 (x)  0.5 (y) .. therefore is also insuff. Combining 1 and 2, and lining them up we get, 2x = Odd int + Odd Int , or 2x = even integer (odd Integer + Odd integer is always an even integer) . Solving further we now know that X is an integer (Even integer divided by 2 is always an integer) .. Similarly substituting this information in any one of the 2 equations we can verify that y is also an integer. Therefore the Answer is C... Hope this helps..
_________________
"When you want to succeed as bad as you want to breathe, then you’ll be successful.”  Eric Thomas



Manager
Joined: 14 Aug 2005
Posts: 74

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
18 Mar 2013, 12:10
vomhorizon wrote: No matter what the value of x and y is (as long as it is an integer) the product will always be an Even number , therefore what this question is asking essentially is whether x and y are integers..
Statement (1) : Simplified we get, x+y = Odd Integer... This is satisfied by x being 2.5 and y being 0.5 , therefore we are not certain whether x and y are integers .. Not Suff.
Statement (2) : x  y = odd integer, this again is satisfied with 3.5 (x)  0.5 (y) .. therefore is also insuff.
Combining 1 and 2, and lining them up we get, 2x = Odd int + Odd Int , or 2x = even integer (odd Integer + Odd integer is always an even integer) . Solving further we now know that X is an integer (Even integer divided by 2 is always an integer) .. Similarly substituting this information in any one of the 2 equations we can verify that y is also an integer.
Therefore the Answer is C...
Hope this helps.. Great explanation!
_________________
One Last Shot



VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1085
Location: India
Concentration: Operations, Marketing
GPA: 3.4
WE: Engineering (Manufacturing)

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
07 Jun 2017, 09:29
Imo C Taking both decimal and integers we can arrive at the solution. Sent from my ONE E1003 using GMAT Club Forum mobile app
_________________
Please give kudos if you found my answers useful



Intern
Joined: 16 Aug 2018
Posts: 29
Concentration: General Management, Strategy

Re: Is product 2*x*5*y an even integer?
[#permalink]
Show Tags
19 Aug 2018, 18:01
i really doubt that GMAT will test on questions like this. most of the even,odd questions are restricted to integers.




Re: Is product 2*x*5*y an even integer? &nbs
[#permalink]
19 Aug 2018, 18:01






