Apr 20 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score. Apr 20 10:00 PM PDT  11:00 PM PDT The Easter Bunny brings … the first day of school?? Yes! Now is the time to start studying for the GMAT if you’re planning to apply to Round 1 of fall MBA programs. Get a special discount with the Easter sale! Apr 21 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Apr 21 10:00 PM PDT  11:00 PM PDT $84 + an extra $10 off for the first month of EMPOWERgmat access. Train to be ready for Round 3 Deadlines with EMPOWERgmat's Score Booster. Ends April 21st Code: GCENHANCED Apr 22 08:00 AM PDT  09:00 AM PDT What people who reach the high 700's do differently? We're going to share insights, tips, and strategies from data we collected on over 50,000 students who used examPAL. Save your spot today! Apr 23 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, April 23rd at 8 pm ET Apr 24 08:00 PM EDT  09:00 PM EDT Maximize Your Potential: 5 Steps to Getting Your Dream MBA Part 3 of 5: Key TestTaking Strategies for GMAT. Wednesday, April 24th at 8 pm ET
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54369

If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
17 Feb 2016, 03:13
Question Stats:
85% (00:36) correct 15% (01:00) wrong based on 144 sessions
HideShow timer Statistics
If P, Q, R, and S are all integers, is product PQRS even? (1) PQ = 42 (2) RS = 35 Kudos for correct solution.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Manager
Joined: 24 Jul 2014
Posts: 90
Location: India
WE: Information Technology (Computer Software)

Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
17 Feb 2016, 20:33
BunuelI have a little doubt here. Since the question stem says is Product PQRS even? Case 1:Shall I assume PQ and RS as product of two numbers ? orCase 2:Shall I assume PQ and RS as two different two digit number? However , If I conceder both the cases , answer can be found Case 1: (1) PQ = 42. since product is even , that means either P or Q is Even. Now multiply this product with anything it will stay even. Hence sufficient (2) RS = 35. Since product is odd , that means both R and S are odd. No that we do not know What is P or Q , we can not infer the final product. Hence Insufficient Answer is (A) Now Case 2: (1) PQ = 42 . P=4 Q=2. Both are even. so their product is also even.Now multiply this product with anything it will stay even. Hence sufficient (2) RS = 35 . R=3 S=5. Both are odd. so their product is also odd.No that we do not know What is P or Q , we can not infer the final product. Hence Insufficient Answer is (A)
_________________
The Mind ~ Muscle Connection My GMAT Journey is Complete.Going to start the MBA in Information Management from 2016 Good Luck everyone.



Math Expert
Joined: 02 Aug 2009
Posts: 7556

Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
17 Feb 2016, 20:43
tryambaks wrote: BunuelI have a little doubt here. Since the question stem says is Product PQRS even? Case 1:Shall I assume PQ and RS as product of two numbers ? orCase 2:Shall I assume PQ and RS as two different two digit number? However , If I conceder both the cases , answer can be found Case 1: (1) PQ = 42. since product is even , that means either P or Q is Even. Now multiply this product with anything it will stay even. Hence sufficient (2) RS = 35. Since product is odd , that means both R and S are odd. No that we do not know What is P or Q , we can not infer the final product. Hence Insufficient Answer is (A) Now Case 2: (1) PQ = 42 . P=4 Q=2. Both are even. so their product is also even.Now multiply this product with anything it will stay even. Hence sufficient (2) RS = 35 . R=3 S=5. Both are odd. so their product is also odd.No that we do not know What is P or Q , we can not infer the final product. Hence Insufficient Answer is (A) Hi, you should take this as CASE I, because of three reasons.. 1) PQRS is written in the same way and has been told in teh Q to be a product.. 2) secondly, P,Q,R,S are all given as integer and not digit, so we cannot take them as digits. 3) If PQ were a two digit number, it would be mentioned as PQ is a two digit number..
_________________



Manager
Joined: 17 Nov 2014
Posts: 51
Location: India

Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
18 Feb 2016, 08:25
PQRS is even implies atleast one of the integer must be even. Simplified question form is any one of the P,Q,R,S is even ? Option 1 given PQ is 42 it implies atleast one of them is even integer. So.A Option 2: RS is 35, 35 is odd so both R,S are odd we have no information about PQ so B is non.conclusive Final answer A



Manager
Status: Build your own dreams,Otherwise some one else will hire you to build there's.
Joined: 30 Apr 2015
Posts: 87
Location: India
Concentration: Finance
GMAT 1: 590 Q45 V26 GMAT 2: 660 Q47 V34
GPA: 3.68

If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
Updated on: 23 Feb 2016, 06:58
We have to find out if P*Q*R*S =X is even? any thing multiplied by even is even. Even if one of the combination is even then result will be even From A X=42RS i.e X will be even no matter what. Now this is true only because we are given that all the numbers are integers. We can not get anything from B
_________________
"Follow your heart and realize that your dream is a dream for a reason" Dori Roberts
Originally posted by mahakmalik on 19 Feb 2016, 00:01.
Last edited by mahakmalik on 23 Feb 2016, 06:58, edited 1 time in total.



Senior Manager
Joined: 20 Aug 2015
Posts: 388
Location: India

Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
23 Feb 2016, 06:16
Bunuel wrote: If P, Q, R, and S are all integers, is product PQRS even?
(1) PQ = 42 (2) RS = 35
Kudos for correct solution. Given: P, Q, R, and S are all integers Required: Is PQRS even? Statement 1: PQ = 42 We know that PQ = 42. Hence atleast one of P or Q is even. Therefore the product PQRS will also have an even number and will be even. SUFFICIENT Statement 2: RS = 35 We know nothing about P and Q. If one of P or Q is even, then PQRS would be even If none of P or Q is even, then PQRS will be odd INSUFFICIENT Option A



Intern
Joined: 01 Feb 2016
Posts: 9
Location: Viet Nam
GMAT 1: 500 Q49 V15 GMAT 2: 680 Q49 V34
WE: Real Estate (Real Estate)

Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
23 Feb 2016, 09:53
1,PQ=42 = 2*21. PQRS=2*21*RS > Even > SUFFICIENT 2,RS= 35. We dont know PQ and RS is odd > cant conclude the product is even or odd since we dont know about PQ > Insufficient
> Answer A



Intern
Joined: 01 Feb 2016
Posts: 9
Location: Viet Nam
GMAT 1: 500 Q49 V15 GMAT 2: 680 Q49 V34
WE: Real Estate (Real Estate)

Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
23 Feb 2016, 09:54
1,PQ=42 = 2*21. PQRS=2*21*RS > Even > SUFFICIENT 2,RS= 35. We dont know PQ and RS is odd > cant conclude the product is even or odd since we dont know about PQ > Insufficient
> Answer A



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7224
GPA: 3.82

Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
23 Feb 2016, 19:03
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 P, Q, R, and S are all integers, is product PQRS even? (1) PQ = 42 (2) RS = 35 When you modify the original condition and the question, they become even*odd=even. If a question asks if multiplication is even, an even condition is usually an answer. Thus, in 1), PQ=42, which is always an even number. So, PQRS is always an even number as well, which is sufficient. Thus, A is the answer. Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $149 for 3 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 01 Feb 2016
Posts: 9
Location: Viet Nam
GMAT 1: 500 Q49 V15 GMAT 2: 680 Q49 V34
WE: Real Estate (Real Estate)

Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
24 Feb 2016, 10:14
Thank you very much



Current Student
Joined: 13 Nov 2014
Posts: 10
Location: United States (FL)
Concentration: Leadership, Marketing
GPA: 3.93
WE: Engineering (Energy and Utilities)

Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
18 Aug 2017, 13:09
Even if we are given PQ is even, R or S could be 0 (0 is also an integer). In that case, product of PQRS will be 0, which is not even.



Retired Moderator
Joined: 19 Mar 2014
Posts: 931
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5

Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
Show Tags
18 Aug 2017, 14:04
rambani87 wrote: Even if we are given PQ is even, R or S could be 0 (0 is also an integer). In that case, product of PQRS will be 0, which is not even. Hello rambani87  ZERO is indeed an EVEN numberCheck out  GMAT Club Quant book  Page No. 3 Hope this helps!
Attachments
Zero.PNG [ 37.14 KiB  Viewed 1628 times ]
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."
Best AWA Template: https://gmatclub.com/forum/howtoget60awamyguide64327.html#p470475




Re: If P, Q, R, and S are all integers, is product PQRS even?
[#permalink]
18 Aug 2017, 14:04






