Mar 27 03:00 PM PDT  04:00 PM PDT Join a free live webinar and learn the winning strategy for a 700+ score on GMAT & the perfect application. Save your spot today! Wednesday, March 27th at 3 pm PST Mar 29 06:00 PM PDT  07:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Mar 29 10:00 PM PDT  11:00 PM PDT Right now, their GMAT prep, GRE prep, and MBA admissions consulting services are up to $1,100 off. GMAT (Save up to $261): SPRINGEXTRAGMAT GRE Prep (Save up to $149): SPRINGEXTRAGRE MBA (Save up to $1,240): SPRINGEXTRAMBA Mar 30 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Mar 31 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Apr 01 08:00 PM EDT  09:30 PM EDT Here are some of the 2 of the questions we will cover. Do the GRE and GMAT test different content? How do business schools perceive the GRE vs. the GMAT? Apr 04 03:00 PM PDT  04:00 PM PDT Join a free live webinar and learn the winning study plan for your GMAT test. Save your spot today!
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 15 Dec 2015
Posts: 115
GPA: 4
WE: Information Technology (Computer Software)

If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
Updated on: 10 Oct 2018, 06:12
Question Stats:
52% (02:42) correct 48% (02:30) wrong based on 88 sessions
HideShow timer Statistics
If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4? (1) The average of p, q and r is a multiple of 2 (2) qr/p is an integer .
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by DHAR on 04 Feb 2018, 12:56.
Last edited by gmatbusters on 10 Oct 2018, 06:12, edited 1 time in total.
Edited OA



examPAL Representative
Joined: 07 Dec 2017
Posts: 913

Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
Updated on: 05 Feb 2018, 00:15
DHAR wrote: If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4?
(1) The average of p, q and r is a multiple of 2 (2) qr/p is an integer . As this question deals with integer properties, we'll go for a Logical approach. Three consecutive integers can be even, odd, even in which case their product is divisible by 4 or odd, even, odd in which case it is divisible by 4 only if the middle number (q) is divisible by 4. We'll look for a statement which gives us this information. (1) p + q + r = p + (p + 1) + (p + 2) = 3p +3 so the average is p + 1. Then p + 1 = q is even. But is q divisible by 4? Insufficient! (2) if qr = (p + 1)(p + 2) = p^2 + 3p + 2 is divisible by p then 2 must be divisible by p. Since p > 1, then p = 2. Sufficient! (B) is our answer. EDIT: I'm surprised that the OA is (E). Don't think I missed anything...
_________________



Intern
Joined: 06 Aug 2017
Posts: 22
Location: India

Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
04 Feb 2018, 15:14
How is it Option E?
Isn't the answer Option D? Could anyone explain?



DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1443
Location: India

Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
04 Feb 2018, 22:40
DavidTutorexamPAL wrote: DHAR wrote: If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4?
(1) The average of p, q and r is a multiple of 2 (2) qr/p is an integer . As this question deals with integer properties, we'll go for a Logical approach. Three consecutive integers can be even, odd, even in which case their product is divisible by 4 or odd, even, odd in which case it is not. We'll look for a statement which gives us this information. (1) p + q + r = p + (p + 1) + (p + 2) = 3p +3 so the average is p + 1. If this is even, then p is odd. Sufficient! (2) if qr = (p + 1)(p + 2) = p^2 + 3p + 2 is divisible by p then 2 must be divisible by p. Since p > 1, then p = 2. Sufficient! (D) is our answer. DHAR : I thought that, if sufficient, (1) and (2) were supposed to give identical answers to the question? In this case (1) gives No and (2) gives Yes... otherwise, nice question! EDIT: I'm surprised that the OA is (E). Don't think I missed anything... Hi Even if the order is odd, even, odd  still the product can be divisible by 4 if the middle number is a mutliple of 4. Eg., 3, 4, 5 or 7, 8, 9.



DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1443
Location: India

Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
04 Feb 2018, 22:50
DHAR wrote: If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4?
(1) The average of p, q and r is a multiple of 2 (2) qr/p is an integer . Let the numbers be p, p+1, p+2 respectively. Their average will be the middle number only. Average = (p + p+1 + p+2)/3 = p+1. We have to determined whether p*(p+1)*(p+2) is divisible by 4. (1) Average = p+1 is even. So p is odd. Even if p is odd, still the product p*(p+1)*(p+2) might or might not be divisible by 4. eg, 3*4*5 is divisible by 4 but 5*6*7 is NOT divisible by 4. So this statement is Not Sufficient. (2) qr/p is an integer, so the product of q*r is divisible by p. Product of (p+1)*(p+2) = (p^2 + 3p + 2) is given to be divisible by p. Now p^2 and 3p are both multiples of p, so these two terms will anyway be divisible by p. But 2 is also divisible by p, This can only happen if p=2 and nothing else (because p>1 given). So from this condition we can determine that the only case possible here is p, q, r as 2, 3, 4 respectively. And their product, as we can see, is divisible by 4. So this statement is Sufficient. Hence answer should be B. (OA is E, either I am missing something or request to please check the OA)



examPAL Representative
Joined: 07 Dec 2017
Posts: 913

Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
05 Feb 2018, 00:12
amanvermagmat wrote: Hi
Even if the order is odd, even, odd  still the product can be divisible by 4 if the middle number is a mutliple of 4. Eg., 3, 4, 5 or 7, 8, 9. You're right! Slipped up there... fixed my reply, thanks.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 53865

Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
05 Feb 2018, 00:17
DHAR wrote: If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4?
(1) The average of p, q and r is a multiple of 2 (2) qr/p is an integer . The question is till flawed. From (1) p = odd and from (2) p = even. On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem.
_________________



Intern
Joined: 21 May 2016
Posts: 28

Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
01 Oct 2018, 11:03
If p,q and r are three consecutive integers, in that order and p>1, is their product divisible by 4? 1. The average of p,q and r is a multiple of 2. 2. \(qr/p\) is an integer
_________________
If you like my post press +1 Kudos



Manager
Joined: 21 Jun 2017
Posts: 234
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)

Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
01 Oct 2018, 11:55
IMO C 1. (p+q+r)/3 = 2*int or p+q+r = 6*int. Consider 5,6,7 and 3,4,5 Insufficient. Another way q is the the average as p,q,r are consecutive integers. Hence q = 2 int 2. rq/p = int rq = p*int therefore pqr = p^2*int. When int is 2 answer is Yes when its 3 Answer is No. Combining, we can get C
_________________
Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.
Dil ye Ziddi hai !!!



Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 709

Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
01 Oct 2018, 12:56
a70 wrote: If p,q and r are three consecutive integers, in that order and p>1, is their product divisible by 4?
1. The average of p,q and r is a multiple of 2.
2. \(qr/p\) is an integer We know that the three integers are consecutive, and that p>1. It's a divisibility problem, so we want to start thinking about what we can deduce regarding divisibility. When you have three consecutive integers, there are only two possibilities regarding even/odd: the integers either go EVENODDEVEN, or ODDEVENODD. Either one of those could be true in this case, given the limited information we have so far. If the integers go EVENODDEVEN, then their product will definitely be divisible by 4. After all, p is divisible by 2, and r is divisible by 2, so pr is divisible by 4 (and therefore pqr is divisible by 4.) If the integers go ODDEVENODD, their product MIGHT be divisible by 4. If the even integer in the middle is divisible by 4 already, then the product will also be divisible by 4. But if it isn't, the product won't be, either. For instance, 3*4*5 is divisible by 4, but 5*6*7 isn't. Statement 1 The average of the three numbers is even. Well, they're consecutive, so their average is equal to the middle number, or q. This statement is actually just saying "q is even". If q is even, we know we're looking at the ODDEVENODD scenario  in which case we don't know whether the product is divisible by 4, as discussed above. Not sufficient. Statement 2 qr/p is an integer. This is an interesting one. There are other ways to think about it (like case testing), but here's how I approached it. Since the integers are consecutive, I can write everything in terms of p. The statement really says, (p+1)(p+2)/p is an integer. Then, I simplified: (p^2 + 3p + 2)/p is an integer. You can split this up as follows: p^2/p + 3p/p + 2/p is an integer, or in other words, p + 3 + 2/p is an integer. I already know that p + 3 is an integer, so 2/p also has to be an integer. When is 2 divided by p an integer? Only if p is 2, 1, 1, or 2. But the first three possibilities are off the table, since the question already says that p > 1. Therefore, this statement really tells us that p = 2. That's sufficient to answer the question. The answer is B.  This isn't a 'wellformed' DS question, by the way. In official DS questions, the two statements will never give contradictory information. In this one, statement 1 tells us that p is odd, but statement 2 tells us that p is equal to 2. Since those contradict, you couldn't see a DS question like this one on the test.
_________________



Intern
Joined: 14 Nov 2015
Posts: 2

Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
Show Tags
10 Oct 2018, 10:55
DavidTutorexamPAL wrote: DHAR wrote: If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4?
(1) The average of p, q and r is a multiple of 2 (2) qr/p is an integer . As this question deals with integer properties, we'll go for a Logical approach. Three consecutive integers can be even, odd, even in which case their product is divisible by 4 or odd, even, odd in which case it is divisible by 4 only if the middle number (q) is divisible by 4. We'll look for a statement which gives us this information. (1) p + q + r = p + (p + 1) + (p + 2) = 3p +3 so the average is p + 1. Then p + 1 = q is even. But is q divisible by 4? Insufficient! (2) if qr = (p + 1)(p + 2) = p^2 + 3p + 2 is divisible by p then 2 must be divisible by p. Since p > 1, then p = 2. Sufficient! (B) is our answer. EDIT: I'm surprised that the OA is (E). Don't think I missed anything...  Hi David, Thanks for the fantastic reply. i understood the explanation but i tried it in a different way. This is my approach Let us take (n1),n and (n+1) as three consecutive integers for P,Q and R. As per second statement QR/P is an integer. So based on the values that i have chosen for P,Q and R i arrived at [n*(n+1)] / (n1) = Intezer (I Assumed some value K) Now if i go to the question stem, whether PQR / 4 or not ?? If I go ahead and substitute the values, then i get the value of expression as [k * (n1)^2] / 4 in this final value whether it is divisible by 4 or not entirely depends on K and n1 value Hence, I concluded that B is not sufficient Please suggest me where I am going wrong in this approach




Re: If p, q and r are three consecutive integers, in that order and p > 1,
[#permalink]
10 Oct 2018, 10:55






