GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Dec 2018, 05:52

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     December 15, 2018

     December 15, 2018

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)

If p, q and r are three consecutive integers, in that order and p > 1,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
User avatar
G
Joined: 15 Dec 2015
Posts: 116
GMAT 1: 660 Q46 V35
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

New post Updated on: 10 Oct 2018, 05:12
4
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (02:27) correct 55% (02:02) wrong based on 83 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 .

Originally posted by DHAR on 04 Feb 2018, 11:56.
Last edited by gmatbusters on 10 Oct 2018, 05:12, edited 1 time in total.
Edited OA
examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 841
Re: If p, q and r are three consecutive integers, in that order and p > 1,  [#permalink]

Show Tags

New post Updated on: 04 Feb 2018, 23:15
1
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...
_________________

Image
Sign up for 7-day free trial
Image


Originally posted by DavidTutorexamPAL on 04 Feb 2018, 13:50.
Last edited by DavidTutorexamPAL on 04 Feb 2018, 23:15, edited 1 time in total.
Intern
Intern
User avatar
S
Joined: 06 Aug 2017
Posts: 21
Location: India
GMAT 1: 660 Q47 V34
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If p, q and r are three consecutive integers, in that order and p > 1,  [#permalink]

Show Tags

New post 04 Feb 2018, 14:14
How is it Option E?

Isn't the answer Option D?
Could anyone explain?
DS Forum Moderator
avatar
P
Joined: 21 Aug 2013
Posts: 1412
Location: India
Premium Member
Re: If p, q and r are three consecutive integers, in that order and p > 1,  [#permalink]

Show Tags

New post 04 Feb 2018, 21:40
1
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
avatar
P
Joined: 21 Aug 2013
Posts: 1412
Location: India
Premium Member
Re: If p, q and r are three consecutive integers, in that order and p > 1,  [#permalink]

Show Tags

New post 04 Feb 2018, 21:50
1
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
User avatar
G
Joined: 07 Dec 2017
Posts: 841
Re: If p, q and r are three consecutive integers, in that order and p > 1,  [#permalink]

Show Tags

New post 04 Feb 2018, 23:12
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.
_________________

Image
Sign up for 7-day free trial
Image

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
Re: If p, q and r are three consecutive integers, in that order and p > 1,  [#permalink]

Show Tags

New post 04 Feb 2018, 23:17
2
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.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
S
Joined: 21 May 2016
Posts: 27
GMAT ToolKit User Premium Member CAT Tests
Re: If p, q and r are three consecutive integers, in that order and p > 1,  [#permalink]

Show Tags

New post 01 Oct 2018, 10:03
1
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
Manager
avatar
S
Joined: 21 Jun 2017
Posts: 157
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
CAT Tests
Re: If p, q and r are three consecutive integers, in that order and p > 1,  [#permalink]

Show Tags

New post 01 Oct 2018, 10:55
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.

Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 649
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: If p, q and r are three consecutive integers, in that order and p > 1,  [#permalink]

Show Tags

New post 01 Oct 2018, 11:56
1
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 EVEN-ODD-EVEN, or ODD-EVEN-ODD. Either one of those could be true in this case, given the limited information we have so far.

If the integers go EVEN-ODD-EVEN, 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 ODD-EVEN-ODD, 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 ODD-EVEN-ODD 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 'well-formed' 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.
_________________

Image

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!

Intern
Intern
User avatar
B
Joined: 14 Nov 2015
Posts: 2
GMAT ToolKit User
Re: If p, q and r are three consecutive integers, in that order and p > 1,  [#permalink]

Show Tags

New post 10 Oct 2018, 09:55
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 (n-1),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)] / (n-1) = 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 * (n-1)^2] / 4
in this final value whether it is divisible by 4 or not entirely depends on K and n-1 value
Hence, I concluded that B is not sufficient
Please suggest me where I am going wrong in this approach
GMAT Club Bot
Re: If p, q and r are three consecutive integers, in that order and p > 1, &nbs [#permalink] 10 Oct 2018, 09:55
Display posts from previous: Sort by

If p, q and r are three consecutive integers, in that order and p > 1,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.