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

It is currently 16 Dec 2018, 23:35

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
  • 10 Keys to nail DS and CR questions

     December 17, 2018

     December 17, 2018

     06:00 PM PST

     07:00 PM PST

    Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong.
  • R1 Admission Decisions: Estimated Decision Timelines and Chat Links for Major BSchools

     December 17, 2018

     December 17, 2018

     10:00 PM PST

     11:00 PM PST

    From Dec 5th onward, American programs will start releasing R1 decisions. Chat Rooms: We have also assigned chat rooms for every school so that applicants can stay in touch and exchange information/update during decision period.

If n and p are positive integers, what is the ratio of n to p? (1) n

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

Hide Tags

Manager
Manager
avatar
G
Joined: 02 Jun 2015
Posts: 191
Location: Ghana
Premium Member
If n and p are positive integers, what is the ratio of n to p? (1) n  [#permalink]

Show Tags

New post 26 May 2017, 06:55
1
3
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

49% (02:05) correct 51% (02:05) wrong based on 87 sessions

HideShow timer Statistics

If n and p are positive integers, what is the ratio of n to p?

(1) np = 48
(2) p^2 - n^2 = 28

_________________

Kindly press kudos if you find my post helpful

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51233
Re: If n and p are positive integers, what is the ratio of n to p? (1) n  [#permalink]

Show Tags

New post 26 May 2017, 07:43
2
1
If n and p are positive integers, what is the ratio of n to p?

(1) np = 48. Clearly insufficient. Consider n = 48 and p = 1 AND n = 1 and p = 48.


(2) p^2 - n^2 = 28

(p + n)(p - n) = 28. Notice here that p must be greater than n, so p + n must be greater than p - n.

The product of two positive integers is 28. 28 = 28*1 = 14*2 = 7*4.

p + n = 28 and p - n = 1 --> no integer solution.
p + n = 14 and p - n = 2 --> p = 8 and n = 6.
p + n = 7 and p - n = 4 --> no integer solution.

Only one possible set: p = 8 and n = 6. Ratio = n/p = 6/8. Sufficient.

Answer: B.
_________________

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

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3240
Location: Canada
Re: If n and p are positive integers, what is the ratio of n to p? (1) n  [#permalink]

Show Tags

New post 26 Feb 2018, 09:54
Top Contributor
1
duahsolo wrote:
If n and p are positive integers, what is the ratio of n to p?

(1) np = 48
(2) p² - n² = 28


Target question: What is the ratio of n to p?

Given: n and p are positive integers

Statement 1: np = 48
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of n and p that satisfy statement 1. Here are two:
Case a: n = 1 and p = 48. In this case, the ratio of n to p is 1 to 48
Case b: n = 48 and p = 1. In this case, the ratio of n to p is 48 to 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: p² - n² = 28
Factor the left side to get: (p - n)(p + n) = 28

IMPORTANT: If p and n are integers, then p-n and p+n will also be integers.
Also, if p+n is ODD then p-n must also be ODD
Likewise, if p+n is EVEN then p-n must also be EVEN

Since (p - n)(p + n) = 28, we know that p+n and p-n must BOTH be EVEN
Why is this?
Well, the product of two ODD numbers cannot be EVEN (28).

When we examine pairs of INTEGERS that multiply to get 28, we see that there is only ONE pair such that both values are EVEN: 2 and 14
At this point, we can conclude that p - n = 2 and p + n = 14
Here we have two equations with 2 variables:
p - n = 2
p + n = 14

When we solve the system, we get: p = 8 and n = 6
This means the ratio of n to p is 6 to 8 (aka 3 to 4)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

GMAT Club Bot
Re: If n and p are positive integers, what is the ratio of n to p? (1) n &nbs [#permalink] 26 Feb 2018, 09:54
Display posts from previous: Sort by

If n and p are positive integers, what is the ratio of n to p? (1) n

  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®.