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

 It is currently 17 Jan 2019, 13:26

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

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.

# If p and n are positive integers and p > n, what is the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52231
Re: If p and n are positive integers and p > n, what is the  [#permalink]

### Show Tags

07 Jul 2016, 03:31
iliavko wrote:
Am I underestimating this question?

For me when taking both 1 and 2:

We know that p+n=5q+1 and p-n=3q+1

well just plug the same value for each q and get: for q=1 (6*4) and just divide it by 15 to get R9. then plug q=2 and get that 77/15 has R2 so that's it, end of story, insufficient.

Am I missing something?

No, that's not correct. You cannot put the same quotient in both cases. Each solution on previous page makes this clear.
_________________
Manager
Joined: 19 Aug 2016
Posts: 84
Re: If p and n are positive integers and p > n, what is the  [#permalink]

### Show Tags

13 Feb 2018, 19:44
Bunuel wrote:
If p and n are positive integers and p>n, what is the remainder when p^2 - n^2 is divided by 15?

First of all $$p^2 - n^2=(p+n)(p-n)$$.

(1) The remainder when p + n is divided by 5 is 1. No info about p-n. Not sufficient.

(2) The remainder when p - n is divided by 3 is 1. No info about p+n. Not sufficient.

(1)+(2) "The remainder when p + n is divided by 5 is 1" can be expressed as $$p+n=5t+1$$ and "The remainder when p - n is divided by 3 is 1" can be expressed as $$p-n=3k+1$$.

Multiply these two --> $$(p+n)(p-n)=(5t+1)(3k+1)=15kt+5t+3k+1$$, now first term (15kt) is clearly divisible by 15 (r=0), but we don't know about 5t+3k+1. For example t=1 and k=1, answer r=9 BUT t=7 and k=3, answer r=0. Not sufficient.

OR by number plugging: if $$p+n=11$$ (11 divided by 5 yields remainder of 1) and $$p-n=1$$ (1 divided by 3 yields remainder of 1) then $$(p+n)(p-n)=11$$ and remainder upon division 11 by 15 is 11 BUT if $$p+n=21$$ (21 divided by 5 yields remainder of 1) and $$p-n=1$$ (1 divided by 3 yields remainder of 1) then $$(p+n)(p-n)=21$$ and remainder upon division 21 by 15 is 6. Not sufficient.

Hi Bunuel

I plugged in numbers

So i had chosen 31 which is divisble by 3 and 5. Hence, i chose C

Could u pls explain what im missing out on?
Math Expert
Joined: 02 Sep 2009
Posts: 52231
Re: If p and n are positive integers and p > n, what is the  [#permalink]

### Show Tags

13 Feb 2018, 19:53
zanaik89 wrote:
Bunuel wrote:
If p and n are positive integers and p>n, what is the remainder when p^2 - n^2 is divided by 15?

First of all $$p^2 - n^2=(p+n)(p-n)$$.

(1) The remainder when p + n is divided by 5 is 1. No info about p-n. Not sufficient.

(2) The remainder when p - n is divided by 3 is 1. No info about p+n. Not sufficient.

(1)+(2) "The remainder when p + n is divided by 5 is 1" can be expressed as $$p+n=5t+1$$ and "The remainder when p - n is divided by 3 is 1" can be expressed as $$p-n=3k+1$$.

Multiply these two --> $$(p+n)(p-n)=(5t+1)(3k+1)=15kt+5t+3k+1$$, now first term (15kt) is clearly divisible by 15 (r=0), but we don't know about 5t+3k+1. For example t=1 and k=1, answer r=9 BUT t=7 and k=3, answer r=0. Not sufficient.

OR by number plugging: if $$p+n=11$$ (11 divided by 5 yields remainder of 1) and $$p-n=1$$ (1 divided by 3 yields remainder of 1) then $$(p+n)(p-n)=11$$ and remainder upon division 11 by 15 is 11 BUT if $$p+n=21$$ (21 divided by 5 yields remainder of 1) and $$p-n=1$$ (1 divided by 3 yields remainder of 1) then $$(p+n)(p-n)=21$$ and remainder upon division 21 by 15 is 6. Not sufficient.

Hi Bunuel

I plugged in numbers

So i had chosen 31 which is divisble by 3 and 5. Hence, i chose C

Could u pls explain what im missing out on?

One example is not enough to get sufficiency. Also, when asking a question, please be more specific and show you work.
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6810
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If p and n are positive integers and p > n, what is the  [#permalink]

### Show Tags

17 Feb 2018, 22:09
BANON wrote:
If p and n are positive integers and p > n, what is the remainder when p^2 - n^2 is divided by 15 ?

(1) The remainder when p + n is divided by 5 is 1.
(2) The remainder when p - n is divided by 3 is 1.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (p and n) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first.

Conditions 1) & 2):
$$p + n = 6, p - n = 4 : p = 5, n = 1 : p^2 - n^2 = 25 - 1 = 24$$, its remainder is $$4$$.
$$p + n = 11, p - n = 7 : p = 9, n = 2 : p^2 - n^2 = 81 - 4 = 77$$, its remainder is $$2$$.

Thus, both conditions together are not sufficient, since the remainder is not unique.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only 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 Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 14 Jun 2018
Posts: 8
If p and n are positive integers and p > n, what is the  [#permalink]

### Show Tags

01 Nov 2018, 21:55
once we've narrowed down to C/E
can we test the relationship in a simultaneous equation setup by adding p+n = 5Q+1 and p-n = 3K+1 which
works out to 2p = 5Q + 3K + 2 i.e. three variables requiring three assumptions hence unsolvable ?
Thus E is the best answer.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8789
Location: Pune, India
Re: If p and n are positive integers and p > n, what is the  [#permalink]

### Show Tags

02 Nov 2018, 06:47
1
once we've narrowed down to C/E
can we test the relationship in a simultaneous equation setup by adding p+n = 5Q+1 and p-n = 3K+1 which
works out to 2p = 5Q + 3K + 2 i.e. three variables requiring three assumptions hence unsolvable ?
Thus E is the best answer.

No, this does not work out. There is no point looking for p. We need p^2 - n^2. Sometimes, you need less information to get the value of what you need even though you may not be able to get the value of each variable independently.

p + n = 5Q + 1

p - n = 3K + 1

Now, what you need is (p + n)*(p - n)

(p + n)*(p - n) = (5Q + 1)*(3K + 1) = 15QK + 3K + 5Q + 1

Is this divisible by 15? We know that the first term (15QK) is but what about the sum of the other 3 terms? We don't know since that depends on the values of Q and K.
If K = 5 and Q = 3, this is not divisible by 15.
If K = 3 and Q = 4, this is divisible by 15.
Hence, both statements are insufficient.
_________________

Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 14 Jun 2018
Posts: 8
Re: If p and n are positive integers and p > n, what is the  [#permalink]

### Show Tags

02 Nov 2018, 07:57
understood, thank you
Manager
Joined: 01 May 2018
Posts: 61
Re: If p and n are positive integers and p > n, what is the  [#permalink]

### Show Tags

09 Dec 2018, 06:07
Bunuel wrote:
If p and n are positive integers and p>n, what is the remainder when p^2 - n^2 is divided by 15?

First of all $$p^2 - n^2=(p+n)(p-n)$$.

(1) The remainder when p + n is divided by 5 is 1. No info about p-n. Not sufficient.

(2) The remainder when p - n is divided by 3 is 1. No info about p+n. Not sufficient.

(1)+(2) "The remainder when p + n is divided by 5 is 1" can be expressed as $$p+n=5t+1$$ and "The remainder when p - n is divided by 3 is 1" can be expressed as $$p-n=3k+1$$.

Multiply these two --> $$(p+n)(p-n)=(5t+1)(3k+1)=15kt+5t+3k+1$$, now first term (15kt) is clearly divisible by 15 (r=0), but we don't know about 5t+3k+1. For example t=1 and k=1, answer r=9 BUT t=7 and k=3, answer r=0. Not sufficient.

OR by number plugging: if $$p+n=11$$ (11 divided by 5 yields remainder of 1) and $$p-n=1$$ (1 divided by 3 yields remainder of 1) then $$(p+n)(p-n)=11$$ and remainder upon division 11 by 15 is 11 BUT if $$p+n=21$$ (21 divided by 5 yields remainder of 1) and $$p-n=1$$ (1 divided by 3 yields remainder of 1) then $$(p+n)(p-n)=21$$ and remainder upon division 21 by 15 is 6. Not sufficient.

Hello
When the question stem says that The remainder when p + n is divided by 5 is 1, doesn't it implicitly place a constraint on p-n? So dont we need to check p-n too?
While solving the question, I calculated p+n based on the criteria, p-n for the chosen numbers and then p^2-n^2 and finally checked divisibility. I started running out of time and had to guess and move.
Manager
Joined: 01 May 2018
Posts: 61
Re: If p and n are positive integers and p > n, what is the  [#permalink]

### Show Tags

10 Dec 2018, 02:51
singh8891 wrote:
Bunuel wrote:
If p and n are positive integers and p>n, what is the remainder when p^2 - n^2 is divided by 15?

First of all $$p^2 - n^2=(p+n)(p-n)$$.

(1) The remainder when p + n is divided by 5 is 1. No info about p-n. Not sufficient.

(2) The remainder when p - n is divided by 3 is 1. No info about p+n. Not sufficient.

(1)+(2) "The remainder when p + n is divided by 5 is 1" can be expressed as $$p+n=5t+1$$ and "The remainder when p - n is divided by 3 is 1" can be expressed as $$p-n=3k+1$$.

Multiply these two --> $$(p+n)(p-n)=(5t+1)(3k+1)=15kt+5t+3k+1$$, now first term (15kt) is clearly divisible by 15 (r=0), but we don't know about 5t+3k+1. For example t=1 and k=1, answer r=9 BUT t=7 and k=3, answer r=0. Not sufficient.

OR by number plugging: if $$p+n=11$$ (11 divided by 5 yields remainder of 1) and $$p-n=1$$ (1 divided by 3 yields remainder of 1) then $$(p+n)(p-n)=11$$ and remainder upon division 11 by 15 is 11 BUT if $$p+n=21$$ (21 divided by 5 yields remainder of 1) and $$p-n=1$$ (1 divided by 3 yields remainder of 1) then $$(p+n)(p-n)=21$$ and remainder upon division 21 by 15 is 6. Not sufficient.

Hello
When the question stem says that The remainder when p + n is divided by 5 is 1, doesn't it implicitly place a constraint on p-n? So dont we need to check p-n too?
While solving the question, I calculated p+n based on the criteria, p-n for the chosen numbers and then p^2-n^2 and finally checked divisibility. I started running out of time and had to guess and move.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8789
Location: Pune, India
Re: If p and n are positive integers and p > n, what is the  [#permalink]

### Show Tags

11 Dec 2018, 05:01
1
singh8891 wrote:
Bunuel wrote:
If p and n are positive integers and p>n, what is the remainder when p^2 - n^2 is divided by 15?

First of all $$p^2 - n^2=(p+n)(p-n)$$.

(1) The remainder when p + n is divided by 5 is 1. No info about p-n. Not sufficient.

(2) The remainder when p - n is divided by 3 is 1. No info about p+n. Not sufficient.

(1)+(2) "The remainder when p + n is divided by 5 is 1" can be expressed as $$p+n=5t+1$$ and "The remainder when p - n is divided by 3 is 1" can be expressed as $$p-n=3k+1$$.

Multiply these two --> $$(p+n)(p-n)=(5t+1)(3k+1)=15kt+5t+3k+1$$, now first term (15kt) is clearly divisible by 15 (r=0), but we don't know about 5t+3k+1. For example t=1 and k=1, answer r=9 BUT t=7 and k=3, answer r=0. Not sufficient.

OR by number plugging: if $$p+n=11$$ (11 divided by 5 yields remainder of 1) and $$p-n=1$$ (1 divided by 3 yields remainder of 1) then $$(p+n)(p-n)=11$$ and remainder upon division 11 by 15 is 11 BUT if $$p+n=21$$ (21 divided by 5 yields remainder of 1) and $$p-n=1$$ (1 divided by 3 yields remainder of 1) then $$(p+n)(p-n)=21$$ and remainder upon division 21 by 15 is 6. Not sufficient.

Hello
When the question stem says that The remainder when p + n is divided by 5 is 1, doesn't it implicitly place a constraint on p-n? So dont we need to check p-n too?
While solving the question, I calculated p+n based on the criteria, p-n for the chosen numbers and then p^2-n^2 and finally checked divisibility. I started running out of time and had to guess and move.

Note the information given to you about (p + n). The remainder when you divide it by 5 is 1.

So (p+n) can be 6/11/16/21/26/31/36... etc. This gives us limitless values for (p-n) with all possible different remainders when divided by 5.

Yes, a particular small value for (p+n) could have put a constraint on (p - n). Such as (p+n) = 6. Now (p - n) could take a few values only.
_________________

Karishma
Veritas Prep GMAT Instructor

Re: If p and n are positive integers and p > n, what is the &nbs [#permalink] 11 Dec 2018, 05:01

Go to page   Previous    1   2   [ 30 posts ]

Display posts from previous: Sort by