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

 It is currently 17 Nov 2018, 01:08

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

November 18, 2018

November 18, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

# If p and q are distinct integers, is 4 a factor of p – q?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50621
If p and q are distinct integers, is 4 a factor of p – q?  [#permalink]

### Show Tags

06 Nov 2016, 08:11
00:00

Difficulty:

5% (low)

Question Stats:

89% (00:46) correct 11% (00:53) wrong based on 151 sessions

### HideShow timer Statistics

If p and q are distinct integers, is 4 a factor of p – q?

(1) 4 is a factor of p.
(2) 4 is a factor of q.

_________________
Current Student
Joined: 12 Aug 2015
Posts: 2633
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If p and q are distinct integers, is 4 a factor of p – q?  [#permalink]

### Show Tags

06 Nov 2016, 08:19
Here is my approach =>
Here we need to see whether p-q is divisible by 4 or not.
Statement 1=>
4 is a factor of p.
p/4=integer
In other words=>
p is divisible by 4
Lets use test cases=>
p=4
q=2 =>p-q=2 Clearly not divisible by 4
p=16
q=12
p-q=4 Clearly divisibly be 4

Hence insufficient
Statement 2
Q/4=integer.
Lets use the test cases again
q=4
p=8
p-q=4=> Clearly divisible by 4
q=4
p=5
p-q=1=>clearly not divisible by 4
Hence Insufficient.
Combining them
we can say that p=4x
and q=4y
for some integer x and y
hence p-q=4(x-y) => It is divisible by 4

Alternatively we could use the property => When we add (or subtract) two multiples of n => We get a multiple of n
Hence C
_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

CEO
Joined: 11 Sep 2015
Posts: 3122
Re: If p and q are distinct integers, is 4 a factor of p – q?  [#permalink]

### Show Tags

06 Nov 2016, 08:22
Top Contributor
Bunuel wrote:
If p and q are distinct integers, is 4 a factor of p – q?

(1) 4 is a factor of p.
(2) 4 is a factor of q.

Target question: Is 4 a factor of p – q?

Statement 1: 4 is a factor of p
Since we don't have any information about q, there's now way to tell whether 4 is factor of p – q
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 4 is a factor of q
Since we don't have any information about p, there's now way to tell whether 4 is factor of p – q
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1: 4 is a factor of p. This means we can write p = 4k, for some integer k
Statement 2: 4 is a factor of q. This means we can write q = 4j, for some integer j
So, p - q = 4k - 4j = 4(k - j)
From this, we can see that p - q is equal to the product of 4 and some integer (k-j)
So, 4 must be a factor of p – q
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4212
Location: India
GPA: 3.5
If p and q are distinct integers, is 4 a factor of p – q?  [#permalink]

### Show Tags

06 Nov 2016, 09:03
Bunuel wrote:
If p and q are distinct integers, is 4 a factor of p – q?

(1) 4 is a factor of p.
(2) 4 is a factor of q.

There can be multiple ways to approach this question , I will try to approach this question by plugging in some number...

FROM STATEMENT - I ( INSUFFICIENT)

Let p = 8 & q = 2

p - q = 6 ; Not divisible by 4

Again -

Let P = 16 & q = 8

p - q = 8 ; Divisible by 4

Thus no unique solution can be obtained....

FROM STATEMENT - II ( INSUFFICIENT)

Let p = 16 & q = 8

p - q = 8 ; Divisible by 4

Again -

Let P = 14 & q = 8

p - q = 6 ; Not divisible by 4

Thus no unique solution can be obtained....

FROM STATEMENT - I & II ( SUFFICIENT)

When both p & q are multiples of 4 , 4 can be common factor and thus p - q will be divisible by 4

Hence, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked, answer will be (C)

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Senior Manager
Joined: 06 Jun 2016
Posts: 259
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
Re: If p and q are distinct integers, is 4 a factor of p – q?  [#permalink]

### Show Tags

06 Nov 2016, 22:23
Bunuel wrote:
If p and q are distinct integers, is 4 a factor of p – q?

(1) 4 is a factor of p.
(2) 4 is a factor of q.

IMO C
p and q are distinct integers

From statement 1
4 is a factor of p i.e., p is divisible by 4
but no information is given regarding q.
p can be 12 and q can be 1 in which case the answer is NO
p can be 12 and q can be 4 in which case the answer is YES
Hence insufficient

From statement 2
4 is a factor of q i.e., q is divisible by 4
no information is given regarding p.
hence insufficient (following similar discussion as in statement 1)

Combining
p and q are divisible by 4 giving p-q is divisible by 4
p=16 q=4 p-q=12 or p=4 q=12 p-q=-8 (both cases divisible by 4)
Hence C
Manager
Joined: 06 Jun 2013
Posts: 157
Location: India
Concentration: Finance, Economics
Schools: Tuck
GMAT 1: 640 Q49 V30
GPA: 3.6
WE: Engineering (Computer Software)
If p and q are distinct integers, is 4 a factor of p – q?  [#permalink]

### Show Tags

27 Nov 2016, 00:11
from statement 1 :
p=4*a , but we don't have any information about q
not sufficient

from statement 2 :
q=4b, but we don't have any information about p
not sufficient

combining 1 and 2 :

p-q = 4a- 4b = 4(a-b)

irrespective of the values of a and b, 4 will always be a factor of p-q

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 477
If p and q are distinct integers, is 4 a factor of p – q?  [#permalink]

### Show Tags

31 Aug 2018, 07:04
Bunuel wrote:
If p and q are distinct integers, is 4 a factor of p – q?

(1) 4 is a factor of p.
(2) 4 is a factor of q.

$$p \ne q\,\,\,{\text{ints}}$$

$$\frac{{p - q}}{4}\,\,\,\mathop = \limits^? \,\,\,\operatorname{int}$$

We will prove that each statement ALONE is insufficient to answer the question asked (in a unique way), through what we call an ALGEBRAIC BIFURCATION:

$$\left( 1 \right)\,\,\,\,\frac{p}{4} = \operatorname{int} \,\,\,\,\left\{ \begin{gathered} \,\,Take\,\,\left( {p,q} \right) = \left( {0,1} \right)\,\,\,\, \Rightarrow \,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \,\,Take\,\,\left( {p,q} \right) = \left( {0,4} \right)\,\,\,\, \Rightarrow \,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\ \end{gathered} \right.$$

$$\left( 2 \right)\,\,\,\,\frac{q}{4} = \operatorname{int} \,\,\,\,\left\{ \begin{gathered} \,\,Take\,\,\left( {p,q} \right) = \left( {1,0} \right)\,\,\,\, \Rightarrow \,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \,\,Take\,\,\left( {p,q} \right) = \left( {4,0} \right)\,\,\,\, \Rightarrow \,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\ \end{gathered} \right.$$

$$\left( {1 + 2} \right)\,\,\,\,\frac{{p - q}}{4} = \frac{p}{4} - \frac{q}{4} = \operatorname{int} - \operatorname{int} = \operatorname{int} \,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,$$

The above follows the notations and rationale taught in the GMATH method.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

If p and q are distinct integers, is 4 a factor of p – q? &nbs [#permalink] 31 Aug 2018, 07:04
Display posts from previous: Sort by