GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 21 Jan 2020, 19:52

### 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

# If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60555
If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is  [#permalink]

### Show Tags

12 Nov 2019, 02:06
1
2
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:01) correct 36% (02:32) wrong based on 59 sessions

### HideShow timer Statistics

If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is divisible by 4, all of the following could be the value of j - k EXCEPT:

A. 43
B. 33
C. 21
D. 13
E. 5

Are You Up For the Challenge: 700 Level Questions

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5701
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is  [#permalink]

### Show Tags

12 Nov 2019, 03:11
from given info
we can say
j-2-k+5/4
j-k+3/4
plug in values for j-k from given options
only option A ; 43 is not divisible
IMO A 43

Bunuel wrote:
If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is divisible by 4, all of the following could be the value of j - k EXCEPT:

A. 43
B. 33
C. 21
D. 13
E. 5

Are You Up For the Challenge: 700 Level Questions
Rice (Jones) School Moderator
Joined: 18 Jun 2018
Posts: 329
Location: United States (AZ)
Concentration: Finance, Healthcare
GMAT 1: 600 Q44 V28
GPA: 3.36
Re: If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is  [#permalink]

### Show Tags

12 Nov 2019, 05:51
$$\frac{j - 2}{4}$$= m (where m is an integer) and $$\frac{k - 5}{4}$$ = n (where n is an integer) ==> $$\frac{j - 2}{4}$$ - $$\frac{k - 5}{4}$$ = p (where p is an integer) ==> j - k = 4p - 3 ==> check the answer choices, and the answer that cannot be expressed in this form is the correct answer

A. 43
B. 33 = 4(9) - 3
C. 21 = 4(6) - 3
D. 13 = 4(4) - 3
E. 5 = 4(2) - 3

Intern
Joined: 08 Apr 2017
Posts: 2
Re: If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is  [#permalink]

### Show Tags

12 Nov 2019, 11:13
J=4p+2
K=4q+5
j-k = 4(p-q)-3
Insert values from options. Correct answer after adding 3 to it will be divisible by 4.
4(p-q)-3=43 ; 46 not divisible by 4
4(p-q)-3=33 ; 36 divisible by 4
4(p-q)-3=21 ; 24 divisible by 4
4(p-q)-3=13 ; 16 divisible by 4
4(p-q)-3=5 ; 8 divisible by 4

Hence, correct answer choice is A.
VP
Joined: 19 Oct 2018
Posts: 1293
Location: India
Re: If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is  [#permalink]

### Show Tags

12 Nov 2019, 12:06
1
j-2=4x
j=4x+2

k-5=4y
k=4(y+1)+1

All the options are positive; hence j>k

j-k= 4(x-y-1)+1
j-k leaves remainder 1, when divided by 4

All options except A leaves remainder 1, when divided by 4.

Bunuel wrote:
If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is divisible by 4, all of the following could be the value of j - k EXCEPT:

A. 43
B. 33
C. 21
D. 13
E. 5

Are You Up For the Challenge: 700 Level Questions
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9088
Location: United States (CA)
Re: If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is  [#permalink]

### Show Tags

20 Nov 2019, 18:52
Bunuel wrote:
If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is divisible by 4, all of the following could be the value of j - k EXCEPT:

A. 43
B. 33
C. 21
D. 13
E. 5

Are You Up For the Challenge: 700 Level Questions

Since j - 2 and k - 5 are both divisible by 4, their difference is also divisible by 4; that is:

j - 2 - (k - 5) = j - k + 3 is divisible by 4.

Since j - k + 3 is divisible by 4, then when j - k is divided by 4, it should have a remainder of 1 (notice that if j - k is 1, then j - k + 3 = 4). Therefore, we are looking for the choice that doesn’t yield a remainder of 1 when it is divided by 4, and we see that is the number 43 (all the other choices do indeed yield a remainder of 1 when divided by 4).

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3219
Re: If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is  [#permalink]

### Show Tags

24 Nov 2019, 20:10

Solution

Given:
• j and k are positive integers
• j – 2 is divisible by 4
• k – 5 is divisible by 4

To find:
• Which cannot be the value of j - k

Approach and Working Out:
• From the given information we can write,
o $$j – 2 = 4p_1$$, where $$p_1$$ is an integer
 Implies, $$j = 4p_1 + 2$$
o Similarly, $$k – 5 = 4p_2$$, where, $$p_2$$ is an integer
 $$k = 4p_2 + 5$$
• Thus, $$j – k = 4p_1 + 2 – 4p_2 – 5 = 4(p_1 – p_2) – 3 = 4(p_1 – p_2) – 4 + 1 = 4(p_1 – p_2 – 1) + 1= 4p + 1$$
• The only option which is not in the form of 4p + 1 is option A, 43

Hence, the correct answer is Option A.

_________________
Re: If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is   [#permalink] 24 Nov 2019, 20:10
Display posts from previous: Sort by