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

It is currently 22 Oct 2019, 15:02

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

When integer a is divided by 4 the remainder is 2, and when integer b

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58427
When integer a is divided by 4 the remainder is 2, and when integer b  [#permalink]

Show Tags

New post 01 Mar 2017, 05:39
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (02:43) correct 59% (03:12) wrong based on 132 sessions

HideShow timer Statistics

GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4018
Location: Canada
Re: When integer a is divided by 4 the remainder is 2, and when integer b  [#permalink]

Show Tags

New post 01 Mar 2017, 06:33
2
Top Contributor
Bunuel wrote:
When integer a is divided by 4 the remainder is 2, and when integer b is divided by 5 the remainder is 1. How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?

A. Zero
B. One
C. Two
D. Three
E. Four


When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
------NOW ONTO THE QUESTION----------------------------

When integer a is divided by 4 the remainder is 2
So, the possible values of a are: 2, 6, 10, 14, 18, 22, 26,....

When integer b is divided by 5 the remainder is 1
So, the possible values of b are: 1, 6, 11, 16, 21, 26, 31,....

How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?
Let's see which sums we CAN get:
20 = 14 + 6
21 = 10 + 11
22 = 6 + 16
23 = 2 + 21
24 = 18 + 6
25 = 14 + 11
26 = 10 + 16
27 = 26 + 1
28 = 22 + 6
29 = 18 + 11
We can get ALL of the sums.

Answer: A

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
User avatar
B
Joined: 30 Jun 2017
Posts: 13
Location: India
Concentration: Technology, General Management
WE: Consulting (Computer Software)
GMAT ToolKit User
Re: When integer a is divided by 4 the remainder is 2, and when integer b  [#permalink]

Show Tags

New post 17 Aug 2017, 02:52
1
GMATPrepNow wrote:
Bunuel wrote:
When integer a is divided by 4 the remainder is 2, and when integer b is divided by 5 the remainder is 1. How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?

A. Zero
B. One
C. Two
D. Three
E. Four


When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
------NOW ONTO THE QUESTION----------------------------

When integer a is divided by 4 the remainder is 2
So, the possible values of a are: 2, 6, 10, 14, 18, 22, 26,....

When integer b is divided by 5 the remainder is 1
So, the possible values of b are: 1, 6, 11, 16, 21, 26, 31,....

How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?
Let's see which sums we CAN get:
20 = 14 + 6
21 = 10 + 11
22 = 6 + 16
23 = 2 + 21
24 = 18 + 6
25 = 14 + 11
26 = 10 + 16
27 = 26 + 1
28 = 22 + 6
29 = 18 + 11
We can get ALL of the sums.

Answer: A


Is there no other way except putting in number values to solve this problem?
Intern
Intern
avatar
B
Joined: 01 Jun 2016
Posts: 27
Re: When integer a is divided by 4 the remainder is 2, and when integer b  [#permalink]

Show Tags

New post 17 Aug 2017, 19:30
1
1
saswatdodo wrote:
GMATPrepNow wrote:
Bunuel wrote:
When integer a is divided by 4 the remainder is 2, and when integer b is divided by 5 the remainder is 1. How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?

A. Zero
B. One
C. Two
D. Three
E. Four


When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
------NOW ONTO THE QUESTION----------------------------

When integer a is divided by 4 the remainder is 2
So, the possible values of a are: 2, 6, 10, 14, 18, 22, 26,....

When integer b is divided by 5 the remainder is 1
So, the possible values of b are: 1, 6, 11, 16, 21, 26, 31,....

How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?
Let's see which sums we CAN get:
20 = 14 + 6
21 = 10 + 11
22 = 6 + 16
23 = 2 + 21
24 = 18 + 6
25 = 14 + 11
26 = 10 + 16
27 = 26 + 1
28 = 22 + 6
29 = 18 + 11
We can get ALL of the sums.

Answer: A


Is there no other way except putting in number values to solve this problem?


saswatdodo This is how I solved it:
A = 4q + 2.
B = 5p + 1.

Add both of them.
A + B = 4q + 5p + 3.

now, 20 <= 4q + 5p + 3 <= 29
17<= 4q + 5p <=26

plugin in a couple of numbers and you will find that it will satisfy the whole range.
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8129
Location: United States (CA)
Re: When integer a is divided by 4 the remainder is 2, and when integer b  [#permalink]

Show Tags

New post 24 Aug 2017, 13:43
Bunuel wrote:
When integer a is divided by 4 the remainder is 2, and when integer b is divided by 5 the remainder is 1. How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?

A. Zero
B. One
C. Two
D. Three
E. Four


We use the “quotient remainder theorem,” which states: dividend = divisor x quotient + remainder.
We can create the following equations:

a = 4Q + 2

b = 5Z + 1

So, a can be 2, 6, 10, 14, 18, 22, and 26.

So, b can be 1, 6, 11, 16, 21, and 26.

We see that a + b can be the following:

14 + 6 = 20

10 + 11 = 21

6 + 16 = 22

22 + 1 = 23

18 + 6 = 24

14 + 11 = 25

10 + 16 = 26

6 + 21 = 27

22 + 6 = 28

18 + 11 = 29

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 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.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13412
Re: When integer a is divided by 4 the remainder is 2, and when integer b  [#permalink]

Show Tags

New post 11 Feb 2019, 20:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: When integer a is divided by 4 the remainder is 2, and when integer b   [#permalink] 11 Feb 2019, 20:19
Display posts from previous: Sort by

When integer a is divided by 4 the remainder is 2, and when integer b

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





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