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

It is currently 14 Dec 2019, 16:39

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

Which of the following MUST yield an integer when divided by 5?

  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: 59725
Which of the following MUST yield an integer when divided by 5?  [#permalink]

Show Tags

New post 15 Jul 2015, 03:20
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

84% (01:11) correct 16% (01:26) wrong based on 115 sessions

HideShow timer Statistics

Which of the following MUST yield an integer when divided by 5?

A. The sum of five consecutive positive integers.
B. The square of a prime number.
C. The sum of two odd integers.
D. The product of three consecutive odd numbers.
E. The difference between a multiple of 8 and a multiple of 3.


Kudos for a correct solution.

_________________
Manager
Manager
avatar
Joined: 14 Sep 2014
Posts: 86
WE: Engineering (Consulting)
Re: Which of the following MUST yield an integer when divided by 5?  [#permalink]

Show Tags

New post 15 Jul 2015, 04:02
1
A . let numbers be x-2, x-1, x, x+1, x+2; their sum 5x --> Always Divisible
Problems wither options

B. Prime number can be 3,7.

C. again 3+9 = 12

D. 3 consecutive odd integers may be = 17,19,21 (Not divisible by 5)

E. Multiple of 8 : 8x, Multiple of 3 : 3y; Their Difference 8x-3y (Not Necessarily divisible by 5, Only possible if x=y)
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2560
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: Which of the following MUST yield an integer when divided by 5?  [#permalink]

Show Tags

New post 15 Jul 2015, 04:47
Bunuel wrote:
Which of the following MUST yield an integer when divided by 5?

A. The sum of five consecutive positive integers.
B. The square of a prime number.
C. The sum of two odd integers.
D. The product of three consecutive odd numbers.
E. The difference between a multiple of 8 and a multiple of 3.


Kudos for a correct solution.


Straightforward question:

As this is a MUST be true question, the correct answer MUST stay true for all possible values.

A can be proven as follows : The 5 consecutive integers can be represenetd as : x, x+1, x+2, x+3, x+4 (x can be any positive integer value). Thus their sum = 5x+10 =5(x+2)---> Thus this sum is ALWAYS divisible by 5 and is thus the correct answer.

For proving other statements as false:

B : 2^2 is not divible by 5.
C: 3+11 is not divisble by 5
D: 7*9*11 is not divisible by 5
E: 24-3 is not divisble by 5
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Jun 2015
Posts: 279
Concentration: Finance
GPA: 3.5
Re: Which of the following MUST yield an integer when divided by 5?  [#permalink]

Show Tags

New post 15 Jul 2015, 05:50
1
For option A: Let the numbers be (x-2), (x-1), (x), (x+1), (x+2).

Now, (x-2)+(x-1) + (x) + (x+1) + (x+2) = 5(x). Hence A is true. No need to check other answers since there can only be one correct answer.

So, Ans(A).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Manager
Manager
avatar
Joined: 20 Jul 2011
Posts: 78
GMAT 1: 660 Q49 V31
GMAT ToolKit User
Re: Which of the following MUST yield an integer when divided by 5?  [#permalink]

Show Tags

New post 17 Jul 2015, 22:39
Bunuel wrote:
Which of the following MUST yield an integer when divided by 5?

A. The sum of five consecutive positive integers.
B. The square of a prime number.
C. The sum of two odd integers.
D. The product of three consecutive odd numbers.
E. The difference between a multiple of 8 and a multiple of 3.


Kudos for a correct solution.


A. Plugin numbers: 1+2+3+4+5= 15/5, 12+13+14+15+16=70/5, Hence this holds true for all cases. Lets check the other options as well.
B. 2^2 = 4/5(Not divisible), 5^2(divisible). Not always true.
C. 5+3 not divisible, but 3 + 7 is divisible. Not always true.
D. 1*3*5 is divisible, but 7*9*11 is not. Not always true.
E. 8-3 is divisible, but 16-3 is not.

Hence answer is option A.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59725
Re: Which of the following MUST yield an integer when divided by 5?  [#permalink]

Show Tags

New post 19 Jul 2015, 13:12
Bunuel wrote:
Which of the following MUST yield an integer when divided by 5?

A. The sum of five consecutive positive integers.
B. The square of a prime number.
C. The sum of two odd integers.
D. The product of three consecutive odd numbers.
E. The difference between a multiple of 8 and a multiple of 3.


Kudos for a correct solution.


800score Official Solution:

(A) Another way to phrase the question is: Which of the following is divisible by 5?

Choice (A) might take some time to figure out. Others are easier.

(B) is wrong — many squares of primes, such as 2², are not divisible by 5.

(C) is also wrong: consider 3 + 9 = 12.

(D) is incorrect; one example is (7)(9)(11), which is not divisible by 5.

(E) can be shown to be wrong as well: For instance, the difference between 16 and 9 is 7.

Choice (A), then, must be correct. If the first of the five consecutive positive integers is x, the full list is:
x + (x +1) + (x + 2) + (x + 3) + (x + 4) = 5x + 10

Since x is an integer, 5x is divisible by 5. 10 is also divisible by 5. Then, 5x + 10 is divisible by 5.
_________________
GMAT Club Bot
Re: Which of the following MUST yield an integer when divided by 5?   [#permalink] 19 Jul 2015, 13:12
Display posts from previous: Sort by

Which of the following MUST yield an integer when divided by 5?

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





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