BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

If when a certain integer x is divided by 5, the remainder

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Tue Jan 22, 2019 2:24 pm
swerve wrote:If when a certain integer x is divided by 5, the remainder is 2, then each of the following could also be an integer EXCEPT:

A. x/17
B. x/10
C. x/6
D. x/3
E. x/11
Since dividing x by 5 yields a remainder, x is not a multiple of 5 and thus not a multiple of 10.
Since x is not a multiple of 10, x/10 cannot yield an integer value.

The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Jan 22, 2019 2:32 pm
swerve wrote:If when a certain integer x is divided by 5, the remainder is 2, then each of the following could also be an integer EXCEPT:

A. x/17
B. x/10
C. x/6
D. x/3
E. x/11

The OA is B

Source: Princeton Review
Here's another (longer) approach:

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.

When a certain integer x is divided by 5, the remainder is 2
So, the possible values of x are as follows: 2, 7, 12, 17, 22, 27, 32, . . . etc
Let's use these values to ELIMINATE answer choices

If x = 12, then x/3 is an integer. ELIMINATE D
If x = 12, then x/6 is an integer. ELIMINATE C
If x = 17, then x/17 is an integer. ELIMINATE A
If x = 22, then x/11 is an integer. ELIMINATE E

By the process of elimination, the correct answer is B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

by fskilnik@GMATH » Wed Jan 23, 2019 3:30 am
swerve wrote:If when a certain integer x is divided by 5, the remainder is 2, then each of the following could also be an integer EXCEPT:

A. x/17
B. x/10
C. x/6
D. x/3
E. x/11
Source: Princeton Review
$$x = 5M + 2,\,\,\,M\,\,\operatorname{int} \,\,\,\,\,\,\left( * \right)$$
$$?\,\,\,:\,\,\,{\text{not}}\,\,\,{\text{integer}}$$

$$\left( {\text{A}} \right)\,\,M = 3\,\,{\text{refutes}}$$
$$\left( {\text{B}} \right)\,\,\frac{x}{{10}} = \operatorname{int} \,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,2} \,\,\,\,\frac{x}{5} = \operatorname{int} \,\,\,\, \Rightarrow \,\,\,x\,\,{\text{divisible}}\,\,{\text{by}}\,\,5\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{\text{impossible}}$$


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Sun Jan 27, 2019 6:38 pm
swerve wrote:If when a certain integer x is divided by 5, the remainder is 2, then each of the following could also be an integer EXCEPT:

A. x/17
B. x/10
C. x/6
D. x/3
E. x/11

The OA is B

Source: Princeton Review
Since, when x is divisible by 5, the remainder is 2, x can be values such as:

2, 7, 12, 17, 22

So we see that x/17, x/6, x/3, and x/11 can all be integers. Thus x/10 cannot be an integer.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1