Properties of numbers Quant Review 2nd Ed #172

Expert replies

runningguy: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Jul 22, 2013 4:40 pm; Thanked: 1 times

by runningguy » Fri Sep 20, 2013 2:05 pm

If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A) x+z/z
B) y+z/x
C) x+y/z
D) xy/z
E) yz/x

Like this post

Source: Beat The GMAT — Problem Solving | Fri Sep 20, 2013 2:05 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Sep 20, 2013 2:27 pm

runningguy wrote:If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A) x+z/z
B) y+z/x
C) x+y/z
D) xy/z
E) yz/x

Let y=20.
Since x is a factor of y, let x=10.
Since x is a multiple of z, let z=5.

A: (x+z)/z = (10+5)/5 = 3.
B: (y+z)/x = (20+5)/10 = 2.5.

B is not necessarily an integer.
No need to check the remaining answer choices.

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

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Sep 20, 2013 2:42 pm

runningguy wrote:If x, y, and z are positive integers such that x is a factor of y, and x is a multiple of z, which of the following is NOT necessarily an integer?

A) (x+z)/z
B) (y+z)/x
C) (x+y)/z
D) (xy)/z
E) (yz)/x

Note: To avoid confusion, I added some brackets to your answer choice.
Mitch already showed the approach of looking for values of x, y and z, such that we get a non-integer.

Here's another approach:

x is a multiple of z
So, we can say that x = kz (for some integer k)

x is a factor of y
In other words, y is a multiple of x.
So, we can say that y = jx (for some integer j)
IMPORTANT: Since we already know that x = kz, let's replace x with kz to get: y = jkz

So, x = kz, y = jkz and z = z.
Let's plug in these values to see what we get:

A) (x+z)/z = (kz+z)/z = k+1 (= INTEGER)
B) (y+z)/x = (jkz+z)/kz = (jk+1)/k (not necessarily an integer)
C) (x+y)/z = (kz+jkz)/z = k+jk (= INTEGER)
D) (xy)/z = [(kz)(jkz)]/z = jkÂ²z (= INTEGER)
E) (yz)/x = [(jkz)(z)]/kz = jz (= INTEGER)

Answer = B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sat Sep 21, 2013 5:32 am

X * _ = y
Z * _ = x
Let,
z=2
x=4
y=8
(A) (4+2)/2 -- INTEGER
(B) (8+2)/4 -- NOT AN INTEGER
(C) (4+8)/2 -- INTEGER
(D) 4*8/2 -- INTEGER
(E) 8*2/4 -- INTEGER

ANSWER [spoiler]{B}[/spoiler]

R A H U L

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review