 It is currently 09 Aug 2020, 01:13 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If x, y, and z are integers, y + z = 13, and xz = 9, which o  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Retired Moderator Joined: 07 Jun 2014
Posts: 4804
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 167

Kudos [?]: 2823 , given: 394

If x, y, and z are integers, y + z = 13, and xz = 9, which o [#permalink]
Expert's post 00:00

Question Stats: 77% (01:33) correct 22% (01:18) wrong based on 48 sessions
If x, y, and z are integers, y + z = 13, and xz = 9, which of the following must be true?

(A) x is even
(B) x = 3
(C) y is odd
(D) y > 3
(E) z < x
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Manager  Joined: 06 Jun 2018
Posts: 94
Followers: 2

Kudos [?]: 77  , given: 0

Re: If x, y, and z are integers, y + z = 13, and xz = 9, which o [#permalink]
3
KUDOS
sandy wrote:
If x, y, and z are integers, y + z = 13, and xz = 9, which of the following must be true?

(A) x is even
(B) x = 3
(C) y is odd
(D) y > 3
(E) z < x

xz = 9

Possible combinations:

3*3 = 9

1*9 = 9

9*1= 9

Now we can fint out the different values of y substituting the value of z.

y + z = 13

y + 3 = 13

y = 10

again,

y + z = 13

y + 1 = 13

y = 12

again,

y + z = 13

y + 9 = 13

y = 4.

In all cases y>3. GRE Instructor Joined: 10 Apr 2015
Posts: 3652
Followers: 141

Kudos [?]: 4196  , given: 67

Re: If x, y, and z are integers, y + z = 13, and xz = 9, which o [#permalink]
1
KUDOS
Expert's post
sandy wrote:
If x, y, and z are integers, y + z = 13, and xz = 9, which of the following must be true?

(A) x is even
(B) x = 3
(C) y is odd
(D) y > 3
(E) z < x

The most limiting fact is that x, y, and z are INTEGERS

So, if xz = 9, there are only 6 possible cases:
CASE A: x = 1 and z = 9
CASE B: x = -1 and z = -9
CASE C: x = 9 and z = 1
CASE D: x = -9 and z = -1
CASE E: x = 3 and z = 3
CASE F: x = -3 and z = -3

Since we also know that y + z = 13, we can add the corresponding y-value to each of the 6 possible CASES to get:

CASE A: x = 1, z = 9, and y = 4
CASE B: x = -1, z = -9, and y = 22
CASE C: x = 9, z = 1, and y = 12
CASE D: x = -9, z = -1, and y = 14
CASE E: x = 3, z = 3, and y = 10
CASE F: x = -3, z = -3, and y = 16

When we scan the answer choices, we can see that D must be true since all 6 possible y-values are greater than 3.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll love my GRE prep course! Manager Joined: 19 Mar 2018
Posts: 58
Followers: 1

Kudos [?]: 23 , given: 14

Re: If x, y, and z are integers, y + z = 13, and xz = 9, which o [#permalink]
xz = 9
y + z = 13

xz = 9--> x or y can be -3/ +3/ -9/ +9/-1/+1 --> we also don't know which is x and which is z. But each can have 6 values

y + z = 13

10+3 = 16 - 3 = 12 + 1 = 14 - 1 = 13 (all equations come to 13)

so y is even

Out of the options:
(A) x is even --> no
(B) x = 3 --> no and yes / not suff
(C) y is odd --> no its even
(D) y > 3 --> YES in all cases
(E) z < x --> we don't know exact value of x or z, not suff

D is best Re: If x, y, and z are integers, y + z = 13, and xz = 9, which o   [#permalink] 13 Sep 2018, 12:15
Display posts from previous: Sort by

# If x, y, and z are integers, y + z = 13, and xz = 9, which o  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.