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

 It is currently 19 May 2019, 00:15 ### 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. ### Request Expert Reply # In the figure above, if x, y and z are integers such that x < y < zIn

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

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55150
In the figure above, if x, y and z are integers such that x < y < zIn  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 53% (02:15) correct 47% (02:17) wrong based on 47 sessions

### HideShow timer Statistics In the figure above, if x, y and z are integers such that x < y < z, then the least and the greatest possible values of x + z are

(A) 59 and 91
(B) 59 and 135
(C) 91 and 178
(D) 120 and 135
(E) 120 and 178

Attachment: 2017-08-15_1321_001.png [ 5.38 KiB | Viewed 1094 times ]

_________________
BSchool Forum Moderator V
Joined: 28 Mar 2017
Posts: 1211
Location: India
GMAT 1: 730 Q49 V41 GPA: 4
Re: In the figure above, if x, y and z are integers such that x < y < zIn  [#permalink]

### Show Tags In the figure above, if x, y and z are integers such that x < y < z, then the least and the greatest possible values of x + z are

(A) 59 and 91
(B) 59 and 135
(C) 91 and 178
(D) 120 and 135
(E) 120 and 178

For max value:
x=1 and y=2; Thus, z=177 => x+z=178

For min value:
x=1 and y=89; Thus, z=90 => x+z=91

Answer "C"
_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7667
Re: In the figure above, if x, y and z are integers such that x < y < zIn  [#permalink]

### Show Tags

Bunuel wrote: In the figure above, if x, y and z are integers such that x < y < z, then the least and the greatest possible values of x + z are

(A) 59 and 91
(B) 59 and 135
(C) 91 and 178
(D) 120 and 135
(E) 120 and 178

Attachment:
2017-08-15_1321_001.png

Hi..

x<y<z....
x+y+z=180..
LEAST value of x+z...
Make y the MAX. For this make y=z-1 and z the least that is 1..
So z+y=180-1=179.....z+z-1=179....2z=180.....z=90 and y=z-1=90-1=89...
$$x+z=1+90=91$$

MAX value of x+z...
Make y the least. For this make x=1 and y=2, so z=177...
$$x+z=1+177=178$$

C
_________________
Intern  B
Joined: 15 Sep 2014
Posts: 10
Location: India
Concentration: General Management, International Business
GPA: 3.36
WE: Programming (Consulting)
Re: In the figure above, if x, y and z are integers such that x < y < zIn  [#permalink]

### Show Tags

Hi chetan2u,

How did you deduce this "For this make y=z-1 and z the least that is 1"?
Can you kindly explain?

Thanks,
Abhishek
Manager  B
Joined: 31 Oct 2016
Posts: 106
Re: In the figure above, if x, y and z are integers such that x < y < zIn  [#permalink]

### Show Tags

The answer is C.

x+y+z = 180
For the greatest value of x+z, y must be minimal, but greater than 1: 1+2+177 = 180. 1+177 = 178
For least value of x+z, y must be maximal, but less than 90: 1+89+90 = 180. 1+90 = 91
Intern  Joined: 21 Jun 2015
Posts: 6
Re: In the figure above, if x, y and z are integers such that x < y < zIn  [#permalink]

### Show Tags

Why C?
180-91=89 which could be y
and z>y
Why not D

Sent from my iPhone using GMAT Club Forum
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: In the figure above, if x, y and z are integers such that x < y < zIn  [#permalink]

### Show Tags

Bunuel wrote: In the figure above, if x, y and z are integers such that x < y < z, then the least and the greatest possible values of x + z are

(A) 59 and 91
(B) 59 and 135
(C) 91 and 178
(D) 120 and 135
(E) 120 and 178

Since x, y, and z are the interior angles of a triangle, the relation x + y + z = 180 holds. Passing y to the right-hand side of the equality, we get x + z = 180 - y. Therefore, if we can determine the least and the greatest possible value for y, we will be able to determine the greatest and the least possible value of x + z.

Since x and y are integers and x cannot be zero, the least possible value of x is 1. Therefore, the least possible value of y is 2. Then, the greatest possible value of x + z is 180 - 2 = 178.

Let’s determine the greatest possible value of y. To do that, we need to minimize the values of x and z. We already know the smallest possible value of x is 1. Thus, we are looking for the greatest integer value of y where y < z and y + z = 179. We note that y attains its greatest value when y and z are as close to each other as possible. Since 179/2 = 89.5, we see that the greatest integer value of y is 89 (and the smallest possible integer value of z is 90). Then, the least possible value of x + z is 180 - 89 = 91.

Answer: C
_________________

# Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

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. Re: In the figure above, if x, y and z are integers such that x < y < zIn   [#permalink] 18 Aug 2017, 09:10
Display posts from previous: Sort by

# In the figure above, if x, y and z are integers such that x < y < zIn

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  