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

 It is currently 24 Jun 2018, 11:14

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46316
In the figure above, if x, y and z are integers such that x < y < zIn [#permalink]

### Show Tags

15 Aug 2017, 02:25
00:00

Difficulty:

45% (medium)

Question Stats:

46% (01:43) correct 54% (01:26) wrong based on 59 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 779 times ]

_________________
Joined: 28 Mar 2017
Posts: 1022
Location: India
Concentration: Finance, Technology
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

15 Aug 2017, 03:40

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

_________________

Kudos if my post helps!

Long And A Fruitful Journey - V21 to V41; If I can, So Can You!!

My study resources:
1. Useful Formulae, Concepts and Tricks-Quant
2. e-GMAT's ALL SC Compilation
3. LSAT RC compilation
4. Actual LSAT CR collection by Broal
5. QOTD RC (Carcass)
6. Challange OG RC
7. GMAT Prep Challenge RC

Math Expert
Joined: 02 Aug 2009
Posts: 5938
Re: In the figure above, if x, y and z are integers such that x < y < zIn [#permalink]

### Show Tags

15 Aug 2017, 04:15
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Intern
Joined: 15 Sep 2014
Posts: 10
Location: India
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

15 Aug 2017, 10:27
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
Joined: 31 Oct 2016
Posts: 87
Re: In the figure above, if x, y and z are integers such that x < y < zIn [#permalink]

### Show Tags

15 Aug 2017, 10:41

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

15 Aug 2017, 14:07
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
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: In the figure above, if x, y and z are integers such that x < y < zIn [#permalink]

### Show Tags

18 Aug 2017, 09:10
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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

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