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

 It is currently 18 May 2019, 23:37

### 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

# In the figure above, x = y/2, and z = 3y/8. What is the degree measure

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55150
In the figure above, x = y/2, and z = 3y/8. What is the degree measure  [#permalink]

### Show Tags

08 Aug 2017, 10:26
00:00

Difficulty:

25% (medium)

Question Stats:

87% (01:41) correct 13% (01:37) wrong based on 32 sessions

### HideShow timer Statistics

In the figure above, x = y/2, and z = 3y/8. What is the degree measure of the smallest angle of the triangle?

(A) 96
(B) 72
(C) 48
(D) 36
(E) 12

Attachment:

2017-08-08_2125.png [ 6.04 KiB | Viewed 650 times ]

_________________
Director
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: In the figure above, x = y/2, and z = 3y/8. What is the degree measure  [#permalink]

### Show Tags

08 Aug 2017, 11:21
Bunuel wrote:

In the figure above, x = y/2, and z = 3y/8. What is the degree measure of the smallest angle of the triangle?

(A) 96
(B) 72
(C) 48
(D) 36
(E) 12

Attachment:
2017-08-08_2125.png

Sum of angles of triangle $$= 180^{\circ}$$

$$x + y + z = 180$$

Given; $$x = \frac{y}{2}$$, and $$z = \frac{3y}{8}$$

$$\frac{y}{2} + y + \frac{3y}{8} = 180$$

$$\frac{4y + 8y + 3y}{8} = 180$$

$$15y = 180 * 8$$

$$y = \frac{180 * 8}{15} => 96$$

$$x = \frac{y}{2} = \frac{96}{2} => 48$$

$$z = \frac{3y}{8} = \frac{3*96}{8} => 36$$

Therefore, degree measure of the smallest angle of the triangle $$= 36$$

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: In the figure above, x = y/2, and z = 3y/8. What is the degree measure  [#permalink]

### Show Tags

08 Aug 2017, 22:20

Since x = $$\frac{y}{2}$$, we can say that y = 2x
Since z = $$\frac{3y}{8}$$ we can say that z = $$\frac{3(2x)}{8}$$ = $$\frac{3x}{4}$$

We know that x+y+z = 180
Substituting these values, we have $$x + 2x + \frac{3x}{4} = 3x + \frac{3x}{4} = 180$$
$$3x + \frac{3x}{4} = 3x(1+\frac{1}{4}) = 3x(\frac{5}{4}) = 180$$
$$3x = 180*\frac{4}{5}$$
Therefore, $$x = \frac{180*4}{5*3} = 12*4 = 48$$

The smallest angle is $$\frac{3x}{4} = \frac{3}{4}*48$$ = 36(Option D)

_________________
You've got what it takes, but it will take everything you've got
Re: In the figure above, x = y/2, and z = 3y/8. What is the degree measure   [#permalink] 08 Aug 2017, 22:20
Display posts from previous: Sort by