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

 It is currently 18 Jun 2018, 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

# Events & Promotions

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

# If four lines intersect as shown in the figure above, what is the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46146
If four lines intersect as shown in the figure above, what is the [#permalink]

### Show Tags

24 Aug 2017, 01:57
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:02) correct 16% (01:12) wrong based on 67 sessions

### HideShow timer Statistics

If four lines intersect as shown in the figure above, what is the value of (x + y)?

(A) 140
(B) 130
(C) 120
(D) 110
(E) 100

Attachment:

2017-08-24_1249_002.png [ 12.2 KiB | Viewed 998 times ]

_________________
Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1389
Location: Viet Nam
Re: If four lines intersect as shown in the figure above, what is the [#permalink]

### Show Tags

24 Aug 2017, 02:44
Bunuel wrote:
If four lines intersect as shown in the figure above, what is the value of (x + y)?

(A) 140
(B) 130
(C) 120
(D) 110
(E) 100

Attachment:

2017-08-24_1249_002.png [ 12.75 KiB | Viewed 854 times ]

As the image above, we have: x = 70 - 30 = 40
y = 180 - x - 60 = 180 - 40 - 60 = 80

x + y = 40 + 80 = 120

_________________
Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: If four lines intersect as shown in the figure above, what is the [#permalink]

### Show Tags

24 Aug 2017, 03:03
we have to find x+y

Here x+y is sum of exterior angle which is 180-(30+30) =120

For understanding properly refer to attached figure :

In Triangle ABC
Sum of x+y = exterior angle = Angle DCE

Angle DCE = 180-30-30 =120

Therefore x+y = 120

(No need to use angle 70 here )

Attachments

4 line intersect.jpg [ 1.23 MiB | Viewed 791 times ]

Manager
Joined: 12 Feb 2017
Posts: 71
Re: If four lines intersect as shown in the figure above, what is the [#permalink]

### Show Tags

24 Aug 2017, 04:24
Hii,
Here is my solution.

Kudos if it helps.
Attachments

abc.jpg [ 755.77 KiB | Viewed 742 times ]

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2738
Location: United States (CA)
Re: If four lines intersect as shown in the figure above, what is the [#permalink]

### Show Tags

29 Aug 2017, 16:23
Bunuel wrote:

If four lines intersect as shown in the figure above, what is the value of (x + y)?

(A) 140
(B) 130
(C) 120
(D) 110
(E) 100

We can see there are several triangles in this diagram, but let’s only concentrate on two of them. The first one (the smaller one) is the one with the two 30-degree angles. The second one (the larger one) is the one that is composed of the triangle with the x-degree angle and the quadrilateral with the y-degree angle.

In the larger triangle we’ve described above, we see that it has the x-degree and the y-degree angle, and the remaining angle (unlabeled) is actually an exterior angle of the smaller triangle we’ve described above. Recall that an exterior angle of a triangle is equal to the two remote interior angles of the triangle. Thus, this unlabeled angle of the larger triangle is equal to the sum of the two 30-degree angles of the smaller triangle, which is 60 degrees. Thus, we have:

60 + x + y = 180

x + y = 120

Alternate Solution:

Let’s look at the smaller triangle, the one that has x as one of its interior angles. Another interior angle of this triangle is 30, and the remote exterior angle is 70. Since an exterior angle is the sum of the two remote interior angles, x + 30 = 70, and thus x = 40.

Next, let’s look at the triangle that has y and 30 as two of its interior angles. The remaining interior angle is found to be 70, and since the interior angles add up to 180, we must have y + 30 + 70 = 180. Then, y = 80, and thus x + y = 40 + 80 = 120.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: If four lines intersect as shown in the figure above, what is the   [#permalink] 29 Aug 2017, 16:23
Display posts from previous: Sort by