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

 It is currently 16 Jan 2019, 21:01

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# Given the figure to the left, is y less than 35?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52164
Given the figure to the left, is y less than 35?  [#permalink]

### Show Tags

09 Feb 2015, 05:41
1
5
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:29) correct 34% (02:30) wrong based on 172 sessions

### HideShow timer Statistics

Attachment:

Q4_1.png [ 19.3 KiB | Viewed 2464 times ]
Given the figure to the left, is y less than 35?

(1) m and n are parallel lines
(2) x is an acute angle

Kudos for a correct solution.

_________________
Manager
Joined: 14 Sep 2014
Posts: 105
Concentration: Technology, Finance
WE: Analyst (Other)
Re: Given the figure to the left, is y less than 35?  [#permalink]

### Show Tags

10 Feb 2015, 05:11
1
See picture attached. Z represents the complimentary angle of x.

(1) m and n are parallel lines [Insufficent] Using the rules of corresponding angles and parallel lines, we can see where the y+25 angle comes into the inner triangle. We also know the complementary angle of 180-y is y, so adding all three angles of the inner triangle together, we get $$(y+25) + y + z = 180$$ or $$2y + z = 155$$. Depending on z, y could still be greater or less than 35.
(2) x is an acute angle [Insufficient] This tells us that z is at least 91 degrees. It does not provide any information of the other angles in the triangle.

Taking both statements together allows us to test different values of z in the equation $$2y + z = 155$$. The larger z becomes the smaller y is, so by testing the smallest possible value of z, we can see how large y can be. If we use z = 91, then $$2y + 91 = 155$$ and $$2y = 44$$ and $$y = 22$$.

Y is less than or equal to 22, so it is definitely less than 35. The correct answer is C.
Attachments

Untitled.jpg [ 12.69 KiB | Viewed 2269 times ]

Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: Given the figure to the left, is y less than 35?  [#permalink]

### Show Tags

10 Feb 2015, 06:22
sterling19 wrote:
See picture attached. Z represents the complimentary angle of x.

(1) m and n are parallel lines [Insufficent] Using the rules of corresponding angles and parallel lines, we can see where the y+25 angle comes into the inner triangle. We also know the complementary angle of 180-y is y, so adding all three angles of the inner triangle together, we get $$(y+25) + y + z = 180$$ or $$2y + z = 155$$. Depending on z, y could still be greater or less than 35.
(2) x is an acute angle [Insufficient] This tells us that z is at least 91 degrees. It does not provide any information of the other angles in the triangle.

Taking both statements together allows us to test different values of z in the equation $$2y + z = 155$$. The larger z becomes the smaller y is, so by testing the smallest possible value of z, we can see how large y can be. If we use z = 91, then $$2y + 91 = 155$$ and $$2y = 44$$ and $$y = 22$$.

Y is less than or equal to 22, so it is definitely less than 35. The correct answer is C.

hi sterling,
there is some problem in your calculations..
Y can take a max value of 32.5...
2y + 91 =155.. 2y=64 so y =32..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: Given the figure to the left, is y less than 35?  [#permalink]

### Show Tags

10 Feb 2015, 06:27
1
ans C..
1) statement one tells us both lines parallel.. so alternate angle can be known... insufficient..
2) it gives z(exterior angle) a max value of 90,.. insufficient

combined max value of Z=90=y+25+y or y=32.5..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 27 Oct 2013
Posts: 210
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Re: Given the figure to the left, is y less than 35?  [#permalink]

### Show Tags

10 Feb 2015, 07:40
2
Here we go:

Is y less than 35?

Lets call the triangle formed in the image as ABC

Angle A = 180 - x (Linear angle property)
Angle C = 180 - (180 - y) = y (Linear angle property)

A + B + C = 180 (Sum of angles of a triangle) ---- (1)

St1: m and n are parallel lines

So alternate angles will be equal.

Hence angle B = y + 25

Substitute in (1)

180 - x + y + y + 25 = 180

x = 2y + 25

We can not say for sure whether y < 35 from the above equation

St1 is not sufficient

St2: x is an acute angle

Clearly not sufficient

Combining St1 and St2

x = 2y + 25, and x is an acute angle.

so 2y + 25 < 90
2y < 65
y < 32.5

Option C is correct
Manager
Joined: 17 Dec 2013
Posts: 57
GMAT Date: 01-08-2015
Re: Given the figure to the left, is y less than 35?  [#permalink]

### Show Tags

10 Feb 2015, 11:34
1
Quote:
Given the figure to the left, is y less than 35?

(1) m and n are parallel lines
(2) x is an acute angle

(1) tells us that the lines are parallel, which leads us to think about alternate angles. Now we know that the triangle n + unnamed lines has y+25 as one of its angles. the other one is y and the other one is 180-x. but we need to know how much x can be, before we know if y can be less than 35.
(2) tells us that x is an acute angle, but thats it.

with (1/2) we can max x as 90 degree. thru this way we can conclude that 2y can me max 180-90-25=65 degrees. so y can be max 32,5 degrees.

C is sufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 52164
Re: Given the figure to the left, is y less than 35?  [#permalink]

### Show Tags

16 Feb 2015, 04:30
Bunuel wrote:

Given the figure to the left, is y less than 35?

(1) m and n are parallel lines
(2) x is an acute angle

Kudos for a correct solution.

The correct response is (C).

Let’s draw a third parallel line that goes through angle x.

We can split x into two angles, let’s call them a and b. We also know that the angle supplemental to 180-y will be equal to y, since supplemental angles sum to 180 (180 – y + y = 180).

We know have two sets of alternate interior angles, which we know must be equal.

a = y + 25, and b = y.

Attachment:

Q4_2.png [ 24.57 KiB | Viewed 2109 times ]

The original angle x = a + b. Using substitution, x = y + 25 + y, or x = 2y + 25.

Since Statement (2) tell us that x is acute, we know x < 90. Therefore 2y + 25 < 90. We can solve for the range of possible y values:

2y + 25 < 90 2y < 65 y < 32.5 Since all values that are less than 32.5 are also less than 35, the correct answer is (C).

If you chose (A), knowing that m and n are parallel is a vital piece of information but without ALSO knowing the approximate size of x, we cannot determine the range of possible y values.

If you chose (B), make you don’t make assumptions about lines on the GMAT. Lines may sometimes look parallel, but are not actually parallel.

If you chose (D), while both pieces of information are valuable, independently they are not enough to be sufficient.

If you chose (E), you may want to review the properties of angles formed when parallel lines are cut by a transversal.
_________________
Manager
Joined: 17 Oct 2015
Posts: 106
Location: India
Concentration: Finance
Schools: ISB '18 (S)
GMAT 1: 690 Q47 V37
GMAT 2: 700 Q44 V41
WE: Corporate Finance (Commercial Banking)
Re: Given the figure to the left, is y less than 35?  [#permalink]

### Show Tags

20 Mar 2016, 02:46
A very classic question. I made an error to assume things from figure and assumed m//n. ignored option 1 and said 2 is sufficient. But later realized, its better not to assume from figures in gmat.
Non-Human User
Joined: 09 Sep 2013
Posts: 9423
Re: Given the figure to the left, is y less than 35?  [#permalink]

### Show Tags

17 Apr 2018, 08:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Given the figure to the left, is y less than 35? &nbs [#permalink] 17 Apr 2018, 08:53
Display posts from previous: Sort by