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

Question

Q4_1.png 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 .

sterling19 · Answer

See picture attached. Z represents the complimentary angle of x.

(1) m and n are parallel lines    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    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 .

chetan2u · Answer

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..

chetan2u · Answer

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..

DesiGmat · Answer

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

eddyki · Answer

(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.

Bunuel · Answer

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. Q4_2.png 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.

Youraisemeup · Answer

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.

lakshya14 · Answer

Bunuel  , 
if the triangle formed has angels y + (y+25) + 91(minimum of acute angle difference) = 180,
the the value of y would be 34. Which satisfies the equation. Also if the acute angle keeps decreasing, then 91 will keep increasing and y will keep decreasing. Which satisfies with (B) only. Where am I getting it wrong?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards