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

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..

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

(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.

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.


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.

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.

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?

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.