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

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

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09 Feb 2015, 06:41
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55% (hard)

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67% (02:29) correct 33% (02:29) wrong based on 168 sessions

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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.

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Re: Given the figure to the left, is y less than 35?  [#permalink]

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10 Feb 2015, 06:11
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.
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Re: Given the figure to the left, is y less than 35?  [#permalink]

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10 Feb 2015, 07:22
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..
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Re: Given the figure to the left, is y less than 35?  [#permalink]

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10 Feb 2015, 07:27
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..
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Given the figure to the left, is y less than 35?  [#permalink]

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10 Feb 2015, 08:40
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
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Re: Given the figure to the left, is y less than 35?  [#permalink]

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10 Feb 2015, 12:34
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.
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Re: Given the figure to the left, is y less than 35?  [#permalink]

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16 Feb 2015, 05:30
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 1977 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.
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Re: Given the figure to the left, is y less than 35?  [#permalink]

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20 Mar 2016, 03:46
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.
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Re: Given the figure to the left, is y less than 35?  [#permalink]

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17 Apr 2018, 09:53
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Re: Given the figure to the left, is y less than 35? &nbs [#permalink] 17 Apr 2018, 09:53
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