Data Sufficiency

data sufficiency question

In the figure above, if x & y are each less than 90 and PS // QR, is the length of segment PQ less than the length of segment SR?

Please explain step by step and some rules I should know.

sorry also below

1) x > y
2) x + y > 90

nickhar130 wrote:sorry also below

1) x > y
2) x + y > 90

Question : Is PQ < SR ?

Statement 1:
x > y
That means PQ < SR -> Sufficient (Think about x being close to 90 degree and SR being 30 degree, SR will be longer. If you want to prove you can do that as well, just draw a perpendicular line from point p and s to the parallel line below it. Then you can deduce a relationship among, x, PQ, PS and the perpendicular drawn).

Statement 2:

x+y > 90

Not sufficient (As in this case either x > y or y> x, and they affect the length of PQ and SR.

Hence, A

Can someone please explain the rationale behind this problem? I didn't really understand the relation between the length of PS & QR and the measure of the angles...Thanks!

Thouraya wrote:Can someone please explain the rationale behind this problem? I didn't really understand the relation between the length of PS & QR and the measure of the angles...Thanks!

Given in the Question

1. Line PS || Line QR
2. Line PQ forms angle x with line QR
3. Line SR forms angle y with line QR
4. X and y are each < 90
Question asked - Is Length of PQ smaller than SR i.e is PQ<SR


Now

Option A
x>y
If you try to visualize the change in length of line with respect to change in angle x, you could say that as the vale of x increases the length of PQ decreases (Since it is given x<90)

So if X>Y than PQ<SR, hence option 1 alone is sufficient








Evaluating Option B
since x+y>90, and considering x & y each<90, x could be greater, equal, or smaller than y....hence Option 2 not sufficient


therefore Ans is A

nickhar130 wrote:

data sufficiency question

In the figure above, if x & y are each less than 90 and PS // QR, is the length of segment PQ less than the length of segment SR?

Please explain step by step and some rules I should know.

Sometimes it helps to think of real world scenarios to help you visualize what's going on in a question.

We know that the top and bottom lines are parallel, but don't know the relationship between the vertical lines (PQ and SR).

Picture a street with houses on both sides. PS is the north sidewalk and QR is the south sidewalk.

You want to cross the street. What's the shortest distance you can take? Directly across. So, if x or y were 90 degrees, we'd create the shortest possible line.

The more "diagonal" you make your crossing, the greater the distance you have to travel. If you cross from your house to the house directly opposite you, it's a short trip; if you cross from your house to the one across and 10 houses down (in a straight line), it's a much longer trip.

In geometric terms, the further the angle is away from 90 degrees, the longer the journey.

With that in mind, here's what the question is really asking:

"Is x greater than y?"

Accordingly, if we know the relationship between x and y, we can answer the question. (1) clearly gives us the relationship and (2) doesn't, so the correct answer is (A).

Option 1: x>y.

if x =60; y=30, PQ < SR
if x =170 y =30 PQ > SR INSUFFICIENT.

Options 2: x+y > 90

if x = 11; y=80, PQ > RS
if x = 80; y=11, PQ < RS INSUFFICIENT.

Option 1 and 2, together: i.e., x>y and x+y>90

if x = 80; y=11, PQ < RS
if x = 170; y=30 , PQ > RS INSUFFICIENT.

Stuart, Could you please correct my approach and guide me where am I wrong? As per the approach given above I am getting E.

bubbliiiiiiii wrote:Option 1: x>y.

if x =60; y=30, PQ < SR
if x =170 y =30 PQ > SR INSUFFICIENT.

Options 2: x+y > 90

if x = 11; y=80, PQ > RS
if x = 80; y=11, PQ < RS INSUFFICIENT.

Option 1 and 2, together: i.e., x>y and x+y>90

if x = 80; y=11, PQ < RS
if x = 170; y=30 , PQ > RS INSUFFICIENT.

Stuart, Could you please correct my approach and guide me where am I wrong? As per the approach given above I am getting E.

Your mistake is a simple one - you didn't take into account the condition set in the question stem:

In the figure above, if x & y are each less than 90 and...

Thanks for pointing that out.