Assumptions in Figures

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 184
Joined: Sat Apr 14, 2007 9:23 am
Location: Madison, WI
Thanked: 17 times

Assumptions in Figures

by ldoolitt » Sat Mar 26, 2011 11:52 am
So given any quant question (this one is taken from the DS section on this site), I understand that you cannot make assumptions about line lengths and angles based off of the scale of the figure. However is it a safe assumption that if a point appears to lie on a line, but is not stated, that it actually lies on the line? In the below example it DOESN'T state that point E lies on segment BD, but the solution assumes that it does. Whats the rule on that?


Image
Source: — Data Sufficiency |

Master | Next Rank: 500 Posts
Posts: 423
Joined: Fri Jun 11, 2010 7:59 am
Location: Seattle, WA
Thanked: 86 times
Followed by:2 members

by srcc25anu » Sat Mar 26, 2011 3:32 pm
point E is on the line ... clearly marked as such. we will not be making any assumption if we take it as given. though we cannot assume the angle it makes with line BD. we cant assume angle AED to be 90 degree even though it seems like one. that would be an assumption.

it would be something similar: like we clearly see that AC is a straight line but its not explicitly mentioned so can we assume AC to be a curve? answer will be no, we should not make such assumptions.

hope i am clear.

Master | Next Rank: 500 Posts
Posts: 423
Joined: Fri Jun 11, 2010 7:59 am
Location: Seattle, WA
Thanked: 86 times
Followed by:2 members

by srcc25anu » Sat Mar 26, 2011 3:36 pm
I think answer should be C

stat 1:tells us nothing about either of the angles of the triangle AEC

stat 2: it tells us one of the angles of triangle AEC but doesnt give any of the sides

together, stat 1 and 2 give us one side and one angle ... with that we can deduce all other sides and angles given the fact that each of angles A, B, C and D are right angles. or that ABCD is a rectangle.

Master | Next Rank: 500 Posts
Posts: 184
Joined: Sat Apr 14, 2007 9:23 am
Location: Madison, WI
Thanked: 17 times

by ldoolitt » Sat Mar 26, 2011 5:49 pm
srcc25anu wrote:point E is on the line ... clearly marked as such. we will not be making any assumption if we take it as given. though we cannot assume the angle it makes with line BD. we cant assume angle AED to be 90 degree even though it seems like one. that would be an assumption.

it would be something similar: like we clearly see that AC is a straight line but its not explicitly mentioned so can we assume AC to be a curve? answer will be no, we should not make such assumptions.

hope i am clear.
True, but the instructions are...
A figure accompanying a problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible. Exceptions will be noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise noted.
With the bolded evidence applying to your statement. It states specifically that lines that appear to be straight are straight. It does not specifically state that points that appear to be on a line are actually on a line, although it does say that the order of points is correct as drawn.

So I am curious what the answer is. Maybe an instructor or someone with massive GMAT experience can chime in.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Thu Mar 31, 2011 12:25 pm
I was asked the same question on gmatclub, so I'll just paste my reply here:

In general, you should not trust the scale of GMAT diagrams, either in Problem Solving or Data Sufficiency. It used to be true that Problem Solving diagrams were drawn to scale unless mentioned otherwise, but I've seen recent questions where that is clearly not the case. So I'd only trust a diagram I'd drawn myself. ...

Here I'm referring only to the scale of diagrams; the relative lengths of line segments in a triangle, for example. ... You can accept the relative ordering of points and their relative locations as given (if the vertices of a pentagon are labeled ABCDE clockwise around the shape, then you can take it as given that AB, BC, CD, DE and EA are the edges of the pentagon; if a line is labeled with four points in A, B, C, D in sequence, you can take it as given that AC is longer than both AB and BC; if a point C is drawn inside a circle, unless the question tells you otherwise, you can assume that C is actually within the circle; if what appears to be a straight line is labeled with three points A, B, C, you can assume the line is actually straight, and that B is a point on the line -- the GMAT would never include as a trick the possibility that ABC actually form a 179 degree angle that is imperceptible to the eye, to give a few examples).

So don't trust the lengths of lines, but do trust the sequence of points on a line, or the location of points within or outside figures in a drawing.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com