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DS Problems Need help!

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DS Problems Need help!

by kguo » Sun Oct 11, 2009 5:57 pm
1. Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

(1) Two of the interior angles of ABCD are right angles.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

I don't get why the answer is what is is... isn't two right angles inside a quadrilateral automatically a rectangle??

E


2. If X and Y are points on the number line, what is the value of x+y?

(1) 6 is halfway between x and y.

(2) y = 2x

I'm probably just interpreting the question wrong why is why i don't understand the answer.

a
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Source: — Data Sufficiency |
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by mehravikas » Sun Oct 11, 2009 8:08 pm
Question 2 is correct. consider points on the number line.

6 is halfway between x and y. therefore values could be:
0 - 6 - 12
3 - 6 - 9
2 - 6 - 10
-6 - 6 - 18

Remember you are not asked about individual values, you need to calculate the sum, which is always 12.
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by bullzeye » Mon Oct 12, 2009 6:49 am
The answer to 1 is also correct.

To your question - no a 2 right angles are not sufficient for a quadrilateral to be a rectangle. You can draw pictures if you want. If you have 2 right angles, the only other think you can take out of this is that the sum of die other two angles is 360 - 2x180 = 180
statement 2 is misleading, esp. considering it in combination with statement 1.

So we have rectangle with 2x90 deg. angles and LABC=2LBCD. Since we have two options:
LABC=90 (stmn 1), or LABC not one of the right angles.
in the first case we get answer "NO" to the qustion -> The angles will be as follows: 90, 45, 135, 90
in the second case the answer is "YES" -> 90, 90, 120,60 will be the measures of the quadrilateral.

So we still don't know. Which leaves us with "E". Remember on the GMAT for something to be sufficient we need to have one and only one solution.
Last edited by bullzeye on Mon Oct 12, 2009 1:01 pm, edited 4 times in total.
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by NikolayZ » Mon Oct 12, 2009 7:19 am
P#1.

Actually I think that the answer is C.

1) stmt says that two of angles are right. we have 2 possibilities for a polygon :
Rectangle in which two right angles are opposite, and a trapezoid, in which left ( or right) pair of angles are 90. Other angles will be 180=x+y. Insufficient.
2) We only know that ABC=2BCD. insufficient.

(1) + (2)
We exclude the rectangle possibility, whereas 90*2 does not equal to 90 =)
then we have the only option that two right angles form one side, hence other two angles' sum =180, x+2x=180, x=60. Sufficient.

Or maybe i misunderstand smth ?
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by mehravikas » Mon Oct 12, 2009 11:38 am
1st one would still be 'E'..it is a really tricky question.

consider - 90, 90, 45, 135

Satisfies statement 1 and 2.
NikolayZ wrote:P#1.

Actually I think that the answer is C.

1) stmt says that two of angles are right. we have 2 possibilities for a polygon :
Rectangle in which two right angles are opposite, and a trapezoid, in which left ( or right) pair of angles are 90. Other angles will be 180=x+y. Insufficient.
2) We only know that ABC=2BCD. insufficient.

(1) + (2)
We exclude the rectangle possibility, whereas 90*2 does not equal to 90 =)
then we have the only option that two right angles form one side, hence other two angles' sum =180, x+2x=180, x=60. Sufficient.

Or maybe i misunderstand smth ?
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