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# In isosceles triangle RST what is the measure of angle R?

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In isosceles triangle RST what is the measure of angle R?  [#permalink]

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08 Mar 2010, 22:46
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In isosceles triangle RST what is the measure of angle R?

(1) The measure of angle T is 100 degrees.

(2) The measure of angle S is 40 degrees.

After looking at this again, how come it can't be
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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20 Mar 2012, 09:45
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In isosceles triangle RST what is the measure of angle R?

Triangle RST is isosceles means that two of its angles are equal.

(1) The measure of angle T is 100 degrees --> since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180-100)/2=40. Sufficient.

(2) The measure of angle S is 40 degrees --> consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. Not sufficient.

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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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09 Mar 2010, 11:00
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gmatgg,

This is a fairly one simple one that you should spend no more than 30 seconds on.

The keyword is "isosceles"---which means 2 sides are the same and also...2 angles are the same

With statement (1), you are told measure of angle T is 100 degrees. You already know an entire triangle = 180 degrees.

So either one of the other angles also equals 100 degrees, or the other two angles not mentioned are equivalent.

Well, it's impossible for one of the other angles to also be 100 degrees, because that would exceed that total of 180 degrees possible in a triangle.

So the only choice that makes sense is to have the other two angles equal and everything adds to 180.

In other words, the other 2 angles combined must equal the difference between 180 and 100.
Mathematically, 180 - 100 = 80 and then divide that by 2 to get 40 degrees.

So (1) by itself is good enough.

Statement (2) is just telling us that one angle is 40 degrees. Well, what possibilities are there? You could have one 40 degrees and then the other two angles are equivalent and all 3 add up to 180. OR you can have another angle that is also 40 degrees and the third angle would add up to 180.
In other words, you'd have two possibilities:

1) 40 - 70 - 70 (adds up to 180)
or 2) 40 - 40 - 100 (also adds up to 180)

Since you have MULTIPLE possibilities with statement (2), then you do not have enough information to definitively say what the answer is. So Statement (2) is not good enough.

With (1) good and (2) no good, answer is (A).

Hope that helps.
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In isosceles triangle RST what is the measure of angle R?  [#permalink]

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Updated on: 12 Aug 2013, 03:25
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In isosceles triangle RST what is the measure of angle R?

(1) The measure of angle T is 100 degrees.

(2) The measure of angle S is 40 degrees.

How come statemen1 is correct and not C?

Is it because of if one angle is 100 then others have to be 40 and 40 as the triangle is isoceles.

But then if that's the case why statement 2 is not sufficient?

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Originally posted by enigma123 on 20 Mar 2012, 09:16.
Last edited by Bunuel on 12 Aug 2013, 03:25, edited 2 times in total.
Edited the question.
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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12 Aug 2013, 03:31
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enigma123 wrote:
In isosceles triangle RST what is the measure of angle R?

(1) The measure of angle T is 100 degrees.

(2) The measure of angle S is 40 degrees.

How come statemen1 is correct and not C?

Is it because of if one angle is 100 then others have to be 40 and 40 as the triangle is isoceles.

But then if that's the case why statement 2 is not sufficient?

IN ISOCELES TRIANGLE ANGLES ARE ALWAYS. X,X,(180-2X)

(1) The measure of angle T is 100 degrees.
CLEARLY X CANT BE equal to 100 because in that case sum of angle will exceed 180 degrees
therefore 180-2X = 100. CLEARLY X=40
SUFFICIENT.

(2) The measure of angle S is 40 degrees.
IF X CAN BE 40 OR 180-2X CAN BE 40
WE ARE GETTING 2 DIFFERENT VALUES OF X.
HENCE INSUFFICIENT.

HENCE A
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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25 Mar 2014, 08:34
I had this question today when I was doing a practice exam on the GMAT Prep software. And I was confused, as I have read on several occasions that the symbol of a triangle (that mini-triangle in front of RST) means that the R starts in the lower corner, S on top and T on the left. When I saw the first option, I assumed that T would be the opposite of R, which was mathematically impossible (2 angles of 100 in a triangle).

But I can conclude now that the order of letters in the description of a triangle, have no meaning at all?
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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30 Mar 2014, 17:28
Saabs wrote:
I had this question today when I was doing a practice exam on the GMAT Prep software. And I was confused, as I have read on several occasions that the symbol of a triangle (that mini-triangle in front of RST) means that the R starts in the lower corner, S on top and T on the left. When I saw the first option, I assumed that T would be the opposite of R, which was mathematically impossible (2 angles of 100 in a triangle).

But I can conclude now that the order of letters in the description of a triangle, have no meaning at all?

I don't think it matters at all in this case what the position of the letters are, since in an isosceles triangle two of the angles are identical.

Statement 1: If T (which is not R) = 100, then the other two must be equal to (180-100)/2 = 40.

In Statement 2: if the measure of angle s = 40, piggybacking off Statement 1 (but not using it), you know that the three angles COULD be 100, 40, 40. If S = 40, then R can be either 40 or 100. And therefore, this statement is not sufficient.
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In isosceles triangle RST what is the measure of angle R?  [#permalink]

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22 Jun 2014, 18:32
Given the isosceles triangle as attached, I don't understand why statement 2 as well is insufficient.
If we know S = 40 degrees and the whole triangle is 180 and it is an isosceles can't we use the following formula:
180 = 40 + 2*R
140 = 2*R
70 = R = T

Why can't we use this information?
Many Thanks,
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iscoceles triangle.png [ 60.46 KiB | Viewed 57267 times ]

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Re: In Isosceles triangle RST, What is the measure of Angle R  [#permalink]

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22 Jun 2014, 19:49
Statement 2 is insufficient because Angle S can be either the base or the isosceles sides

If Angle S is the base,
$$180=40+2*R$$
$$140=2*R$$
$$70=R=T$$

If Angle S is the one of the isosceles sides,
$$180=B+2*40$$
$$180=B+80$$
$$100=B$$

Statement 1 is sufficient because 100 degrees cannot be an isosceles side since it would be beyond the 180 degree restriction for a triangle.
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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23 Jun 2014, 04:04
HI,

Thanks a lot for the reply! That is very useful.
So I suppose for 2, we cannot assume that S is the adjacent angle to two isosceles angles? As this is what I did and I thought that it was sufficient.

Thanks a lot again,

Really appreciate it!

Bunuel wrote:
In isosceles triangle RST what is the measure of angle R?

Triangle RST is isosceles means that two of its angles are equal.

(1) The measure of angle T is 100 degrees --> since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180-100)/2=40. Sufficient.

(2) The measure of angle S is 40 degrees --> consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. Not sufficient.

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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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23 Jun 2014, 04:19
Yela wrote:
HI,

Thanks a lot for the reply! That is very useful.
So I suppose for 2, we cannot assume that S is the adjacent angle to two isosceles angles? As this is what I did and I thought that it was sufficient.

Thanks a lot again,

Really appreciate it!

Bunuel wrote:
In isosceles triangle RST what is the measure of angle R?

Triangle RST is isosceles means that two of its angles are equal.

(1) The measure of angle T is 100 degrees --> since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180-100)/2=40. Sufficient.

(2) The measure of angle S is 40 degrees --> consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. Not sufficient.

Yes, from (2) we cannot assume that S is one of the two angles that are equal.
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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30 Aug 2014, 05:54
I have a general question: The order of the letters after the sign of the triangle, here <RST, does not give any indication of the order of the angles?
Sorry I don't know how to insert the proper angle sign.
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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01 Sep 2014, 07:03
lou34 wrote:
I have a general question: The order of the letters after the sign of the triangle, here <RST, does not give any indication of the order of the angles?
Sorry I don't know how to insert the proper angle sign.

Order of letters for a triangle does not matter. Triangles RST, RTS, STR, ... are all the same.

As for other polygons (quadrilaterals, pentagons, ...): here order of the letters is important meaning that rectangle ABCD (diagonals here are AC and BD) is different from rectangle ACBD (diagonals here are AB and CD). Usually OG uses sequential (ABCDE...) labeling. Also, most of the times the labeling is clockwise but I wouldn't worry about it because if a diagram is not given then this won't be important (meaning that you can consider it clockwise as well as counter-clockwise).
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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03 Sep 2014, 07:32
Ans A.

1) Since it is isosceles, it can´t have 2 100° angles, it must be the odd one and the other 2 angles should be (180 - 100)/2 = 40° each

2) Insufficient since there could be 2 40° angles or there could be 2 70° angles and 1 40°

Hope it helps!
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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09 Nov 2014, 05:53
Hi there, I'm actually wondering (or pointing out) if/that there might be a U.S vs. Europe (or country specific?) definition issue here, because I found that we were allowed to assume triangle RST with S being the "top" angle, and letters always going clockwise and thereby this could be solved assuming statement two as well. Similar problems have occured with, for example, GMAT statement "can this information be inferred", wheras my inital translation/interpretation was that it doesn't matter if the statement is true, only that you can answer the question (it is possible to answer). Questions like these are common to us. Then I quickly realized that the GMAT wants you to also take into consideration if the statement is true. So just as a comment, for us non-Americans, there can be som issues with definitions, or assumptions we make / have been allowed to make, that are not allowed according to U.S standards/GMAT standards.
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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10 Nov 2014, 12:31

statement A: sufficient
An isosceles triangle cannot have 2 interior angles equal to 100 degrees so Angle T must be the largest interior angle. Each of the other angles will be equal to each other and also add up to 80 degrees. Therefore, R and S are each 40 degrees.

Statement B: insufficient
If S is 40 degrees, R could be 40 or R could be 70.
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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20 Nov 2014, 06:14
Bunuel wrote:
In isosceles triangle RST what is the measure of angle R?

Triangle RST is isosceles means that two of its angles are equal.

(1) The measure of angle T is 100 degrees --> since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180-100)/2=40. Sufficient.

(2) The measure of angle S is 40 degrees --> consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. Not sufficient.

Hi Bunuel

How can S=R=40 because that would take it out of the triangle definition isnt it? Sum of two smaller sides wont be greater than the longest side so can it be a valid scenario? Does this rule only apply to sides measure and not angles in a triangle?
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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20 Nov 2014, 08:06
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sinhap07 wrote:
Bunuel wrote:
In isosceles triangle RST what is the measure of angle R?

Triangle RST is isosceles means that two of its angles are equal.

(1) The measure of angle T is 100 degrees --> since no other angle can be equal to 100 degrees (because in this case the sum of the angles will be more than 180 degrees) then the other two angles, R and S, are equal: R=(180-100)/2=40. Sufficient.

(2) The measure of angle S is 40 degrees --> consider two cases: S=R=40 and T=100 AND S=40 and R=T=70. Not sufficient.

Hi Bunuel

How can S=R=40 because that would take it out of the triangle definition isnt it? Sum of two smaller sides wont be greater than the longest side so can it be a valid scenario? Does this rule only apply to sides measure and not angles in a triangle?

Yes, the rule is about the lengths of the sides.

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

For the angles of a triangle we have that their sum must be 180 degrees.

Check for more here: math-triangles-87197.html

Hope it helps.
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In isosceles triangle RST what is the measure of angle R?  [#permalink]

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12 May 2015, 09:06
Isosceles triangle
=> 2 equal angles and 1 unequal angle.

(1) says that T is 100. This clearly means that T is the unequal angle, because there cannot be another equal angle of 100 degrees (since sum of 3 angles is 180).

So, we know that T = 100
=> R=S=40

Sufficient.

(2) says that S = 40

Here, two cases are possible
Case 1: S is one of the 2 equal angles
=> One other angle is 40 and the third angle is 100. But which of these is R, we don't know.

Case 2: S is the unequal angle
=> The other two angles (R and T) are 70 each.

So, in Case 1, we see that we don't know the value of R.

Hence, insufficient.

So, A.
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Re: In isosceles triangle RST what is the measure of angle R?  [#permalink]

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19 Apr 2018, 15:09
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gmatgg wrote:
In isosceles triangle RST what is the measure of angle R?

(1) The measure of angle T is 100 degrees.

(2) The measure of angle S is 40 degrees.

IMPORTANT: In an isosceles triangle there are 2 IDENTICAL angles, and 1 LONE angle.

Target question: What is measure of ∠R?

Statement 1: ∠T = 100 degrees
We should recognize that ∠T CANNOT be one of the identical angles. If this were the case, we'd have two angles with measures of 100 degrees each, which would result in a triangle in which the sum of the angles is GREATER than 180 degree (which is IMPOSSIBLE)
So, we can conclude that ∠T must be the LONE angle, which means ∠R and ∠S are the two IDENTICAL angles.
Since the sum of the 3 angles must be 180, we can conclude that ∠R = 40, ∠S = 40, and ∠T = 100
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: ∠S = 40 degrees
Here are two possible cases to consider:
Case a: ∠S is the LONE angle, in which case the ∠R = 70, ∠S = 40, and ∠T = 70
Case b: ∠S is one of the IDENTICAL angles, in which case we could have ∠R = 40, ∠S = 40, and ∠T = 100
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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