GMAT question 146

No, sorry. How would I be able to draw it myself? I drew the PQR triangle. I never seen a range being used for triangles before
 
Wait, the sum of two sides of a triangle is greater than the third side of the triangle. I think this is what you mean to say. Let me try it out with this idea.
 
Yes, what you said is true.

No, P, Q R from our picture. Draw an angle that is 179 degrees. How long is the 3rd side approximately?
Now draw an angle that is 0.1 degrees. How long is the 3rd side approximately?
 
So with this new idea, I did the PQR triangle and PR is less than 5, as it is less than the sum of QR and PQ, which means it is 4. Then for triangle RST, RT is less than 9 (sum of RS and ST), so RT is 8, 7, and 6. Then with PRT, PT is less than 12, 10, 11, so PT is 5, which is A, which is wrong.
 
How am I supposed to draw a picture of 179 degrees and 0.1, for the GMAT I have like 2 minutes per question?
 
ironsheep said:
How am I supposed to draw a picture of 179 degrees and 0.1, for the GMAT I have like 2 minutes per question?
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The picture is not for this particular problem. It is just for you to see (for the rest of your life) that the 3rd side of a triangle is between the sum and difference of the other two sides.
 
I didn't know there was a theorm like that, but I don't have a tool to help me make degrees. So there is a theorm that says that the third triangle is always between the Sum and Difference of the other two sides!
 
ironsheep said:
So with this new idea, I did the PQR triangle and PR is less than 5, as it is less than the sum of QR and PQ, which means it is 4. Then for triangle RST, RT is less than 9 (sum of RS and ST), so RT is 8, 7, and 6. Then with PRT, PT is less than 12, 10, 11, so PT is 5, which is A, which is wrong.
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There are many many numbers less than 5 and not 4!! Like 3 or 2 or 1 or 4.98 or sqrt(17) etc. When you go outside and are not doing math most things are not 1 or 2 or 3 or 4. Just look at the prices of items when you are shopping. Just like there are numbers other then 1 2, 3, 4...on the outside there are other numbers in math. The 3rd side can be 4.999345.
 
ironsheep said:
I didn't know there was a theorm like that, but I don't have a tool to help me make degrees. So there is a theorm that says that the third triangle is always between the Sum and Difference of the other two sides!
Click to expand...
YES. Now please see far you can go with that with your problem
 
For this problem, I don't want to make it more complicated, so I will go with whole numbers. PR is either 3, 2, and 4. Then make the RST triangle and the range is 1 to 9, so RT is either 2, 3, 4, 5, 6, 7, and 8. Then with PRT triangle, the range is between (6,7,8,9,10,11,12) and (2 and 1), so out of the three choices given: 5, 10, and 15. Between (6,7,8,9,10,11,12) and (2 and 1) is 5, which is A, which is wrong, so what happened?
 
10 is part of the max range and 15 is too big, so 5 is left, but the answer is C-- 5 and 10.
 
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1 < PR < 5
1 < RT < 9
So what is the length of PT between?

DO NOT just pick any number between 1 and 5 AND 1 and 9.
What can the largest sum for PT be? What can the smallest difference be? So what is the answer?
 
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The largest sum we get is 5+9=14 and the smallest non negative difference we get is 0. So PT can have any length between 0 and 14. So PT can be 5 or 10. So C is the answer.
 
I get it now and you have to find the range for each line and how you write the range matters heavily---- this is the wrong way: For this problem, I don't want to make it more complicated, so I will go with whole numbers. PR is either 3, 2, and 4. Then make the RST triangle and the range is 1 to 9, so RT is either 2, 3, 4, 5, 6, 7, and 8. Then with PRT triangle, the range is between (6,7,8,9,10,11,12) and (2 and 1), so out of the three choices given: 5, 10, and 15. Between (6,7,8,9,10,11,12) and (2 and 1) is 5, which is A, which is wrong, so what happened?



This is the right way: Triangle RST yields RT as (1-9). Then Triangle QRT yields QT as (1-11). Triangle QPT yields (2-14). Find the min and max of the range only. Since PT is (2-14), 5 and 10 count. Answer is C. Thank you Jomo.
 
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