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Help me solve these quant problems (taken from ETS)


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I didn't find any explanations for these problems on the software! While I know the correct answers, I'm not sure how to get there. Could anyone explain them? Thanks!



Problem 1:


Problem 2:




Problem 3:


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1. To go from X to Y, you either go forward 4 units, or go backward 4 units. To go from Y to Z, you either go forward 9 units, or go backward 9 units. So, to go from X to Y to Z, we have to either:
go backward 4 units and backward 9 units (total: backward 13)
go backward 4 units and forward 9 units (total: forward 5)
go forward 4 units and backward 9 units (total: backward 5)
go forward 4 units and forward 9 units (total: forward 13)
So, the distance from X to Z is either 5 or 13. Since 13 is not an answer choice, pick 5.


2. Use proportions: train speed = (s miles)/(t hours) = (y miles)/(x hours). Solve to get x = ty/s.

3. Since the experiment has only 3 disjoint outcomes, the probabilities must sum to 1. Thus, p + p/2 + p/4 = 7p/4 = 1, so p = 4/7.

Edited by JimmyK4542
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For question #1, I focused on the information that included either X or Z (since we want to find the length of XZ)

I saw that WX = 2, but didn't spot any info that tied W to Z, so I ignored this information. 


Then I saw YZ = 9 as well as XY = 4. Perfect, these two work together. 

There are only 2 possibilities (basically): 

case 1: X....Y.............Z, in which case XZ = 13

case 2: Y...X......Z, in which case XZ = 5


Check the answer choices . . . answer = B




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On #2, a good tip is also to plug & chug a number or two into your formula once you think you know the answer.


For example, for yt/s , we could substitute "how long would it take a train traveling 50 miles (x) in one hour (t)  to travel 100 miles (y) ?  Well, obviously the answer is 2 hours, but is that what our formula gives us?


yt/s = 100*1/50 = 2 hours.  So we know our formula is good.


Also, make sure you keep your units straight on these formulas.  Per the question in #2 (in how many hours will the train travel...), you know that the formula must equal hours, so be sure that where you put your variables also makes for units in hours.  yt/s would be miles * hours / miles) which has units of hours so that's another double-check.


Edited to add:  everyone's brain works differently on these sorts of problems.  On many/most GRE quant questions there is more than one way to find the correct answer.  Try to figure out which method works best/fastest for you on a particular question type...

Edited by iowaguy
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