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On his trip to Alaska, Joe traveled y percent of the total [#permalink]

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31 Oct 2012, 11:46

Expert's post

9

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00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

70% (03:24) correct
30% (03:10) wrong based on 149 sessions

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On his trip to Alaska, Joe traveled y percent of the total distance at an average speed of 50 miles per hour and the rest of the distance at an average speed of 70 miles per hour. What was Joe’s average speed in miles per hour for the whole trip in terms of y?

(A) 70(50 – y)

(B) (y + 60)/4

(C) 10,000 – 199y

(D) 17,500/(y + 250)

(E) y/2 + 35

If the first part is at 50 mile/h and the second part is 70 miles/h the overall speed is the toral distance / total time.

Pick a number for distance we can use 350. so the time for first part is 7 and for the rest is 5.

in the end we will have 26. something, but testing answer choices nothing comes up (

where I'm wrong

PS: I could use a bit of logic and come to the answer easier, but .............

Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink]

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01 Nov 2012, 06:27

3

This post received KUDOS

Expert's post

5

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carcass wrote:

On his trip to Alaska, Joe traveled y percent of the total distance at an average speed of 50 miles per hour and the rest of the distance at an average speed of 70 miles per hour. What was Joe’s average speed in miles per hour for the whole trip in terms of y?

(A) 70(50 – y)

(B) (y + 60)/4

(C) 10,000 – 199y

(D) 17,500/(y + 250)

(E) y/2 + 35

If the first part is at 50 mile/h and the second part is 70 miles/h the overall speed is the toral distance / total time.

Pick a number for distance we can use 350. so the time for first part is 7 and for the rest is 5.

in the end we will have 26. something, but testing answer choices nothing comes up (

where I'm wrong

PS: I could use a bit of logic and come to the answer easier, but .............

Say y=100%, so say Joe traveled entire trip at an average speed of 50 miles per hour. So, in this case we'd have that his average speed is simply 50 miles per hour.

Now, plug y=100 into the answer choices and see which one yields 50. Only answer choice D fits.

Or: say y=0%. In this case we'd have that Joe's average speed is 70 miles per hour.

Now, plug y=0 into the answer choices and see which one yields 70. Again, only answer choice D fits.

Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink]

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06 Nov 2012, 09:01

BangOn wrote:

As you need a quick logical answer let me try Lety distance be X so Time 1 = XY/100*50 Time 2 = X(100-Y)/100*70

Avg Speed = Total Distance / Total Time = X/ Time 1 + Time 2

Ans D reason is simple...X cancels and Y reamins in denominator only 1 option has the same

I deducted the above within 30 secs but took another 3 mins to solve the whole mess to get to the ans choice. As you rightly said if we notice Y remains in deno for only one choice, life becomes easier.

I tend to go the conventional way every time not the GMAT way

Any other tricks like this which could help save TIME?

Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink]

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06 Nov 2012, 09:10

Another way - less than 2 mins Take Total distance = 100 1) y% of 100 at 50 mi/hr = distance is y miles -- So its y miles at 50 mi/hr 2) remaining (100-y) miles at 70 mi/hr

Avg spd = Total Dist/Total Time = 100/(y/50 + (100-y)/70) -> leads to D.(in case there are more choices with y in deno)

Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink]

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06 Nov 2012, 09:38

Expert's post

HiteshPunjabi wrote:

Another way - less than 2 mins Take Total distance = 100 1) y% of 100 at 50 mi/hr = distance is y miles -- So its y miles at 50 mi/hr 2) remaining (100-y) miles at 70 mi/hr

Avg spd = Total Dist/Total Time = 100/(y/50 + (100-y)/70) -> leads to D.(in case there are more choices with y in deno)

Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink]

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15 Nov 2012, 10:50

i just plugged in some random nos-

say Total distance=100 y=30% Then ball parked to find that D is the ans. _________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink]

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23 Aug 2014, 20:46

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Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink]

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02 Sep 2015, 10:27

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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