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On his trip to Alaska, Joe traveled y percent of the total

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On his trip to Alaska, Joe traveled y percent of the total [#permalink] New post 31 Oct 2012, 10:46
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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 .............
[Reveal] Spoiler: OA

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Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink] New post 31 Oct 2012, 11:41
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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
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Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink] New post 01 Nov 2012, 05:27
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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.

Answer: D.

Hope it helps.
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Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink] New post 06 Nov 2012, 08:01
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?
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Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink] New post 06 Nov 2012, 08:10
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)
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Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink] New post 06 Nov 2012, 08:38
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)


Check here: on-his-trip-to-alaska-joe-traveled-y-percent-of-the-total-141661.html#p1140444
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Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink] New post 15 Nov 2012, 09:50
i just plugged in some random nos-

say Total distance=100
y=30%
Then ball parked to find that D is the ans.
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Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink] New post 16 Nov 2012, 02:22
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rajathpanta wrote:
i just plugged in some random nos-

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


If you plug y=0 or y=100, then you won't need to plug anything for the distance. Check here: on-his-trip-to-alaska-joe-traveled-y-percent-of-the-total-141661.html#p1138511
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: On his trip to Alaska, Joe traveled y percent of the total [#permalink] New post 17 Nov 2012, 15:59
rajathpanta wrote:
i just plugged in some random nos-

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


No need to assume the value of y. Assume total distance = 100. Therefore total time taken = (y/50) + (100-y)/70 = (y + 250)/175

Average speed = 100/( (y + 250)/175) = 175000/ (y + 250)
Re: On his trip to Alaska, Joe traveled y percent of the total   [#permalink] 17 Nov 2012, 15:59
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