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Intern  Joined: 10 Sep 2015
Posts: 26
Nani traveled from her home to work at an average speed of 40 mph, and  [#permalink]

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5 00:00

Difficulty:   45% (medium)

Question Stats: 73% (02:07) correct 27% (01:44) wrong based on 186 sessions

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Nani traveled from her home to work at an average speed of 40 mph, and then immediately returned home. If Nani's average speed for the entire trip was 30mph, what was her average speed (in mph) while returning home?
A) 20
B) 22
C) 24
D) 26
E) 28

Source: GMAT Prep Now - http://www.gmatprepnow.com/module/gmat- ... /video/912
Intern  Joined: 10 Sep 2015
Posts: 26
Re: Nani traveled from her home to work at an average speed of 40 mph, and  [#permalink]

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My question: I understand the solution in the video. How do you use the "test the answers" strategy here?
Intern  Joined: 20 Aug 2015
Posts: 5
Nani traveled from her home to work at an average speed of 40 mph, and  [#permalink]

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skylimit wrote:
My question: I understand the solution in the video. How do you use the "test the answers" strategy here?

Hi Sky,

I don't think "picking the answers" is the efficient way to go (you'll waste time).

If you look at the final equation

1/40 + 1/x = 2/30 = 1/15

because 1/15 > 1/40, you have to pick a number for x so that 1/x becomes greater than 1/40.
Given the answer choices, all of them would satisfy that condition. So it's better to solve directly for x, which is here pretty simple.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7367
GMAT 1: 760 Q51 V42 GPA: 3.82
Nani traveled from her home to work at an average speed of 40 mph, and  [#permalink]

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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

Nani traveled from her home to work at an average speed of 40 mph, and then immediately returned home. If Nani's average speed for the entire trip was 30mph, what was her average speed (in mph) while returning home?
A) 20
B) 22
C) 24
D) 26
E) 28

Let A be the time to take from Nani’s home to work, B be the return time and X be the return speed. Since the entire time is A+B, the distance from home to work is 40*A=X*B and that is the half of entire distance 30*(A+B)(--> 40*A=15(A+B)) and we have :
40*A + X*B = 30(A+B)----*).
By 40*A=15(A+B) we have :
5A=15B --> 5A=3B --> let A=3T, B=5T.
Put these into *) we get :
40*(3T) + X*(5T)=30*8T by cancelling T at both sides --> 120+5X=240 --> 5X=120 --> x=24.
The answer is C).
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Intern  Joined: 10 Sep 2015
Posts: 26
Re: Nani traveled from her home to work at an average speed of 40 mph, and  [#permalink]

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MathRevolution wrote:
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

Nani traveled from her home to work at an average speed of 40 mph, and then immediately returned home. If Nani's average speed for the entire trip was 30mph, what was her average speed (in mph) while returning home?
A) 20
B) 22
C) 24
D) 26
E) 28

Let A be the time to take from Nani’s home to work, B be the return time and X be the return speed. Since the entire time is A+B, the distance from home to work is 40*A=X*B and that is the half of entire distance 30*(A+B)(--> 40*A=15(A+B)) and we have :
40*A + X*B = 30(A+B)----*).
By 40*A=15(A+B) we have :
5A=15B --> 5A=3B --> let A=3T, B=5T.
Put these into *) we get :
40*(3T) + X*(5T)=30*8T by cancelling T at both sides --> 120+5X=240 --> 5X=120 --> x=24.
The answer is C).

I don't understand what T equals here. Does it equal A+B?
Also, what's the IVY approach?
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Joined: 27 Aug 2014
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Location: Canada
Concentration: Strategy, Technology
GMAT 1: 660 Q45 V35 GPA: 3.66
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Re: Nani traveled from her home to work at an average speed of 40 mph, and  [#permalink]

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I used a formula that was used for calculating average speeds.

2xy/x+y = average speed

80y/40+y=30
80y=1200+30y
y=1200/50=24
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9234
Location: Pune, India
Re: Nani traveled from her home to work at an average speed of 40 mph, and  [#permalink]

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skylimit wrote:
Nani traveled from her home to work at an average speed of 40 mph, and then immediately returned home. If Nani's average speed for the entire trip was 30mph, what was her average speed (in mph) while returning home?
A) 20
B) 22
C) 24
D) 26
E) 28

Source: GMAT Prep Now - http://www.gmatprepnow.com/module/gmat- ... /video/912

Yes, you can use the formula of average speed when distance covered is the same.

Average Speed = 2ab/(a+b)

as done in the post above.

Or you can use the "regular" average speed formula

Average Speed = Total distance/Total Time = (d + d)/(d/40 + d/s)= 30
Note that all d's get cancelled and actually this equation comes down to the formula discussed above.

Check this post for more on average speed discussion and these formulas:
http://www.veritasprep.com/blog/2015/02 ... -the-gmat/
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Concentration: General Management, Technology
GMAT 1: 540 Q45 V20 GPA: 2.49
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Re: Nani traveled from her home to work at an average speed of 40 mph, and  [#permalink]

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1
skylimit wrote:
Nani traveled from her home to work at an average speed of 40 mph, and then immediately returned home. If Nani's average speed for the entire trip was 30mph, what was her average speed (in mph) while returning home?
A) 20
B) 22
C) 24
D) 26
E) 28

Source: GMAT Prep Now - http://www.gmatprepnow.com/module/gmat- ... /video/912

Average speed = (Total distance) / (total time)

30 = 2D / (t1 + t2)

30 = 2D / (D/40 + D/s)

30 = 2/(1/40 + 1/s)

S = 24
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Joined: 14 Oct 2015
Posts: 6207
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Re: Nani traveled from her home to work at an average speed of 40 mph, and  [#permalink]

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skylimit wrote:
Nani traveled from her home to work at an average speed of 40 mph, and then immediately returned home. If Nani's average speed for the entire trip was 30mph, what was her average speed (in mph) while returning home?
A) 20
B) 22
C) 24
D) 26
E) 28

We can let the distance to work = d, and the rate coming back = r. Thus:

average = (total distance)/(total time)

30 = 2d/(d/40 + d/r)

30(d/40 + d/r) = 2d

30d/40 + 30d/r = 2d

3/4 + 30/r = 2

Let’s multiply both sides of the equation by 4r:

3r + 120 = 8r

120 = 5r

24 = r

Answer: C
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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Nani traveled from her home to work at an average speed of 40 mph, and   [#permalink] 15 Mar 2018, 10:12
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