When a certain rubber ball is dropped, it rebounds 75 percent as high

Question

When a certain rubber ball is dropped, it rebounds 75 percent as high as the distance it fell. What is the approximate height from which the ball was dropped, if it had traveled a total of 2,146 centimeters vertically by the time it struck the ground for the third time?

A. 400 cm
B. 500 cm
C. 600 cm
D. 700 cm
E. 800 cm

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Official Answer

C

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gmatophobia · Accepted Answer

Initial distance =  d

After the first rebound

Distance travelled upward =  \frac{3}{4} d  
 Distance travelled downward =  \frac{3}{4} d

After the second rebound

Distance travelled upward =  (\frac{3}{4})^2 d  
 Distance travelled downward =  (\frac{3}{4})^2 d

Total vertical distance =  d + 2*\frac{3}{4} d + 2*(\frac{3}{4})^2 d

d(1 + 2*\frac{3}{4} + 2*(\frac{3}{4})^2)

d(1 + \frac{3}{2} +\frac{9}{8})

d(1 + 1.5 +1.125)  =  3.625d

3.625d = 3 + \frac{625}{1000} = 3 + \frac{5}{8} = \frac{29}{8}d

\frac{29}{8}d = 2146

d = 2146 * \frac{8}{29} = 74 * 8 = 592

Option C

KarishmaB · Answer

The calculation here can be a bit tricky but use your knowledge of numbers. h + 2 * \frac{3}{4} h + 2 * \frac{3}{4} * \frac{3}{4} h = 2146 h ( 1 + \frac{3}{2} + \frac{9}{8}) = 2146 \frac{29h}{8} = 2146 I know that 2146 must be divisible by 29. This calculation is already hard enough. GMAT will not give a decimal here. In any case, we are asked for an approximate value. But what do I get when I divide 2146 by 29. Certainly less than 100 because 29*100 = 2900. Also since 2146 ends with a 6, and 29 has 9 at the end, whatever I get, must end with a 4. (Recall the multiplication table of 9) 29*84 is not possible because 30*80 = 2400 which is much greater than 2146. Hence it must be 29*74. We know that 30 * 70 is 2100 so it pans out. h = 74 * 8 = about 150 * 4 = 600 Answer (C) How to estimate is discussed here: https://youtu.be/4Wy7BrQrjkM GMAT-Club-Forum-3c7tol7r.png

Focus7 · Answer

Can someone solve this ?

I was getting 2700 with c and around 2200 with b so decided to go with b

Posted from my mobile device

jackg0101 · Answer

Quick question. You jump from 2146/29 being 74. Is there an easy technique to use to do this? Or have you gone through the process of actually working it out? Thank you!

gmatophobia · Answer

Hey  jackg0101

I solved it. We can use the long division approach, or we can use observation and approximation to choose a number. I used the latter one -

\frac{2146}{29} \approx \frac{2100}{30} \approx 70

So, the quotient will be in the range of 70's

Next, observe that 214 6  ends with a 6 and 2 9  ends with a 9. As 4 * 9 = 3 6 , I would multiply 74 and 29 to see if the resultant value is 2146.

74(30 - 1) = 2220 - 74 = 7146

jackg0101 · Answer

Ok great, thank you!

Jake7Wimmer · Answer

The way I read this was that it traveled 2146cm only by adding up the vertical distance traveled.... So I was sitting here and nothing was adding up. Not sure how I am supposed to know it's talking about the distance going up and down when it literally says "traveled a total of 2146 centimeters vertically...."

Anyone else think this?

Anyone else think this?

Bunuel · Answer

Traveled vertically does not necessarily imply movement only in an upward direction. The term encompasses both upward and downward movements, as dropping down is also a vertical movement.

Kinshook · Answer

yrozenblum 
Given: When a certain rubber ball is dropped, it rebounds 75 percent as high as the distance it fell.
Asked: What is the approximate height from which the ball was dropped, if it had traveled a total of 2,146 centimeters vertically by the time it struck the ground for the third time?

Let the approximate height from which the ball was dropped be h centimeters.

Distance traveled  vertically by the time it struck the ground for the first  time = h
Distance traveled  vertically by the time it struck the ground for the second  time = h + .75h + .75h
Distance traveled  vertically by the time it struck the ground for the third  time = h + .75h + .75h + (.75)^2h + (.75)^2h

h + .75h + .75h + (.75)^2h + (.75)^2h =  h + 2*(3/4)h + 2*(3/4)^2h = 29h/8 = 2146
h = 2146*8/29 = 592 cm = 600 cm

IMO C

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83636 Harsha GMAT-Club-Forum-jv8k410f.png

Pr4n · Answer

Quick and dirty maths can help you out in case you don't want to go to the calculation route.

Even if you don't change to fractions, 3.625 (h) = 2148,

Approximate 2100/3600 = 7/12 which is 0.58, you reduced the numerator more than the denominator hence the actual value would be bigger than 0.58 and as when you removed the decimal point from the denominator you had 1000 in the numerator, which means ans is >580, hence 600

When a certain rubber ball is dropped, it rebounds 75 percent as high

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When a certain rubber ball is dropped, it rebounds 75 percent as high

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards