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14 Oct 2023, 11:10
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C
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Difficulty:
85%
(hard)
Question Stats:
65% (03:07) correct
35%
(03:17)
wrong
based on 1018
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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
GMAT-Club-Forum-jriqzevc.png [ 57.95 KiB | Viewed 7548 times ]
A. 400 cm
B. 500 cm
C. 600 cm
D. 700 cm
E. 800 cm
Attachment:
GMAT-Club-Forum-jriqzevc.png [ 57.95 KiB | Viewed 7548 times ]
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14 Oct 2023, 12:02
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yrozenblum
- 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
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23 Jun 2024, 05:14
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yrozenblum
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
Attachment:
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