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rakshitsood21
Joined: 27 Aug 2018
Last visit: 18 Dec 2021
Posts: 27
Given Kudos: 16
Location: India
Concentration: Strategy, Leadership
Schools: ISB'22 (A) Fuqua '23 (D) IIMA PGPX'22 (WL)
GMAT 1: 670 Q51 V29
GMAT 2: 740 Q51 V38 (Online)
GPA: 4
23 Aug 2020, 04:14
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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To complete a 120-mile trip, a train first travels at a constant rate of x miles per hour (mph) for 80 miles. Then it travels the remaining 40 miles at a constant rate of y mph. If the train had instead completed the entire trip at a constant rate of z mph, the trip would have taken 1 hour longer. Which of the following is the value of z in terms of x and y?
(A) \(\frac{120}{40x + 80y + 1}\)
(B) \(\frac{40x + 80y + xy}{xy}\)
(C) \(\frac{120xy}{40x + 80y +xy}\)
(D) \(120xy + 40x + 80y\)
(E) \(\frac{121}{xy}\)
Source: Advanced Quant Manhattan Prep 2020
(A) \(\frac{120}{40x + 80y + 1}\)
(B) \(\frac{40x + 80y + xy}{xy}\)
(C) \(\frac{120xy}{40x + 80y +xy}\)
(D) \(120xy + 40x + 80y\)
(E) \(\frac{121}{xy}\)
Source: Advanced Quant Manhattan Prep 2020
31 Aug 2020, 10:31
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\(Time = \frac{Distance}{Speed}\)
Total time when traveling at x miles/hour and y miles/hr = \(\frac{80}{x} + \frac{40}{y}= \frac{80y \space + \space 40x}{xy}\)
When traveling the entire distance at z miles/hr, the time taken = \(\frac{120}{z}\) is 1 hour longer
Therefore \(\frac{120}{z} - (\frac{40x \space + \space 80y}{xy}\)) = 1
In terms of z: \(\frac{120}{z} = (\frac{40x \space + \space 80y}{xy}\)) + 1
\(\frac{120}{z} = \frac{40x \space + \space 80y \space + \space xy}{xy}\)
\(\frac{z}{120} = \frac{xy}{40x \space + \space 80y \space + \space xy}\)
Therefore \(z = \frac{120xy}{40x \space + \space 80y \space + \space xy}\)
Option C
Arun Kumar
Total time when traveling at x miles/hour and y miles/hr = \(\frac{80}{x} + \frac{40}{y}= \frac{80y \space + \space 40x}{xy}\)
When traveling the entire distance at z miles/hr, the time taken = \(\frac{120}{z}\) is 1 hour longer
Therefore \(\frac{120}{z} - (\frac{40x \space + \space 80y}{xy}\)) = 1
In terms of z: \(\frac{120}{z} = (\frac{40x \space + \space 80y}{xy}\)) + 1
\(\frac{120}{z} = \frac{40x \space + \space 80y \space + \space xy}{xy}\)
\(\frac{z}{120} = \frac{xy}{40x \space + \space 80y \space + \space xy}\)
Therefore \(z = \frac{120xy}{40x \space + \space 80y \space + \space xy}\)
Option C
Arun Kumar
General Discussion
23 Aug 2020, 04:26
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You can get the answer as below :
Equating the time taken by train as given:
(80/x)+(40/y) = (120/z)-1
will give answer as C!!
IMO C
Equating the time taken by train as given:
(80/x)+(40/y) = (120/z)-1
will give answer as C!!
IMO C
