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# Carlos runs a lap around the track in x seconds. His second

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Carlos runs a lap around the track in x seconds. His second [#permalink]  19 Aug 2018, 03:49
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Question Stats:

20% (01:41) correct 79% (00:54) wrong based on 29 sessions
Carlos runs a lap around the track in x seconds. His second lap is five seconds slower than the first lap, but the third lap is two seconds faster than the first lap. What is Carlos’s average (arithmetic mean) number of minutes per lap, in terms of x?

(A) $$x - 1$$
(B) $$x + 1$$
(C) $$\frac{x-1}{60}$$
(D) $$\frac{x+1}{60}$$
(E) $$\frac{x+3}{60}$$
[Reveal] Spoiler: OA

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Re: Carlos runs a lap around the track in x seconds. His second [#permalink]  16 Sep 2018, 00:05
answer must be c , if not pls. explain??
Retired Moderator
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Re: Carlos runs a lap around the track in x seconds. His second [#permalink]  16 Sep 2018, 14:06
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Explanation

Carlos’s lap times can be expressed as x, x + 5, and x – 2. (Remember, slower race times are greater numbers, so “five seconds slower” means plus 5, not minus 5!) Average the lap times:

$$\frac{x+(x+5)+(x-2)}{3}=\frac{3x+3}{3}=x+1$$

His average time is x + 1 seconds. But the question requires minutes. Since there are 60 seconds in a minute, divide by 60 to get $$\frac{x+1}{60}$$, or choice (D).
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Re: Carlos runs a lap around the track in x seconds. His second [#permalink]  14 Jan 2019, 18:06
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Expert's post
sandy wrote:
Carlos runs a lap around the track in x seconds. His second lap is five seconds slower than the first lap, but the third lap is two seconds faster than the first lap. What is Carlos’s average (arithmetic mean) number of minutes per lap, in terms of x?

(A) $$x - 1$$
(B) $$x + 1$$
(C) $$\frac{x-1}{60}$$
(D) $$\frac{x+1}{60}$$
(E) $$\frac{x+3}{60}$$

The total number of seconds it takes Carlos to run the 3 laps is x + (x + 5) + (x - 2) = 3x + 3. So the number of seconds per lap is (3x + 3)/3 = x + 1, and hence, the number of minutes per lap is (x + 1)/60.

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Re: Carlos runs a lap around the track in x seconds. His second [#permalink]  14 Jan 2019, 18:58
Expert's post
sandy wrote:
Carlos runs a lap around the track in x seconds. His second lap is five seconds slower than the first lap, but the third lap is two seconds faster than the first lap. What is Carlos’s average (arithmetic mean) number of minutes per lap, in terms of x?

(A) $$x - 1$$
(B) $$x + 1$$
(C) $$\frac{x-1}{60}$$
(D) $$\frac{x+1}{60}$$
(E) $$\frac{x+3}{60}$$

Such questions, substituting some value for X is another good way
So let X be 5 secs...so first lap in 5, second in 5+5 and third in 5-2...
Thus 3 laps in 5+10+3=18 seconds, but our answer is in minutes, so the average is 18/3=6 secs or 6/60 minutes..

Look at the choices..
D is (x+1)/60=(5+1)/60=6/60

D
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: Carlos runs a lap around the track in x seconds. His second   [#permalink] 14 Jan 2019, 18:58
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