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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Carlos runs a lap around the track in x seconds. His second  Question banks Downloads My Bookmarks Reviews Important topics
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Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Carlos runs a lap around the track in x seconds. His second [#permalink]
Expert's post 00:00

Question Stats: 23% (01:36) correct 76% (00:54) wrong based on 30 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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Sandy
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Kudos [?]: 2 , given: 5

Re: Carlos runs a lap around the track in x seconds. His second [#permalink]
answer must be c , if not pls. explain??
Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 176

Kudos [?]: 3041 , given: 394

Re: Carlos runs a lap around the track in x seconds. His second [#permalink]
Expert's post
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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Sandy
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Re: Carlos runs a lap around the track in x seconds. His second [#permalink]
1
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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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Joined: 01 Nov 2017
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Kudos [?]: 187 , given: 4

Re: Carlos runs a lap around the track in x seconds. His second [#permalink]
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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