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Alice is paid at a constant rate of $x per hour for the firs

by Max@Math Revolution » Fri Apr 13, 2018 1:30 am
[GMAT math practice question]

Alice is paid at a constant rate of $x per hour for the first 40 hours she works and $30 for each hour she works after the first 40 hours. If Alice works 48 hours and earns $920, what is the value of x?

A. $15
B. $16
C. $17
D. $18
E. $19
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by Keith@ThePrincetonReview » Fri Apr 13, 2018 6:49 pm
Max@Math Revolution wrote:[GMAT math practice question]

Alice is paid at a constant rate of $x per hour for the first 40 hours she works and $30 for each hour she works after the first 40 hours. If Alice works 48 hours and earns $920, what is the value of x?

A. $15
B. $16
C. $17
D. $18
E. $19
Answer choices represent information directly asked for by question, so Plug in the Answers. Begin with choice C, x = $17.

Alice is paid (40hrs)*($17/hr) = $680 for the first 40 hours she works.
Alice is paid (8hrs)*($30/hr) = $240 for the next 8 hours.
$680 + $240 = $920.
Since $920 matches the figure provided by the question stem, the correct answer is choice C.
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by GMATGuruNY » Sat Apr 14, 2018 3:03 am
Max@Math Revolution wrote:[GMAT math practice question]

Alice is paid at a constant rate of $x per hour for the first 40 hours she works and $30 for each hour she works after the first 40 hours. If Alice works 48 hours and earns $920, what is the value of x?

A. $15
B. $16
C. $17
D. $18
E. $19
Since Alice works 8 hours after the first 40 hours, she works 8 hours at the $30 rate:
8*30 = 240.
Remaining earnings = (total earnings) - (earnings for the last 8 hours) - 920-240 = 680.
Since she works 40 hours to earn this $680, her regularly hourly rate = earnings/hours = 680/40 = 17.

The correct answer is C.
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by Max@Math Revolution » Sun Apr 15, 2018 5:33 pm
=>
Total pay = (rate for first 40 hours)*40 hours + ($30)*(number of additional hours)
x * 40 + ( 48 - 40 ) * 30 = 920
x*40 + 8*30 = 920
x * 40 + 240 = 920
x * 40 = 680
x = 680 / 40 = 17

Therefore, C is the answer.
Answer: C
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by Scott@TargetTestPrep » Mon Apr 16, 2018 4:14 pm
Max@Math Revolution wrote:[GMAT math practice question]

Alice is paid at a constant rate of $x per hour for the first 40 hours she works and $30 for each hour she works after the first 40 hours. If Alice works 48 hours and earns $920, what is the value of x?

A. $15
B. $16
C. $17
D. $18
E. $19
We can create the equation:

40x + 30(48 - 40) = 920

40x + 240 = 920

x + 6 = 23

x = 17

Answer: C

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