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# A gym offers 11 levels of fitness classes, and in an attempt to reward

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Math Expert
Joined: 02 Sep 2009
Posts: 52344
A gym offers 11 levels of fitness classes, and in an attempt to reward  [#permalink]

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05 May 2015, 01:37
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Difficulty:

65% (hard)

Question Stats:

61% (02:45) correct 39% (02:57) wrong based on 157 sessions

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A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was$4675. What is the cost for a course at the gym's highest level?

A. $175 B.$245
C. $425 D.$675
E. $725 Kudos for a correct solution. _________________ Manager Joined: 09 Jan 2013 Posts: 75 Concentration: Entrepreneurship, Sustainability GMAT 1: 650 Q45 V34 GMAT 2: 740 Q51 V39 GRE 1: Q790 V650 GPA: 3.76 WE: Other (Pharmaceuticals and Biotech) Re: A gym offers 11 levels of fitness classes, and in an attempt to reward [#permalink] ### Show Tags 05 May 2015, 18:33 2 Let the cost of a course in level 1 = x => Cost of level 2 = x-(50*1)... and so on => cost of level 11 = x-(50*10) = x-500 => Total cost of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500) = 11x -50 (1+2+....+10) = 11x - (50*55) => 11x-2750 = 4675 11x = 7425 x= 675 x-500=175 Answer A Manager Joined: 07 Apr 2015 Posts: 164 Re: A gym offers 11 levels of fitness classes, and in an attempt to reward [#permalink] ### Show Tags 05 May 2015, 23:57 akhilbajaj wrote: Let the cost of a course in level 1 = x => Cost of level 2 = x-(50*1)... and so on => cost of level 11 = x-(50*10) = x-500 => Total cost of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500) = 11x -50 (1+2+....+10) = 11x - (50*55) => 11x-2750 = 4675 11x = 7425 x= 675 x-500=175 Answer A Is there a faster way? Hardly possible to do this in < 2minutes Manager Joined: 09 Jan 2013 Posts: 75 Concentration: Entrepreneurship, Sustainability GMAT 1: 650 Q45 V34 GMAT 2: 740 Q51 V39 GRE 1: Q790 V650 GPA: 3.76 WE: Other (Pharmaceuticals and Biotech) Re: A gym offers 11 levels of fitness classes, and in an attempt to reward [#permalink] ### Show Tags 06 May 2015, 17:24 1 noTh1ng wrote: Is there a faster way? Hardly possible to do this in < 2minutes An alternate way is to consider to cost of level 11 =x since this is the value that needs to be determined, this would save on the last step "x-500=175" and also save some people of the mistake of reporting 675 as the answer. The rest of the solution majorly remains the same. Given below for reference. Let the cost of a course in level 11 = x => Cost of level 10 = x+(50*1)... and so on => cost of level 1 = x+(50*10) = x+500 => Total cost of 1 course in each of the 11 levels = x+(x+50)+(x+100)+.....+(x+500) = 11x + 50 (1+2+....+10) = 11x + (50*55) => 11x+2750 = 4675 11x = 1925 x= 175 Answer A Manager Joined: 12 Nov 2014 Posts: 63 A gym offers 11 levels of fitness classes, and in an attempt to reward [#permalink] ### Show Tags 06 May 2015, 17:42 Hi Bunuel, Good question! But don't you think the question should have mentioned 'equally priced fitness levels'? Here we have to assume that each level is at same price to solve the problem. Ambarish _________________ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Kindly press Kudos if the explanation is clear. Thank you Ambarish Intern Joined: 09 Oct 2014 Posts: 20 Re: A gym offers 11 levels of fitness classes, and in an attempt to reward [#permalink] ### Show Tags 06 May 2015, 18:00 It's basically a question on arithematic progression in which we are given common difference,d=-50 (negative because the value is decreasing) the sum of all terms=$4675

we know that sum of all terms,
Sn=n/2(2a+(n-1)d)
4675=11/2(2a+(11-1)(-50))
on soving giving a=675

we know nth term in AP is, an= a+(n-1)d
so 11th, ie the least amout to be paid is $150 _________________ Appreciate my post with Kudos if it is helpful All the best for your prep Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8803 Location: Pune, India A gym offers 11 levels of fitness classes, and in an attempt to reward [#permalink] ### Show Tags 07 May 2015, 22:31 1 2 noTh1ng wrote: akhilbajaj wrote: Let the cost of a course in level 1 = x => Cost of level 2 = x-(50*1)... and so on => cost of level 11 = x-(50*10) = x-500 => Total cost of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500) = 11x -50 (1+2+....+10) = 11x - (50*55) => 11x-2750 = 4675 11x = 7425 x= 675 x-500=175 Answer A Is there a faster way? Hardly possible to do this in < 2minutes It's possible to do it very quickly if you are comfortable with Arithmetic Progressions (AP). This is an AP with common difference as -50 and 11 total terms. We know the following things about an AP: $$Sum = n/2 [2a + (n-1)*d]$$ $$Last term = a + (n-1)*d$$ $$Sum*2/n = 2a + (n-1)*d$$ Divide the equation by 2 to get: $$Sum/n = a + (n-1)*d/2$$ Add (n-1)*d/2 on both sides to get: $$Sum/n + (n-1)*d/2 = a + (n-1)*d = Last term$$ We know that Sum = 4675, n = 11 and d = -50. Plug in the values to get $$4675/11 + (11 - 1)*(-50)/2 = 175 = Last term$$ Answer (A) For more on AP and the related formulas, check: http://www.veritasprep.com/blog/2012/03 ... gressions/ _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Math Expert Joined: 02 Sep 2009 Posts: 52344 Re: A gym offers 11 levels of fitness classes, and in an attempt to reward [#permalink] ### Show Tags 11 May 2015, 04:16 [url][/url] Bunuel wrote: A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges$50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost for a course at the gym's highest level? A.$175
B. $245 C.$425
D. $675 E.$725

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

One important consideration makes this problem much more solvable in under two minutes:

This is an evenly-spaced set!

Which, of course, means that the median (the middle number) equals the average. So if you divide 4675 by 11 to find the average you'll also have the middle number. 4675/11 isn't the nicest math, but if you break it up:

4400/11 = 400

and

275/11 = 25

So the mean/median is $425. Then think about the increments of$50; if $425 is the sixth of eleven values, then you need to move five increments of$50, a total of $250, to get to the target value. And here's where it pays to double-check the question. They want the highest LEVEL of course which then would have the LOWEST price, so subtract$250 from $425 to get the correct answer,$175.
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Re: A gym offers 11 levels of fitness classes, and in an attempt to reward  [#permalink]

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27 Mar 2016, 19:31
Bunuel wrote:
A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was$4675. What is the cost for a course at the gym's highest level?

A. $175 B.$245
C. $425 D.$675
E. $725 Kudos for a correct solution. my approach: there are 10 courses, each less 50$
so
11th x-10*50
10th x-9*50
9th x-8*50
8th x-7*50
7th x-6*50
etc.

so there is (1+2+3+4+5+6+7+8+9+10)*50
sum of all from 1 to 10 is 10*11/2 = 55
55*50 = 2750
11x = 4675 + 2750
11x = 7450
x=675
11th course is 675 - 10*50 = 175.
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Re: A gym offers 11 levels of fitness classes, and in an attempt to reward  [#permalink]

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03 Apr 2018, 02:23
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Re: A gym offers 11 levels of fitness classes, and in an attempt to reward &nbs [#permalink] 03 Apr 2018, 02:23
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