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If a certain bus line's ridership in July was 3/5 of its

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If a certain bus line's ridership in July was 3/5 of its [#permalink] New post 31 Jan 2013, 16:45
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If a certain bus line's ridership in July was \frac{3}{5} of its ridership in June, and its ridership in August was \frac{1}{3} of its ridership in July, then the bus line's ridership in June was how many times the average (arithmetic mean) of its ridership in July and August?

(A) \frac{1}{2}

(B) 1\frac{2}{3}

(C) 2

(D) 2\frac{1}{2}

(E) 5

Relatively easy problem. For some reason I'm getting different answer when I tried using variables and when I tried using numbers. I think my variable approach is wrong, can someone explain using variable approach?

Source: Sackmann's 1800 set
[Reveal] Spoiler: OA

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Re: If a certain bus line's ridership in July was 3/5 of its [#permalink] New post 31 Jan 2013, 19:40
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megafan wrote:
If a certain bus line's ridership in July was \frac{3}{5} of its ridership in June, and its ridership in August was \frac{1}{3} of its ridership in July, then the bus line's ridership in June was how many times the average (arithmetic mean) of its ridership in July and August?

(A) \frac{1}{2}

(B) 1\frac{2}{3}

(C) 2

(D) 2\frac{1}{2}

(E) 5

Relatively easy problem. For some reason I'm getting different answer when I tried using variables and when I tried using numbers. I think my variable approach is wrong, can someone explain using variable approach?

Source: Sackmann's 1800 set


Let the ridership in June be x. Then in july, the ridership would be 3x/5 and thereby in August be x/5. The mean of riderships in the month of July and August would be 2x/5 (no need to calculate, just pick the in between number).
Now the question asks : the ridership in June is how many times that of the average that we just found.
Therefore x/(2x/5)=5/2.
Hope that helps.
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Re: If a certain bus line's ridership in July was 3/5 of its [#permalink] New post 31 Jan 2013, 19:50
Thanks Marcab. I made a silly mistake when taking the average with the reciprocal and arrived at 8x/5, which of course should be 2x/5. Anyway, I tend to make these silly mistakes once in a while, especially when I am doing the Math in my head. I will practice to make good use of my scratch paper from now.
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Re: If a certain bus line's ridership in July was 3/5 of its [#permalink] New post 31 Jan 2013, 19:50
Thanks Marcab. I made a silly mistake when taking the average with the reciprocal and arrived at 8x/5, which of course should be 2x/5. Anyway, I tend to make these silly mistakes once in a while, especially when I am doing the Math in my head. I will practice to make good use of my scratch paper from now.
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Re: If a certain bus line's ridership in July was 3/5 of its [#permalink] New post 31 Jan 2013, 19:53
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Well, if you commit a mistake then try to use number picking. On the test, the last thing you would want is being stuck to a problem.
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Re: If a certain bus line's ridership in July was 3/5 of its [#permalink] New post 31 Jan 2013, 20:25
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megafan wrote:
Thanks Marcab. I made a silly mistake when taking the average with the reciprocal and arrived at 8x/5, which of course should be 2x/5. Anyway, I tend to make these silly mistakes once in a while, especially when I am doing the Math in my head. I will practice to make good use of my scratch paper from now.


Bad idea! Try to stick to doing the calculations in your mind till it becomes second nature. Then you will feel that writing down is too cumbersome. Initially, there will be more errors but later on, you will get very efficient.
Also, if trying to solve orally, making equations mentally isn't the appropriate approach. Take numbers instead:

So there is a 5 and a 3 in the denominator.
Say ridership in June = 15
Ridership in July = (3/5)*15 = 9
Ridership in Aug = (1/3)*9 = 3
Avg ridership in July and Aug = 6

Required answer = 15/6 = 5/2
Now this can be easily done in your mind. You can write 15, 9, 3 and 6 on your scratch pad if you wish but that should be just to ensure that you don't lose focus.
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Re: If a certain bus line's ridership in July was 3/5 of its   [#permalink] 31 Jan 2013, 20:25
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