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

Question

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

Source: Sackmann's 1800 set

Marcab · Answer

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.

megafan · Answer

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.

Marcab · Answer

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.

KarishmaB · Answer

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.

srikanth9989 · Answer

Let me know if this approach is ok!

Let the ridership in June be 50.
July would be 30 and August would be 10.
Average of 30 and 10 is 20.
50 is 2.5 times 20.

Hence answer would be D.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards