If a phone call costs a cents for the first minute and a/3 cents

Question

If a phone call costs  a  cents for the first minute and a/3 cents for each additional half-minute, how much a  b  minute phone call cost, in cents ?

A.  \frac{(2a+2ab)}{27}

B.  \frac{(a+2ab)}{3}

C.  \frac{(a+ab)}{300}

D.  \frac{(a+ab)}{3}

E.  \frac{ab}{3}

Zinsch123 · Accepted Answer

First, let's set up an equation:

No matter how long the phone call is, we always have to pay a cents for the first minute. Every minute beyond the first minute costs 2a/3 cents.

Cost of phone call = a + (b-1) * 2a/3

Now we have to simplify this equation.

3a/3 + (b-1) * 2a/3
(3a + (b-1) * 2a) / 3
(3a + 2ab - 2a) / 3
(a + 2ab) / 3

mbaiseasy · Answer

Cost = (1)(a) + ((b-1)/(1/2))(a/3)
Cost = a + (2b - 2)(a/3)
Cost = a + (2ab -2a)/3
Cost = (3a - 2a + 2ab) / 3
Cost = (a + 2ab)/3

Answer: B

Blackbox · Answer

Could someone please help with this question? I thought "a b-minute" could also be half-a-minute in which case it costs a/2 cents. IOW, the cost of "b" minutes is  ab , no?

Bunuel · Answer

A call less than or equal to 1 minute costs  a  cents. So, if b = 1/2 minutes the cost would still be  a  cents.

Easy way would be to just plug numbers, say a = 1 cent and b = 1 minute what would be the cost of a call then? It would cost 1 cent. Plug a = b = 1 and check for an option which would give 1. Only B fits.

Blackbox · Answer

Nice! It is much easier to sub-in values and understand. Thanks

pacifist85 · Answer

This is what I though after reading this:

First minute: a --> this actually means "a" times the number of minutes; in this case a*1.
Extra minutes: (2a)/3 --> a/3 for half a minute, so double this for a whole minute.
Based on the logic we used above to calculate the first minute, which is "a", the following minutes will be (2a)/3 times "b", because "b" is the number of minutes the person spoke.

Adding these: a + (2a)/3 times b, so a + (2ab)/3 --> ***if you write down the fractions horizontally it makes much more sense, because you don't use the parenthesis.

sasori · Answer

Cost = (1)(a) + ((b-1)/(1/2))(a/3)
Cost = a + (2b - 2)(a/3)
Cost = a + (2ab -2a)/3
Cost = (3a - 2a + 2ab) / 3
Cost = (a + 2ab)/3

If a phone call costs a cents for the first minute and a/3 cents

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 phone call costs a cents for the first minute and a/3 cents

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