A dealer originally bought 100 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many dollars was each battery sold?

(A) 3q/200
(B) 3q/2
(C) 150q
(D) q/100
(E) 150/q

ALGEBRAIC APPROACH:
The cost of 100 batteries is q dollars, thus the cost of 1 battery is q/100 dollars. Since the selling price is 50% greater than the cost price than the selling price is q/100*1.5=q/100*3/2=3q/200.

Answer: A.

NUMBER PLUGGING APPROACH:
Say q=$200, then the cost of 1 battery is q/100=$2.
The selling price is 2*1.5=$3.

Now, plug q=200 in the answers to see which yields $3. Only answer choice A works.

Answer: A.
_________________

\

Hi Bunuel,

According to your approach the answer comes out to be 2q/300 and not 3q/200. Could you kindly explain?

Thanks,
AJ

Nothing wrong there: q/100*1.5 = q/100*3/2 = 3q/200.
_________________

I don't understand how q can also be used as the price.

I set up an equation like 100 * x = q; with x being the price per battery. Therefore price per battery would be 100x/q...

I just don't get how a equation would be set up without another variable for the price per battery... If anybody could help?

Dear noTh1ng

The correct equation to write from the highlighted part above is: x = q/100.

That is, price per battery = q/100

The mistake that you did was in the red part.

Please let me know if something is still not clear.

Best Regards

Japinder
_________________

EgmatQuantExpert

my god, what a stupid mistake. Thank you very much for clarification, sometimes I just don't see the wood for the trees...

nice question. But I doubt this can be 700 level question especially when considering some of Bunuel and Egmatquant questions, which are absoulte killers.

Hi All,

This question can also be solved by TESTing VALUES.

We're told that 100 identical batteries cost a total of Q dollars.

Let's TEST....
Q = 200
So we bought 100 batteries for $200; that is $2/battery.

Next, we're told that each battery was sold at 50 percent above the original cost per battery...

Buy price = $2/battery
Sell price = (1.5)(2) = $3/battery

We're asked for how many dollars each battery was sold.....so we're looking for an answer that equals 3 when Q = 200...

Answer A: 3Q/200 = 600/200 = 3 This IS a match
Answer B: 3Q/2 = 600/2 = 300 NOT a match
Answer C: 150Q = 30,000 NOT a match
Answer D: Q/100 = 200/100 = 2 NOT a match
Answer E: 150/Q = 150/200 = 3/4 NOT a match

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

I think its easier to calculate like 1.5*q/100 = 3q/200
_________________

Hi apoorv601,

One of the great things about most GMAT questions is that they can be approached in a variety of different ways. Ultimately, when dealing with any individual question, you want to know MORE than one way to answer the question AND you want to use whatever method is fastest and easiest for you. If you think that an Algebra-based approach is easiest for this prompt, then that's fine, BUT an Algebra-based approach will NOT be the easiest approach for every prompt. To deal with that contingency on Test Day, you have to be practicing other approaches now, so that you'll be flexible enough to not get 'stuck' during the actual Exam.

GMAT assassins aren't born, they're made,
Rich
_________________

Total Cost = Q
Cost per Unit = Q/100
Sale Price = 3/2 * Q/100 = 3Q/200 (A)

We are given that 100 batteries cost a TOTAL of q dollars. We are also given that EACH battery was sold at 50% above the original cost. The first thing we must do is create an equation for q. Remember that q is the TOTAL COST. So if we make b = the original cost per battery we can say:

100 x b = q

b = q/100

We now have the original cost per battery in terms of q. Next, we determine the selling price when we increase the cost by 50%. To calculate this increase we simply multiply q/100 by 1.5. We have:

(q/100) x 1.5

(q/100) x 3/2 = 3q/200

Answer: A

If you don't like working with variables, you could instead substitute a convenient number for q. Normally I would not suggest the plugging-in method in a problem such as this; however, since we have only one variable, the method will be sufficient.

Let's say we make the total cost of the 100 batteries q = 200. This is a convenient number that will work well with the numbers presented in the problem. We can now set up a similar equation to what we did above, where b = the original price per battery.

100 x b = 200

b = 200/100

b = 2

The cost per battery is $2. Now we need to show the selling price per battery by increasing $2 by 50%.

2 x 1.5 = 3

The answer 3 is the selling price of the battery.

The last step is to now plug our value of q = 200 into each answer choice to see which one provides us with a value of 3. This will yield the correct answer.

(A) 3q/200

(3 x 200)/200 = 3

This IS equal to 3.

(B) 3q/2

(3 x 200)/2 = 600/2 = 300

This IS NOT equal to 3.

(C) 150q

150 x 200 = 30,000

This IS NOT equal to 3.

(D) q/100

200/100 = 2

This IS NOT equal to 3.

(E) 150/q

150/200 = 15/20 = ¾

This IS NOT equal to 3.

Answer choice A is the only one that is equal to 3.
_________________

Could someone chime in and explain if this method works as well?

q/100 + (q/100 * 50/100) and simplify from here. I get the following after simplification:

q/100 + 50q/10000
100q/10000 + 50q/10000
150q/10000
15q/1000 (divided by 5)
3q/200

A

from problem stem 100 (x) = q

so assume x = 2 and q = 200
50% increase => x = 3 and q = 300

substitute new q and x values in each option, Option A satisfies

cost price per battery = \(\frac{q}{100}\)
selling price per batter = \(1.5 * (\frac{q}{100}) = \frac{3}{2} * (\frac{q}{100}) = \frac{3q}{200}\)
_________________

Why we have taken sales price =3/2 ?

Sent from my MI 5 using GMAT Club Forum mobile app

We are told that each battery was sold at 50 percent above the original cost per battery:

50 percent above = times 1.5, so times 3/2.
_________________

Yes.. Thank you so much Bunuel

Sent from my MI 5 using GMAT Club Forum mobile app

hello niks18,

q/100*1.5 this part means that selling price of each item is increaed by 50% - shouldnt 1.5q/100 be the answer? ;?

and this one q/100*3/2 what does it mean ? where from do we get 2/3 and what is it