Problem Solving

A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 50 percent of what the collector had paid. The shop then sold the clock again at a profit of 80 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $100, for how much did the shop sell the clock the second time?
$270
$250
$240
$220
$200


When I saw this question I started with the original cost of item as 100 and then worked all the way to 108 and then realized the values I have chosen does not represent the question because of $100 difference.

My question - when I see a question, should I first read the question completely and then start working on the question or start working from the first sentence the way I did what is the fastest way to solve something like this. Would really like some idea

OA is A

If we try solving the problem in terms of the original price then it might help

Lets say the Price is X.

Store sells to collector at 20% more : 1.2X

Stores buys from Collector at 50% of sold price : 50% of 1.2X = .6X

so it means : X -.6X = 100 or X = 250

Now he sells it at a 80% Profit on .6X this means :

.6 *250 + .6*250*.8 = 150 + 120 = 270

Hope this helps

Thanks,

but my question is - did you first read the problem and then picked the pen to start solving or did you just started scriblliing on the notepad from the very first sentence?

vineetbatra wrote:Thanks,

but my question is - did you first read the problem and then picked the pen to start solving or did you just started scriblliing on the notepad from the very first sentence?

I could see why it was so tempting to begin solving while reading!

Aside from understanding the fundamentals, having a cosistent and effective procedure is likely the most important thing for the GMAT.

Step 1 of the Kaplan method for problem solving is to analyze all of the information first, while step 2 is to then state the task.

(Step 3 is to approach strategically, thinking about what approach would be best for the question at hand. In step 4, we confirm the answer, making sure we`re answering the right question, and that our answer makes commonsense).

This question is a good endorsement of the method. Following the method we first would have read the whole text; next, we would state the task (what does the correct answer represent). Only then, would we have thought about approach: do we want to use algebra, pick numbers, backsolve, employ reasoning. (I guess, unfortunately, you selected an approach (picking numbers), and started solving the question before stating the task!)

Thanks Testluv, that is exactly what I did, I picked numbers even before reading the whole question to save time.

So do you recommend reading all the PS questions first and then figure out a way to solve?

Vineet

vineetbatra wrote:Thanks Testluv, that is exactly what I did, I picked numbers even before reading the whole question to save time.

So do you recommend reading all the PS questions first and then figure out a way to solve?

Vineet

Yes, I do!

I follow the Kaplan method for problem-solving:

Step 1: Analyze the information (what do I know and not know?)

Step 2: State the task (what exactly is the question asking? what does the correct answer represent?)

Step 3: Approach strategically (can I use reasoning/answer choices/picking numbers or is the algbra quick and straightforward?)

Step 4: Confirm your answer (am I answering the right question, and does my answer make sense?)

vineetbatra wrote:Thanks Testluv, that is exactly what I did, I picked numbers even before reading the whole question to save time.

So do you recommend reading all the PS questions first and then figure out a way to solve?

Vineet

Hi Vineet,

One thing which I want to point out here is the way you've done is absolutely correct. That's the beauty of %ges that you can pick 100 ( that's what per-cent stands for ! ) and arrive at the correct solution.

You said you got 108 as the final answer and you stopped! why buddy ? you were correct all the time! it's just that there was one more step after it.

The question says that the difference was $100. And you got 40 as the difference in your system .

Fine! that means your 40 is equal to $100 . Therefore, your 108 is equal to = 108/40 * 100 = $270 .


There you are !

working with 100 in percentage problems always works. It's just that you may have to think a bit more.

Thanks Harsha,

the reason I stopped is I just noticed a twist in the question and sorta panicked. And you know what happens when you panic.

So I am questioning my technique, should have I read the entire question and then started solving or tried not to panic .

I am sort of struggling with the timing of Quant and this is causing a dip in my score.

Thanks,

Vineet

vineetbatra wrote: And you know what happens when you panic.

I sure do! yes it happens all the time with me as well.

vineetbatra wrote: should have I read the entire question and then started solving or tried not to panic .

Yes, that's what I've learnt as well. Whenever I've tried to increase my speed, compromising on the right-technique which Testluv has explained in the previous post, I've always suffered. It is always advisable to read all the information carefully, no matter if it takes much of the problem time.

vineetbatra wrote: I am sort of struggling with the timing of Quant and this is causing a dip in my score.

me too

Good One !

here's how i approached it:

x= original price of clock
then sold for 20% more, so
x+0.2x=1.2x
then, bought back by store at 50% of price sold, so
0.5*1.2x=0.6x
then sold at 80% profit, so
0.8*0.6x+0.6x=1.08x

original cost-clock buy back =100
so plug in from above
x-0.6x=100
x=250

then plug in 1.08*250=
270