QR question

[dentist_dude]

A stock falls in price by 30%. The next day it rises by 17%. The third day, it falls to 6% of the second day value. What is the approximate overall percent change in the stock price?
I usually assume that the original price is 100 and apply the percent changes that it went through and then do original - new/original*100 but this not working here!!

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[DAT Destroyer]

A stock falls in price by 30%. The next day it rises by 17%. The third day, it falls to 6% of the second day value. What is the approximate overall percent change in the stock price?
I usually assume that the original price is 100 and apply the percent changes that it went through and then do original - new/original*100 but this not working here!!

That should work. Check your calculations.
If you start with 100 after a decrease of 30% you get 70. After an increase of 17% you get 17+.17(17)=81.9. Then it decreased by 6% of the value of the second day which is 70. 6% of 70 is 4.2. 81.9-4.2= 77.7
100-77.7=22.3
Final answer 22.3%

Hope that helps!

 

[Gunacaik]

That should work. Check your calculations.
If you start with 100 after a decrease of 30% you get 70. After an increase of 17% you get 17+.17(17)=81.9. Then it decreased by 6% of the value of the second day which is 70. 6% of 70 is 4.2. 81.9-4.2= 77.7
100-77.7=22.3
Final answer 22.3%

Hope that helps!

I would like to correct this.

The actual answer is found this way:

You start out with 100, so.... 100 * .70 = 70
Next, 70 * 1.17 = 81.9
Next, 81.9 * 0.06 = 4.914 (it decreased by 6% OF the value of the second day; the wording initially threw me off; thought it was .94 at first)

And finally, 100 - 4.914 = ~95% decrease, which can also be written as -95%

This question is from DAT Bootcamp QR
EDIT: spelling mistake

 

[Bingwen]

A stock falls in price by 30%. The next day it rises by 17%. The third day, it falls to 6% of the second day value. What is the approximate overall percent change in the stock price?
I usually assume that the original price is 100 and apply the percent changes that it went through and then do original - new/original*100 but this not working here!!

One way that I quickly approximated this in my head was doing 0-30+17-6= 19%
So depending on the answer choices this might get you close enough. It will obviously be different because you have to compensate for it not being 100% each day which should tell you it will be a slightly larger percentage. Hope this helped.

 

[DarkVoid11]

That should work. Check your calculations.
If you start with 100 after a decrease of 30% you get 70. After an increase of 17% you get 17+.17(17)=81.9. Then it decreased by 6% of the value of the second day which is 70. 6% of 70 is 4.2. 81.9-4.2= 77.7
100-77.7=22.3
Final answer 22.3%

Hope that helps!

I know this might be improper, but I would just use the calculator since it would be faster than thinking.

-If you take 100 stocks for example,

• "A stock falls in price by 30%" means you're obviously left with 70 stocks. I.e. (100%-30%) is the same thing here, left with 70% or multiple by .7

• "The next day it rises by 17%" means a multiple of 1.17.

I.e. because of an increase of 17% it's the same thing as saying you have 100% of your stocks, but you also have 17% more. That "17% of the value" can be determined by multiplying your value by .17. And you add them up you get your number.
1+.17=1.17 (if that makes sense)
If there was no increase or decrease the value would be multiplied by 1 (1*70=70)

• The third day, it falls to 6% of the second day value. This just means that you have 6% of your stocks left or multiply this by .06

Overall my calculation would look like this,

100 stocks x .70 = 70 stocks (day 1)
70 stocks x 1.17= 81.9 stocks (day 2)
81.9 stocks x .06= 4.914 stocks (day 3)

What is the approximate overall percent change in the stock price?
You had 100 stocks and now you have 4.914 stocks on day 3. 100-4.9= 95.1 or 95.1% decrease or you kept 4.91% of the original value.

THIS is the same thing as using the percent change formula : [(X2-X1)/X1]* 100 or [(4.91-100)/100]*100%= -95.1%

 

[Bingwen]

I know this might be improper, but I would just use the calculator since it would be faster than thinking.

-If you take 100 stocks for example,

• "A stock falls in price by 30%" means you're obviously left with 70 stocks. I.e. (100%-30%) is the same thing here, left with 70% or multiple by .7

• "The next day it rises by 17%" means a multiple of 1.17.

I.e. because of an increase of 17% it's the same thing as saying you have 100% of your stocks, but you also have 17% more. That "17% of the value" can be determined by multiplying your value by .17. And you add them up you get your number.
1+.17=1.17 (if that makes sense)
If there was no increase or decrease the value would be multiplied by 1 (1*70=70)

• The third day, it falls to 6% of the second day value. This just means that you have 94% of your stocks left or multiply this by .94

I.e. As in if I took 5% of your $100, you have $95 left. Or you could just do this with multiplication like you have 95% left, which is the same thing as multiplying with .95.



Overall my calculation would look like this,

100 stocks x .70 = 70 stocks (day 1)
70 stocks x 1.17= 81.9 stocks (day 2)
81.9 stocks x .94= 76.986 stocks (day 3)

What is the approximate overall percent change in the stock price?
You had 100 stocks and now you have 76.986 stocks on day 3. 100-77= 23 or 23% decrease or you kept 77% of the original value.

THIS is the same thing as using the percent change formula : [(X2-X1)/X1]* 100 or [(77-100)/100]*100%= -23%

That would be a way to do it but I would also be careful. The QR section tends to be very high paced because you very little time per question and it would not shock me to see both 77% and 23% on there. So I would just make sure that you read the question carefully because it would not be hard to accidentally click the wrong answer for that.

 

[DarkVoid11]

That would be a way to do it but I would also be careful. The QR section tends to be very high paced because you very little time per question and it would not shock me to see both 77% and 23% on there. So I would just make sure that you read the question carefully because it would not be hard to accidentally click the wrong answer for that.

True, the only mishaps would not reading what the question wants. But for me this method is the quickest.

 

[bentley13]

A stock falls in price by 30%. The next day it rises by 17%. The third day, it falls to 6% of the second day value. What is the approximate overall percent change in the stock price?
I usually assume that the original price is 100 and apply the percent changes that it went through and then do original - new/original*100 but this not working here!!

Don't overthink it. You can't go through paragraphs of thought process on this. There isn't time... enter into your calculator this(each individual step separated by commas): 100, *, .7, =, *, 1.17, =, *, .06, =

The "=" are crucial as the calculator is touchy. This can be a 20-30 second problem, and when you figure out the calculator, this will be the type of gimme problem you'll want to see on test day. Good luck!

Note: the answer is the % change. So 100 minus whatever the calculator says. Just take your final number you get in the calculator and subtract 100. Ignore the negative sign and there's the answer.

 

[bentley13]

I know this might be improper, but I would just use the calculator since it would be faster than thinking.

-If you take 100 stocks for example,

• "A stock falls in price by 30%" means you're obviously left with 70 stocks. I.e. (100%-30%) is the same thing here, left with 70% or multiple by .7

• "The next day it rises by 17%" means a multiple of 1.17.

I.e. because of an increase of 17% it's the same thing as saying you have 100% of your stocks, but you also have 17% more. That "17% of the value" can be determined by multiplying your value by .17. And you add them up you get your number.
1+.17=1.17 (if that makes sense)
If there was no increase or decrease the value would be multiplied by 1 (1*70=70)

• The third day, it falls to 6% of the second day value. This just means that you have 94% of your stocks left or multiply this by .94

I.e. As in if I took 5% of your $100, you have $95 left. Or you could just do this with multiplication like you have 95% left, which is the same thing as multiplying with .95.



Overall my calculation would look like this,

100 stocks x .70 = 70 stocks (day 1)
70 stocks x 1.17= 81.9 stocks (day 2)
81.9 stocks x .94= 76.986 stocks (day 3)

What is the approximate overall percent change in the stock price?
You had 100 stocks and now you have 76.986 stocks on day 3. 100-77= 23 or 23% decrease or you kept 77% of the original value.

THIS is the same thing as using the percent change formula : [(X2-X1)/X1]* 100 or [(77-100)/100]*100%= -23%

Good work, but the 2nd day should be multiplied by .06, not .94. Small mistake- huge difference in answers.

 

[bentley13]

That should work. Check your calculations.
If you start with 100 after a decrease of 30% you get 70. After an increase of 17% you get 17+.17(17)=81.9. Then it decreased by 6% of the value of the second day which is 70. 6% of 70 is 4.2. 81.9-4.2= 77.7
100-77.7=22.3
Final answer 22.3%

Hope that helps!

Again, decreased to 6%, not by 6%.

This thread is a great example of why you need to read problems carefully.

 

[DarkVoid11]

Good work, but the 2nd day should be multiplied by .06, not .94. Small mistake- huge difference in answers.

Gotcha. Thanks for making me see it!