The table above shows the percent of change from the previous month in

Question

https://gmatclub.com/forum/download/file.php?id=50472 The table above shows the percent of change from the previous month in Company X's sales for February through June of last year. A positive percent indicates that Company X's sales for that month increased from the sales for the previous month, and a negative percent indicates that Company X's sales for that month decreased from the sales for the previous month. For which month were the sales closest to the sales in January? A. February B. March C. April D. May E. June PS43481.01 2019-09-21_1849.png

KarishmaB · Accepted Answer

When the percentage changes are numbers such as 10, 15, 20 etc, it is easier to use the formula:

Total change = a + b + ab/100

March total change = 10 - 15 -10*15/100 = -6.5
April total change = -6.5 + 20 -6.5*20/100 = 12 (approx)
May total change = -10 + 12 -10*12/100 = 0.6 (approx)

Next change is increase of 5% so it will increase the total change. Hence May has the smallest overall change from Jan of about 0.6%.
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Can you explain the total change approach please? I'm really lost and the article you have linked is not opening the relevant blog. KarishmaB

akadiyan · Answer

Lets substitute number to solve this problem

Let January sales be 100
February - +10% = 110
March = -15% = 93.5
April = +20% = 112.2
May = -10% = 100.98  
June = +5% = 106.029

Ans:   D

thinkvision · Answer

IMO the answer is D (May) which approximately equals 100. Also, I believe the tag should be rectified from 700+ to 600-700. The question is just involves tedious calculation!

- K

Archit3110 · Answer

Let sales In January = 100
Feb = 110
March =110*.85; 93.5
APril= 93.5*1.2;112
May = 112*.9 =  100 
Correct
IMO D

monikakumar · Answer

Hi, is it not taking much time to do all these calculations...may I know how much time on an average on has to take for this kind of problem..and would like to know average time should be taken for solving Ps questions...anyone pls shed some light on this.  Archit3110

SvelteNigerian · Answer

I added the percetntages together to assess the net impact.

After Feb +10% change
After March -5% change
After April +15% change
 after May +5% change 
after June +10% change

This 5% is the  closest  to what it would have been in January as its even less than what it would have been in February due to the 10% change

Does this approach work?  Bunuel

Unknown_ · Answer

OmotayoH going by your approach, even March has a difference of absolute 5% change. How did you choose May over March? Moreover, its incorrect to add up the percentage changes as you have done. If you look at it mathematically, Jan = 100 (lets assume this) Feb = 100 + (+10%) = 110 March = 110 + (-15%) = 0.85*110= 93.5 (if you notice, going by your logic, March was net -5% change with respect to Jan and if we compute basis your logic the value for March comes out to be 0.95*100 ie 95) Apr = 93.5 +(+20%) = 112.2 May = 112.2 +(-10%) = 100.98 Jun = 100.98 + (+5%) = 106.029 In reality, successive % changes are multiplied and not added. Jan=100 Feb=1.1*100 Mar=0.85*1.1*100 Apr=1.2*0.85*1.1*100 May=0.9*1.2*0.85*1.1*100 June=1.05*0.9*1.2*0.85*1.1*100 Hope this helps!

Chidinho · Answer

VeritasKarishma Please is there a way to easily solve this question by using successive percentages together (say 100 * 11/10 * 17/20 * 6/5 * 9/10 * 21/20) and trying understand what successive product (say 11/10 *17/20*6/5) is closest to 1. Instead of doing the multiplication at every step?

Bunuel chetan2u

Bunuel   chetan2u

jaykayes · Answer

Since each percentage change is applied on a different base, we cannot simply add up the percentages and apply it to the original amount.
Also, the changes are too close to each other to look for overall logic.
Calculation of each successive month’s sales will be tedious and time-consuming.
We will therefore use an estimation-based approach as follows:
Let the sales in the base month of January be 100
— Feb sales = 100 + 10% = 110
— March sales = 110 – 15% = slightly less than 95
— April sales = 95 + 20% = slightly less than 115
— May sales = 115 – 10% = slightly less than 104 (because 10% of 115 is slightly more than 11)
— June sales = 104 + 5% = slightly more than 109
May sales are the closest to 100
Answer choice: D

spaghetttti · Answer

When the percentage changes are numbers such as 10, 15, 20 etc, it is easier to use the formula:

Total change = a + b + ab/100

March total change = 10 - 15 -10*15/100 = -6.5
April total change = -6.5 + 20 -6.5*20/100 = 12 (approx)
May total change = -10 + 12 -10*12/100 = 0.6 (approx)

Next change is increase of 5% so it will increase the total change. Hence May has the smallest overall change from Jan of about 0.6%.
------------------------------------------

Can you explain the total change approach please? I'm really lost and the article you have linked is not opening the relevant blog.  KarishmaB

siddhantvarma · Answer

The question can be solved arithmetically. But it’s easier to assume sales in January to be a whole number like 110 and then calculate the sales after each month’s change. Even this approach involves tedious calculations.

Instead, the most time-efficient approach to solve this question would be using the formula for calculating successive percentages. Full link to that thread:  https://gmatclub.com/forum/excellent-method-for-calculating-successive-percentages-185973.html?srsltid=AfmBOooQgNBIHJ7aJJ1DPZ79qTGATRpIh8z9lfNtK2z8wlWlZ53CZEzN 
 
The formula states that if a quantity increased by a% and then increased by b%, the overall total increase is given by: a+b+ab/100

For ex: If the increase is 10% and 20 %, the successive increase will be 10+20+200/100 => 32%
Let’s say the quanity was at 100. A 10% increase => 110 
A 20% increase => 110 + 110/5 => 110 + 22 => 132
Total increase: ((132-100)/100)*100 = 32%

If there's an increase and a decrease, in that case, the decrease will be considered a negative value.

Now back to the question:

Feb: 10%
March: 10-15-150/100 => -6.5%
April: -6.5 + 20 -6.5*20/100 => 13.5 - 1.3 => 12.2%
May: 12.2 - 10 -122/100 => 2.2 - 1.22 => ~1

June is an increase over May so we know it will definitely be far off from Jan than May. Hence May is the closest to Jan. 
(D)

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The table above shows the percent of change from the previous month in

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