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Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
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happyface101 wrote:
Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. In which month were sales closest to Jan?

a. Feb
b. Mar
c. Apr
d. May
e. June

What's the easiest / quickest way to solve this?


Find the missing link ( Much like Darwin's missing link )

Quote:
10% greater in February than in January
15% less in March than in Feb
20% greater in April than in March
10% less in May than in April
5% greater in June than in May


Can you find the link ? Yes you are correct, sales of next month depends on the sale of This month............

So, Assume Sales in Jan as 1000 or x as you wish and proceed.....

Abhishek


PS : This is a calculation intensive Problem and will result in decimal numbers so, it will be better to assume the sales figure of Jan as X and solve algebraically ( My personal Opinion)
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
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VeritasPrepKarishma wrote:
happyface101 wrote:
Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. In which month were sales closest to Jan?

a. Feb
b. Mar
c. Apr
d. May
e. June

What's the easiest / quickest way to solve this?


You can do this question easily if you understand number properties. Let me try to explain. Note that explaining takes quite a bit of time though if you understand this, thinking through doesn't take more than a few seconds:

There is an increase, then a decrease, then an increase, then a decrease and an increase again.
Most probably, when you apply an increase and then a decrease, the figure will come back close to its original value. So March or May are the best bets.

The first iteration (Feb-March) will take it much lower since after you increase by 10%, you are decreasing by a number greater than 10%. Actually, to come back to original, you need to decrease by a number slightly smaller than 10%.
Take an example: original value = 100
Increase by 10% to get 110.
Now if you decrease it by about 9%, you will get 100 back. But you actually decrease by 15% so it goes down. So March is unlikely.

Next iteration is April-May. You increase a number smaller than 100 by 20% and then bring it down by 10%. This should be the answer in all probability. Though 20% seems like a big increase compared to the 10% decrease so it looks like the figure might be much greater than original but the next step (5% increase) is a further increase so June is anyway not possible.
Just to be sure, let's see the effect of these 4 operations on the original value:
(11/10)*(17/20)*(6/5)*(9/10) = (99/100)*(102/100) (club together first and last terms to get 99/100 and second and third terms to get 102/100)
This would be extremely close to 1.

So answer would be May.

Answer (D)



Why do we club 2nd and 3rd ?

(11/10)*(17/20)*(6/5)*(9/10) = (99/100)*(102/100) (club together first and last terms to get 99/100 and second and third terms to get 102/100)
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
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parvgugnani wrote:
VeritasPrepKarishma wrote:
happyface101 wrote:
Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. In which month were sales closest to Jan?

a. Feb
b. Mar
c. Apr
d. May
e. June

What's the easiest / quickest way to solve this?


You can do this question easily if you understand number properties. Let me try to explain. Note that explaining takes quite a bit of time though if you understand this, thinking through doesn't take more than a few seconds:

There is an increase, then a decrease, then an increase, then a decrease and an increase again.
Most probably, when you apply an increase and then a decrease, the figure will come back close to its original value. So March or May are the best bets.

The first iteration (Feb-March) will take it much lower since after you increase by 10%, you are decreasing by a number greater than 10%. Actually, to come back to original, you need to decrease by a number slightly smaller than 10%.
Take an example: original value = 100
Increase by 10% to get 110.
Now if you decrease it by about 9%, you will get 100 back. But you actually decrease by 15% so it goes down. So March is unlikely.

Next iteration is April-May. You increase a number smaller than 100 by 20% and then bring it down by 10%. This should be the answer in all probability. Though 20% seems like a big increase compared to the 10% decrease so it looks like the figure might be much greater than original but the next step (5% increase) is a further increase so June is anyway not possible.
Just to be sure, let's see the effect of these 4 operations on the original value:
(11/10)*(17/20)*(6/5)*(9/10) = (99/100)*(102/100) (club together first and last terms to get 99/100 and second and third terms to get 102/100)
This would be extremely close to 1.

So answer would be May.

Answer (D)



Why do we club 2nd and 3rd ?

(11/10)*(17/20)*(6/5)*(9/10) = (99/100)*(102/100) (club together first and last terms to get 99/100 and second and third terms to get 102/100)


You don't have to - you can to help you in your calculation. The denominators multiply to give 100. The numerator is something very close to 100. So you know that by clubbing, you can easily approximate.
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
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All of the increases and decreases can be represented in base-10, so pick a fairly large number that's base-10 and work through the calculations.

\(January=$10,000\)
\(February=$10,000*1.1 = $11,000\)
\(March=$11,000 *.85 = $10,000*.85 + $1,000*.85=$8,500 + $850 =$9,350\)
\(April=$9,350*1.2=$9,350+.2*$9,350=$9,350+$1,870=$11,220\)
\(May=$11,220*.9=$11,220-.1*$11,220=$11,220-$1,122=$10,098\)

Don't calculate June - obviously, if \($10,098\) gets larger, then it's farther from \($10,000\) than May. The important piece here is being able to quickly do calculations with numbers in base-10. You should know shortcuts for these operations, or GMAT estimation questions will frustrate you and devour the clock.

Answer D
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
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Let the sales is May is 100.
Then June sell = 100+5=105
April sell=100+10=110
March sell=110-20=90
Feb sell=90+15=105
Jan sell=105-15=90.
Hence, January sell is near to May sell.
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
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Hi All,

TESTing VALUES (the approach used by a number of the posters in this thread) works perfectly in these types questions. You can also approach these types of questions algebraically (you just have to be careful with the 'math work').

January = X dollars in sales
February = 1.1X dollars in sales
March = 1.1X - (.15)(1.1X) = 1.1X - .165X = .935X dollars in sales
April = .935X + (.2)(.935X) = 1.122X dollars in sales
May = 1.122X - (.1)(1.122X) = 1.0098X dollars in sales
June = 1.0098X + .(.05)(1.0098X) = clearly more than the dollar sales in May

We're asked for the month that was closest to January in sales (so closer to X). That is clearly May.

Looking at this work, you should be able to see how TESTing VALUES is an easier approach.

Final Answer:

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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
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For me it was easier to solve using 1$ as the sales amount for jan

10% greater in February than in January ---> Feb = 1.1x1 =1.1
15% less in March than in Feb ---> Mar = 1.1x0.85=0.93
20% greater in April than in March ---> Apr = 0.93x1.2=1.12
10% less in May than in April ---> May = 1.12x0.9=1.004
5% greater in June than in May --->Jun = 1.0x1.05=1.05

Hence, May is the closest.
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
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If you look at the % changes, you can see that the 15% is the trickiest one to handle. Try to choose a number that can handle that easily.

Jan, Feb (+10%), Mar (-15%), Apr (+20%), May (-10%), Jun (+5%)

Let's choose Mar = 85, then:
* Feb = 100, Jan = ~90
* Apr = 102, May = ~90, Jun =~95

Pretty clear that Jan and May are the closest.
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
VeritasPrepKarishma wrote:
happyface101 wrote:
Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. In which month were sales closest to Jan?

a. Feb
b. Mar
c. Apr
d. May
e. June

What's the easiest / quickest way to solve this?


You can do this question easily if you understand number properties. Let me try to explain. Note that explaining takes quite a bit of time though if you understand this, thinking through doesn't take more than a few seconds:

There is an increase, then a decrease, then an increase, then a decrease and an increase again.
Most probably, when you apply an increase and then a decrease, the figure will come back close to its original value. So March or May are the best bets.

The first iteration (Feb-March) will take it much lower since after you increase by 10%, you are decreasing by a number greater than 10%. Actually, to come back to original, you need to decrease by a number slightly smaller than 10%.
Take an example: original value = 100
Increase by 10% to get 110.
Now if you decrease it by about 9%, you will get 100 back. But you actually decrease by 15% so it goes down. So March is unlikely.

Next iteration is April-May. You increase a number smaller than 100 by 20% and then bring it down by 10%. This should be the answer in all probability. Though 20% seems like a big increase compared to the 10% decrease so it looks like the figure might be much greater than original but the next step (5% increase) is a further increase so June is anyway not possible.
Just to be sure, let's see the effect of these 4 operations on the original value:
(11/10)*(17/20)*(6/5)*(9/10) = (99/100)*(102/100) (club together first and last terms to get 99/100 and second and third terms to get 102/100)
This would be extremely close to 1.

So answer would be May.

Answer (D)


This is genius and right off the bat narrows it down to 2 choices (since There is an increase, then a decrease, then an increase, then a decrease and an increase again). The logic makes perfect sense. If one is under time pressure, this is a much more efficient approach then using algebra or picking 'smart' numbers which are time consuming to calculate in this case.
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
I solved this by plugging-in $1000, but I agree it's fairly calculation intensive and there is a greater chance of error under pressue.

VeritasKarishma to clarify...
so you just took the percentage fluctuations 11/10 * 85/100 * 6/5 * 9/10 to indicate that after the affect of May's percentage change, the net movement is 99/100 *102/100 - a number close to 1, thus May is correct since a further increase would obviously deviate from how close May is from 1 and thus from its original value
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
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This is a problem of successive percentage change
So if there is a percentage change by a% and then by b%, resultant % change is given by formula-

Resultant % change = a + b + \(\frac{( a * b )}{100}\)

For Feb ;
Resultant % change = 10 % ---- (Given)

Till Mar ; (15% less)
Resultant % change = 10 + (-15) + \(\frac{(10 * (-15))}{100}\) = -6.5%
Similarly,

Till Apr ; (20% greater)
Resultant % change = -6.5 + 20 + \(\frac{((-6.5) * 20)}{100}\) = 13.5 - 1.3 ~ 12 %

Till May ; (10% less)
Resultant % change = 12 + (-10) + \(\frac{(12 * (-10))}{100}\) = 0.8 %

Till Jun ; (5% greater)
Resultant % change = 0.8 + 5 + \(\frac{(0.8 * 5)}{100}\) = 6.xx %

So , Least change is in May (0.8%) ... Ans : D
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
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I answered this correctly during my practice exam, but it was very time consuming so I wanted to test what was the best and fastest way to solve this.

After testing out all of these methods posted previously here, I found the fastest explanation for me was from VeritasKarishma from a concept standpoint. However I also realized that simple number testing is especially effective for this problem because all of the percentage changes are multiples of 5, so the numbers can be quickly calculated by plugging values for 10% or 5%. Being under a time crunch and with wanting to see numbers to verify under pressure while testing this may be very effective for people without needing to deal with a lot of successive percentage change fractions.

To illustrate:

Let January = $100
February is 10% greater --> 10% of $100 is $10 so this = $110
March is 15% less --> 15% is 10% + 5%. So 10% of $110 is $11, and half of that is approx. $6. so $110 - $11 - $6 = $93
April is 20% greater --> 10% of $93 is approx. $9, so 20% is $18, so $93 + $18 = $111
May is 10% less --> THIS IS WHERE IT CLICKS! 10% of $111 is $11. $111 - $11 = $100
We could continue a step further to May which is 5% greater, but we can already quickly tell then that it would be $105, and therefore May is the closest to January.

Answer D
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Last year, sales at Company X were 10% greater in February than in January, 15% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 5% greater in June than in May. In which month were sales closest to Jan?

a. Feb
b. Mar
c. Apr
d. May
e. June

If you know the basics of the Percentage less/more and the 10 % base rule, you can easily tackle this question in less than 2 mins.

When you analyze the percentages used here i.e 10%, 15 %,20%, and 5 %. They are very easy to calculate by using the 10 % percent base method.

For those who don't know what is 10 percent base method is, let me give you a brief.

10 % of No = \(\frac{10}{100} \)* No = \(\frac{No}{10}\).
So 10 % of any number is very easy to find, i.e you need to divide the number by 10.

For eg. 10 % of 450 = 45 ---> Divide 450/10
10 % of 45 = 4.5 ---> Divide 45/10

By using 10 % as the base, you can calculate other percentages as well.

20 % of a No = 10 % of No * 2
5 % of a No = 10 % of No / 2
15 % of a No = 10 % of No + 5 % of No

So practice and try to do these calculations in mind. It will help you in saving time.


Just an overview of % less/more, before going forward to the explanation .

X is 10 % less than Y i.e X= Y - 10 % of Y or X = 90% of Y

Similarly, If X is 10 % more than Y i.e X = Y + 10 % of Y or X = 110 % of Y

Here, in this question, let's try to apply both concepts we just learned.

Assume that the sales in Jan be 100. Now, we are going to find the sales in each month as per the data given here and find which month's sales will be close to Jan.

a. Feb
The sales at Company X were 10% greater in February than in January.

Sales in Feb = Sales in Jan + 10 % of Sales in Jan = 100 + 10 = 110.

You can blindly eliminate this option as it's clearly given that sales in Feb are 10 % greater than in Jan. So it's nowhere close to Jan

b. Mar

The sales at Company X were 15% less in March than in Feb.
Sales in March = Sales in Feb - 15 % of sales in Feb = 110 - 15 % of 110= 110 - 16.5 = 94.5

Since 94.5 is not close to 100, you can eliminate this option.
Also if you analyze logically, March won't be the correct answer because 10 % increase and 15 % decrease successively will not get back to the original value ( 0% change )


c. Apr
The sales at Company X were 20% greater in April than in March.
Sales in April= Sales in March + 20 % of sales in March = 94.5 + 20 % of 94.5 = 94.5 + 19 = 113.5

Note: You can use the 10 % percent base method to find 20 % of 94.5.
10% of 94.5 = 9.45
20 % of 94.5 = 9.45 * 2 ~ 19

We don't need to find the exact value here. An approximate value will serve our purpose as we are comparing the sales.

113.5 is way greater than 100, So we can eliminate Option C as well.


d. May
The sales at Company X were 10% less in May than in April.

Sales in May = Sales in April - 10 % of Sales in April = 113.5 - 11.35 = ~ 102 Which is very close to 100 i.e sales in month of Jan

e. June

The sales at Company X were 5% greater in June than in May.
We can eliminate option E as sales in June is 5 % more than in May (~102 ). So it definitely won't be close to 100.

Option D, May is the correct answer as it's very close to 100 i.e Jan sales.

Thanks,
Clifin J Francis,
GMAT QUANT SME
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Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink]
karim2982 wrote:
This can be solved using smart numbers: Let January = $100. (Keep in mind we are using "approximate" values, as per the problem). We have:
Jan = $100
10% greater in February than in January ---> Feb = 1.1 Jan = $110
15% less in March than in Feb ---> Mar = 0.85 Feb = $93.5
20% greater in April than in March ---> Apr = 1.2 Mar = $112
10% less in May than in April ---> May = 0.9 Apr = $101 (we have a winner)
5% greater in June than in May --->Jun = 1.05 May = $106

Ans D


this still requires quite a bit of math.

is there a shorter way? with multiple estimations? It would take me 20 minutes to do it this way
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