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# Last year, sales at Company X were 10% greater in February than in Jan

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Intern
Joined: 05 Aug 2015
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Last year, sales at Company X were 10% greater in February than in Jan  [#permalink]

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24 Apr 2016, 22:36
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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

What's the easiest / quickest way to solve this?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10634
Location: Pune, India
Re: Last year, sales at Company X were 10% greater in February than in Jan  [#permalink]

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28 Apr 2016, 20:41
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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?

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.

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Karishma
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Last year, sales at Company X were 10% greater in February than in Jan  [#permalink]

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28 Apr 2016, 13:16
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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 ##### General Discussion Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 5012 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Last year, sales at Company X were 10% greater in February than in Jan [#permalink] ### Show Tags 25 Apr 2016, 01:37 2 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) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Intern Joined: 11 Aug 2014 Posts: 9 Location: United States Concentration: International Business, Entrepreneurship Schools: HBS '18 GPA: 3.9 Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink] ### Show Tags 21 Jul 2016, 03:35 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) Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 10634 Location: Pune, India Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink] ### Show Tags 21 Jul 2016, 20:17 1 1 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. _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Intern Joined: 06 Apr 2017 Posts: 28 Location: United States (OR) Concentration: Finance, Leadership Schools: Haas EWMBA '21 GMAT 1: 730 Q48 V44 GMAT 2: 730 Q49 V40 GPA: 3.98 WE: Corporate Finance (Health Care) Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink] ### Show Tags 03 Aug 2017, 09:16 8 2 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 Intern Joined: 29 May 2017 Posts: 14 Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink] ### Show Tags 01 Sep 2017, 17:49 1 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. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 17021 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink] ### Show Tags 21 Jan 2018, 12:10 1 1 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: GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at: Rich.C@empowergmat.com The Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★ Intern Joined: 14 Jul 2017 Posts: 25 Re: Last year, sales at Company X were 10% greater in February than in Jan [#permalink] ### Show Tags 24 Mar 2018, 07:41 1 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.
Intern
Joined: 04 Feb 2018
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Re: Last year, sales at Company X were 10% greater in February than in Jan  [#permalink]

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04 Apr 2018, 18:03
1
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]

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03 Jun 2018, 13:43
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.

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]

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10 Jul 2019, 16:14
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.

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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11 Jul 2019, 08:10
4
2
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
Re: Last year, sales at Company X were 10% greater in February than in Jan   [#permalink] 11 Jul 2019, 08:10