Two countries, Lativia and Manavia, have different business

Question

Two countries, Lativia and Manavia, have different business cycles: in Lativia, two downturn years are always separated by exactly 10 expansion years, while in Manavia, two downturn years are always separated by 18 expansion years. In each country, any calendar year is either a downturn year or an expansion year. 1904 was a downturn year for Manavia and 1905 was a downturn year for Latavia. In which decade will the two countries' economies contract in the same year?

 (A) 2011-2020 (B) 2021-2030 (C) 2031-2040 (D) 2041-2050 (E) 2051-2060

kevincan · Answer

Nobody likes countries with strange names?

Yurik79 · Answer

On the real exam I ll go with C on this question
I struggled about 2 min but has no clue how to solve it))And C is my bet blind shoot answer choice.

game over · Answer

This question is very tricky (or I am stupid ...)

First, observe that he text doesn't state wheter Manavia's economy contracts in 1903 or in 1905. 

Manavia's business cycle is either 03-04, 05-22, 23-24, 25-42 ... (2003-2004, 2005-2022) or 04-05, 06-23, 24-25 ...( 2004-2005, 2006-2023).

Lativia's business cycle is 05-06, 7-16, 17-18 ....
It is easier to write this as follows: 6, 16, 18, 28, 30, 40, 42, 52, 54, 64, 66, 76, 78, 88, 90, 100, 102, 112, 114, 124, 126, 136, 138, 148, 150, 160 ...
(the number shows us, when the expansion or contraction phase ends). 

Now: Compare both business cycles. 
You can see that both economies contracts in 2025 for the first time. 

Hence, B is the correct answer (I think). 
(Note: If Manavia's economy contracts in 1903 and 1904 there is no date between 2010 and 2060 where both economies contract)

Aah ... ok. 
Paddy is right. 2037

MA · Answer

your question is little unclear. when the lativia's economic downturn ended? in 1904 (begaining or ending) or 1905 or 1906?

kevincan · Answer

I've changed the wording to make it clearer. Thanks for your feedback!

paddyboy · Answer

C.

I got the series of downturn years for Lativia and for Manavia, comparing the lists, got 2037 as the common year.

Is there any faster method? This one took a long time...

kevincan · Answer

I get 2048= 1904+144=104+18*8=1905+143=1905+13*11

Any ideas on how we can get this quickly (less than 2-3 minutes)?

Clue: Forget about the actual years!

jaynayak · Answer

Another way is the LCM of the 10 and 18 that is 60

So only after a gap of 60 years there economies will contract.

Hence only after 2026 will there economies contract. The decade after 2036 is 2031-2040

hence C.

It is a hard question considering that you should not chose 2021-2030.... because the event will only happen after that.

kevincan · Answer

Any ideas on how we can get this quickly (less than 2-3 minutes)?

Clue:  Forget about the actual years! 
In Lativia, contraction years happen once every   11   years, whereas in Manavia, they occur every   19   years

We have to find positive integers m and n such that

1905+11m=1904+19n
1+11m=19n

i.e. Find smallest positive integer value of n such that 19n divided by 11 yields a remainder of 1.

Look at positive multiples of 19, subtract multiples of 11 to find remainder when divided by 11

n=1......19............... remainder 8
n=2......8+19=27..... remainder 27-22=5
n=3......5+19=24..... remainder 24-22=2
n=4......2+19=21..... remainder 10
n=5......29............... remainder 7
n=6......26............... remainder 4
n=7......23................ remainder 1 19*7=133

So n is 7 and the year in which both economies contract is 1904+133=2037

Check: 1905+11*12=2037

Two countries, Lativia and Manavia, have different business

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards