Inspired wrote:If Carlos, Eric, Jeff, and Nigel together have a total of 100 guitars, and each guitar has only one owner, then Nigel has how many more guitars than Eric does?

(1) Carlos has two more guitars than Jeff does: Eric has twelve fewer guitars than Jeff does.
(2) If Nigel had three times as many guitars as he does, he would have two fewer guitars than Carlos and Jeff together have now.

Given in the question c + e + j + n = 100 --- (1)

u need to know (n-e)

1. gives

c = j+ 2 ---- (2)

e + 12 = j ---- (3)

2. gives

3n + 2 = c + j --- (4)

Now together you have 4 equations and you can find out n and e and find out n - e

(4) in (1) implies 4n + e = 98 ---- (6)

(2) in (3) implies c = e+14 ----(5)

(5) and (3) in 1 implies = 3e+26 +n = 100

3e+ n = 74 --------(7)

solving (7) and (6) simultaneously we get n = 20 e =18

n-e = 2

Answer would be C. Both (1) and (2) independently are insufficient because each leaves you with formulas with two unknowns.

Inspired wrote:If Carlos, Eric, Jeff, and Nigel together have a total of 100 guitars, and each guitar has only one owner, then Nigel has how many more guitars than Eric does?

(1) Carlos has two more guitars than Jeff does: Eric has twelve fewer guitars than Jeff does.
(2) If Nigel had three times as many guitars as he does, he would have two fewer guitars than Carlos and Jeff together have now.

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Statement 1:No mention of Nigel,hence straightaway we can point out that it is independently insufficient.

Statement2:Considering it independently,3n=(c+j)-2
Adding n+e on both sides 4n+e=(c+j+n+e)-2
=>4n + e=100-2 [total ownership of 100 guitars]
=>4n+e=98 -----(1)
=>n=(98-e)/4 .....here we are getting more than one solution.
Statement 1 & 2 together: e=98-4n(from (1))
From statement 1,we get c=j+2;e+12=j which yields e+14=c
now 100=c+j+e+n
putting the values of j,c,e from above,we get 100=(e+14) + (e+12) +(e) + {(98 - e)/4}
which gives 198 = 11e =>e=18 and n=20
Hence,using both the statements,we can get the answer.

The above method applied by me ,though correct,can take some time.But in data sufficiency ,it is important not to solve the questions(in order to save time for quant) and just identify the no. of equations and the corresponding variables.We just have to check whether they match or not.

Alternatively the question can be solved as

Statement 1:Get 3 equations [linear relationship of (c&j),(e&j) thus (c&e)]....No mention of nigel thus we are left with 2 variables,hence insufficient...MOVING ON to
Statement 2:we get relationship of n&e...but insufficient independently as 2 variables are still remaining.
Statement 1 & 2 :we have 4 equations and 4 variables,hence we can find the solution.

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I personally find myself saving 4 minutes when i don't actually solve the question.....in this time i can attempt 2 more questions......thus in DS ,time management is of utmost importance...

Thanks Ian ,would definitely keep your tips in mind.Actually in lot of tests I find myself pressed for time and I find DS to be the only way to save some time in the quant section.........Hope,I get only linear equations......Going by the OG I dont think though that there are too many questions involving equations of higher order.

Ian Stewart wrote:

harsh.champ wrote:The above method applied by me ,though correct,can take some time.But in data sufficiency ,it is important not to solve the questions(in order to save time for quant) and just identify the no. of equations and the corresponding variables.We just have to check whether they match or not.

Statement 1 & 2 :we have 4 equations and 4 variables,hence we can find the solution.

I explained in these threads:

www.beatthegmat.com/n-variables-n-disti ... 20728.html
www.beatthegmat.com/triangles-data-suff ... 49289.html

why it can be very risky to apply an 'n equations/n unknowns' "rule" to GMAT DS questions. There is a straightforward rule when dealing with 2 linear equations and 2 unknowns, but there is no straightforward rule when you have more than 2 equations/unknowns, or when your equations are non-linear. On the particular question in the post above, you might be able to see quickly that the equations are independent, but that is often difficult to judge. There are several real GMAT questions (I point out a few in one of the threads above) designed specifically to trap the test taker who only counts equations and unknowns, so be careful!