Problem Solving

Hey guys,

Found my self fighting with the following question:

OG Quant. Review/PS Q131 looks as follows:

In the sequence x0, x1, x2,...,xn each term from x1 to xk is 3 greater than the previous term, and each term from xk+1 to xn is 3 less than the previous term, where n and k are positive integers and k < n. If x0 = xn = 0 and xk = 15, what is the value of n?

(A) 5
(B) 6
(C) 9
(D) 10
(E) 15

What I fully understand:

Since x0 = 0 and each term from x1 to xk is 3 greater than the previous term, then xk= 0+ (k)*(3). Since xk = 15, then 15=3k and k = 5.

That sounds all very logical to me. However, the rest of the explanation comes as follows:

Since each term from xk+1 to xn is 3 less than the previous term, then xn=xk-(n-k)*(3). Substituting the known values for xk,xn, and k gives 0=15-(n-5)*(3), from which it follows that 3n=30 and n=10.

In particular, I wonder about the expression in bold. Substituting the values is no problem for me. But how did they get to the expression? I tried noting down the elements of the sequence on a number line and found that xk+1 has to be 18. If I go from 18 to zero in steps of -3, I end up with a sequence of 7 elements. Taken 7 and 5 together I would have a sequence including a total of 12 elements. However, xk and xk+1 do not count towards the elements included in xn. Therefore, xn includes 12-2 elements = 10 elements. But this isnt really an explanation for the bold expression?

Can anyone help?

Kind regards,

Tobi

Honestly, if you get the problem from plugging in numbers, you are good to go. That problem solving technique is imperative on the GMAT, when most often you won't have time to derive the formula.

Well ok.. but how would you have tackled this problem solving question ?
I dont think my approach was really good ?!

There must be better ways ?!

I would love help on this too! I understand the first part (k=5), but not how to get n.

0,X1,X2,X3,X4,...15,

0,3,6,9,12,15,12,9,6,3,0

n = 10

Seems as though it is not really challenging anyone...

I was thinking about this question for a while before I could even solve it but I think this is the way:

We know X0=0 and Xk=15. Also X1->Xk is 3 greater than the previous number, we can derive the following:

X0=0
X1=3
X2=6
X3=9
X4=12
X5=15.... Therefore we can conclude that K=5.

Then we see that Xk+1 to Xn is 3 less than the previous term and K<N.. So that means:

X6=15-3=12
X7=12-3=9
X8=9-3=6
X9=6-3=3
X10=3-3=0.... So if X0=Xn, than n must equal 10 which would be answer choice D

Basically you need twice of (15/3) =2*5=10

In the sequence X0, X1, X2...., Xn, each term from X1 to Xk is 3 greater than the previous term, and each term from Xk+1 to Xn is 3 less than the previous term, where n and k are positive integers and k < n. If X0 = Xn = 0 and if Xk = 15, what is the value of n?

A) 5
B) 6
C) 9
D) 10
E) 15

xâ‚€ = 0 and x(k) = 15.
From xâ‚€ to x(k), each term is 3 greater than the previous term.
Thus:
xâ‚€ = 0.
x� = 3.
xâ‚‚ = 6.
x₃ = 9.
xâ‚„ = 12.
xâ‚… = 15.
Since x(k) = 15, k=5.

x(k) = 15 and x(n) = 0.
From x(k+1) -- in other words, from x₆ -- to x(n), each term is 3 less than the previous term.
Thus:
x₆ = 12.
x₇ = 9.
x₈ = 6.
x₉ = 3.
x�₀ = 0.
Since x(n) = 0, n=10.

The correct answer is D.