Can't follow this question for some reason. Maybe you guys can break it down and tailor it a bit better than the brief Quant explanation
131)
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
this question overwhelms me, and I understand sequences for the most part.
Thanks!!
Derek
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Quant Sequence Problem #131
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GMATGuruNY
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xâ‚€ = 0 and x(k) = 15.DCS80 wrote:Can't follow this question for some reason. Maybe you guys can break it down and tailor it a bit better than the brief Quant explanation
131)
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
this question overwhelms me, and I understand sequences for the most part.
Thanks!!
Derek
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.
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Followed here and elsewhere by over 1900 test-takers.
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ceilidh.erickson
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The real difficulty with this problem is translating what they're really asking for. So try to break it down sentence by sentence:
each term from X1 to Xk is 3 greater than the previous term
Ok, this means that we're increasing by 3, until we get to a certain term "k."
each term from Xk+1 to Xn is 3 less than the previous term
So after the "kth" term, every term after that decreases by 3, until we get to the "nth" term
If X0 = Xn = 0 and if Xk = 15
Ok, if X0 and Xn are both 0, that means that we start and end at 0. Increase by 3 until we get to 15, then decrease by 3 til we're back to 0:
0, 3, 6, 9, 12, 15, 12, 9, 6, 3, 0
Here we have 11 terms. But as GMATGuru pointed out, the first term was actually X0, so the 11th term is X10. Answer: D.
each term from X1 to Xk is 3 greater than the previous term
Ok, this means that we're increasing by 3, until we get to a certain term "k."
each term from Xk+1 to Xn is 3 less than the previous term
So after the "kth" term, every term after that decreases by 3, until we get to the "nth" term
If X0 = Xn = 0 and if Xk = 15
Ok, if X0 and Xn are both 0, that means that we start and end at 0. Increase by 3 until we get to 15, then decrease by 3 til we're back to 0:
0, 3, 6, 9, 12, 15, 12, 9, 6, 3, 0
Here we have 11 terms. But as GMATGuru pointed out, the first term was actually X0, so the 11th term is X10. Answer: D.
Ceilidh Erickson
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Anaira Mitch
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Thanks Mitch,GMATGuruNY wrote:xâ‚€ = 0 and x(k) = 15.DCS80 wrote:Can't follow this question for some reason. Maybe you guys can break it down and tailor it a bit better than the brief Quant explanation
131)
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
this question overwhelms me, and I understand sequences for the most part.
Thanks!!
Derek
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.
This is a very sweet solution.
