Operations on rational numbers Quant Review 2nd Ed #131

[runningguy]

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

I do not even know how to begin this problem and the explanation in the book makes no sense to me at all.

[Mike@Magoosh]

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

I do not even know how to begin this problem and the explanation in the book makes no sense to me at all.

Dear runningguy,
I'm happy to help.

For the start, "each term from X1 to Xk is 3 greater than the previous term", and we know x0 = 0, so let's start there.
x0 = 0
x1 = 3
x2 = 6 --- notice, we are just adding three for each new term
x3 = 9
x4 = 12
x5 = 15
Whoa! We reached the turn-around point. k = 5, and at this point, the rules change: "each term from XK+1 to Xn is 3 less than the previous term" --- in other words, now we subtract three to get to each new term. To continue
x6 = 12
x7 = 9
x8 = 6
x9 = 3
x10 = 0
Therefore, n = 10. Answer = [spoiler](D)[/spoiler]

Does all this make sense?

Mike

[GMATGuruNY]

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

I do not even know how to begin this problem and the explanation in the book makes no sense to me at all.

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.

[ganeshrkamath]

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

I do not even know how to begin this problem and the explanation in the book makes no sense to me at all.

X0 = 0
Xk = 15
0,3,6,9,12,15
The 6th term is 15.
So k = 5

12,9,6,3,0
The 5th term after X5 is 0
Xn = 0
n = 10

Choose D

Cheers

[runningguy]

Thank you both for the great explanations! Where might I find more practice on problems like this one?

[vipulgoyal]

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?

experts if you notice only the underlined portion is increasing by 3, I mean x1 could be 3,6,.. but multiple of 3 because we have to reach at xk = 15
now if we take x1=6
then x0,x1,x2,x3,x4,x5,x6,x7,x8,x9 = 0,6,9,12,15,12,9,6,3,0
tn this case n = 9 which is also right

it should be either x1 to xk inclusive or x0 to xk

[theCodeToGMAT]

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?

experts if you notice only the underlined portion is increasing by 3, I mean x1 could be 3,6,.. but multiple of 3 because we have to reach at xk = 15
now if we take x1=6
then x0,x1,x2,x3,x4,x5,x6,x7,x8,x9 = 0,6,9,12,15,12,9,6,3,0
tn this case n = 9 which is also right

it should be either x1 to xk inclusive or x0 to xk

Vipul, you misunderstood the question.
The question says "each term from X1 to Xk is 3 greater than the previous term,"

For x1, the previous term is x0

So, if you make a series such as 0,6,9,12,15,12,9,6,3,0 where x0=0, x1=6 then you are voilating the question

Solution for problem requires a series : 0,3,9,12,15,12,9,6,3,0 and the value of n = terms - 1 = 10

Answer [D]

[vipulgoyal]

HI Rahul, I was waiting for right example to show you what i am trying to ask, the qustion must needs to mention "inclusive"

see the qustion in the recent post

https://www.beatthegmat.com/if-integer-c ... 69766.html

[theCodeToGMAT]

HI Rahul, I was waiting for right example to show you what i am trying to ask, the qustion must needs to mention "inclusive"

see the qustion in the recent post

https://www.beatthegmat.com/if-integer-c ... 69766.html

For this I will ask you a question:

From the class of 100 Students, each student with roll no. from 12 to 20 will be offered a special gift

--> How do you depict this problem? Students from roll number 13 to 19?? or 12 to 20?

This means Inclusive only.

[vipulgoyal]

Rahul, it may be either case as per the people's assumptions, now let me ask you a qustion, why in that qustion( in the pasted link) qustion writer had mentioned inclusive, I guess just to avoid this confusion.

[theCodeToGMAT]

Rahul, it may be either case as per the people's assumptions, now let me ask you a qustion, why in that qustion( in the pasted link) qustion writer had mentioned inclusive, I guess just to avoid this confusion.

Vipul, it cannot be either case; if you say so, then you are voilating the english which we have studied since childhood.

Yes, the "inclusive" in the Link is definately mentioned to be precise enough to avoid such question.. But, that doesn't mean that the Question under consideration is wrongly written.

I lived in Mumbai from 1999 to 2001 --> Do you think I want to say that I lived in Mumbai in the year 2000?

[Mike@Magoosh]

HI Rahul, I was waiting for right example to show you what i am trying to ask, the question must needs to mention "inclusive"

Dear vipulgoyal,
You are perfectly correct that the idea of "inclusive" is crucially important in many GMAT Quant problems, including those that deal with counting scenarios. I discuss this in this blog:
https://magoosh.com/gmat/2012/inclusive- ... -the-gmat/
Be careful, though. With all due respect, the idea of "inclusive" doesn't always include the word "inclusive" ----- Here I must agree with Mr. Rahul. If we talk about "each room from Room #6 to Room #23" or "every day of September from the 3rd to the 29th", then in GMAT terms, that unambiguously indicates an inclusive set, even though the word "inclusive" does not appear. The "from P to Q" idiom is inherently an inclusive idiom, especially in a mathematical context.
Does all this make sense?
Mike

[vipulgoyal]

thanks Mike and Rahul