help on this

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

alltimeacheiver: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Feb 09, 2011 3:08 am; Location: Delhi; Thanked: 1 times; Followed by:5 members

help on this

by alltimeacheiver » Fri Feb 11, 2011 1:48 am

The infinite sequence a1, a2,..., an,... is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an =
an-4 for n > 4. What is the sum of the first 97 terms of the sequence?
A. 72
B. 74
C. 75
D. 78
E. 80
------------------------------------------------------------------------------------------------------------
If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y?
A. 3
B. 5
C. 6
D. 8
E. 9

Quote

Source: Beat The GMAT — Problem Solving | Fri Feb 11, 2011 1:48 am

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Fri Feb 11, 2011 4:54 am

Question 1:

It is given that an = an-4 for n > 4 so a5 = a1, a6 = a2, a7 = a3, a8 = a4

Therefore, the sequence is 2, -3, 5, -1, 2, -3, 5, -1, ...

It can be seen that the sum of 1st 4 terms = 2 + (-3) + 5 + (-1) = 3
Since the sequence repeats itself in sets of 4, so the sum of 1st 96 terms = 3 * 24 = 72
Hence, sum of 1st 97 terms = 72 + 2 = 74

[spoiler]The correct answer is B.[/spoiler]

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

Quote

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Fri Feb 11, 2011 5:01 am

1 + x + y + xy = 15
1 + x + y(1 + x) = 15
(1 + x)(1 + y) = 15

It is given that x and y are positive integers and 15 can be expressed as a multiple of 2 integers: (1, 15) and (3, 5).
If (1 + x)(1 + y) = 1 * 15 implies 1 + x = 1 and 1 + y = 15 or x = 0 and y = 14
So, x + y = 14
If (1 + x)(1 + y) = 3 * 5 implies 1 + x = 3 and 1 + y = 5 or x = 2 and y = 4
So, x + y = 6
From the above two values of x + y, 6 is the only choice.

[spoiler]The correct answer is C.[/spoiler]

Quote

gtestprep: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Thu Jun 24, 2010 3:56 am; Thanked: 3 times

by gtestprep » Fri Feb 11, 2011 5:02 am

alltimeacheiver wrote: If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y?
A. 3
B. 5
C. 6
D. 8
E. 9

First factor 1 + x + y + xy = 15. You get (1 + x)(1 + y) = 15.
Because it is stated that x and y are both positive integers, the only possible values could be [(1,15) , (3,5)]
if (x,y) = (1,15) or (15,1) then x + y = 14. However, this means that either one of x or y will have to take the value of 0 which is not acceptable based on the conditions stated in the question. So, that leaves us only with the possibility of (x,y) = (3,5) or (5,3) then x + y = 6. So the answer is C.

Quote

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pm; Thanked: 127 times; Followed by:10 members

by Night reader » Fri Feb 11, 2011 6:05 am

https://www.beatthegmat.com/help-on-this ... tml#339273

Anurag@Gurome wrote:1 + x + y + xy = 15
1 + x + y(1 + x) = 15
(1 + x)(1 + y) = 15

It is given that x and y are positive integers and 15 can be expressed as a multiple of 2 integers: (1, 15) and (3, 5).
If (1 + x)(1 + y) = 1 * 15 implies 1 + x = 1 and 1 + y = 15 or x = 0 and y = 14
So, x + y = 14
If (1 + x)(1 + y) = 3 * 5 implies 1 + x = 3 and 1 + y = 5 or x = 2 and y = 4
So, x + y = 6
From the above two values of x + y, 6 is the only choice.

[spoiler]The correct answer is C.[/spoiler]