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help on this

by alltimeacheiver » Fri Feb 11, 2011 1:51 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
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by GMATGuruNY » Fri Feb 11, 2011 3:00 am
alltimeacheiver wrote:The infinite sequence a1, a2,..., an,... is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an =
a(n-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
The sequence repeats in a pattern of four: 2, -3, 5, -1...2, -3, 5, -1...2, -3, 5, -1...
The sum of this pattern = 2+ -3 + 5 + -1 = 3.
Since 24*4 = 96, this pattern will be repeated 24 times.
24*3 = 72.
The 97th term = the first term in the pattern = 2.
Sum = 72+2 = 74.

The correct answer is B.
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by towerSpider » Fri Feb 11, 2011 3:01 am
alltimeacheiver wrote: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
solving:

x+y=14-xy

since x and y are positive, xy could either be 12 or less: xy<13 (in worst case when both are equal to 1)

lets check:

12: 14-1*12 != 13, 14-2*6 != 2+6, 14-3*4 != 3+4

11: 14-1*11 != 12

10: 14-2*5 != 7, 14-5*5 != 10, 14-1*10 != 11

9: 14-3*3 != 6, 14-1*9 != 10

8: 14-1*8 != 9, 14-2*4 = 6!

C is answer!
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by GMATGuruNY » Fri Feb 11, 2011 3:02 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
x=2 and y=4 works, because 1 + 2 + 4 + 2*4 = 15.
x+y = 2+4 = 6.

The correct answer is C.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
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by Night reader » Fri Feb 11, 2011 4:34 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
(y+1)(x+1)=15 <> {15*1; 3*5; 5*3; 15*1}
(0+1)(14+1) --> 0+14=14, eliminate
(2+1)(4+1) --> 2+4=6
(4+1)(2+1) --> 4+2=6
(14+1)(0+1) --> 14+0=14, eliminate

answer C
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