gmat_crack wrote:

Professor wrote:

gmat_crack wrote:

In sequence P, P4 and P5 are 11 and 9 espectively. Each term after the first two terms in sequence P is either the sum of the previous two terms if that sum is odd, or half the sum of the previous two terms if the sum is even. What is the largest possible product of P1 and P2?

(A) 40

(B) 14

(C) 12

(D) 10

(E) 7

A. 40

p5 = 9, p4 = 11, p3 = 7, p2 = 4, p1 = 10

so p1p2 = 40

or

p5 = 9, p4 = 11, p3 = 7, p2 = 4, p1 = 3

so p1p2 = 12

can u explain how you got these numbers?

while answering this question, i didn't think that it was this much lengthy and cumbersome. actually the following is the detail values for p1, p2 and p3 using simulation technique:

if p4+p3 is odd, then p5 = p4+p3. so p3 = 9-11 = -2

if p4+p3 is even, then p5 = (p4+p3)/2. so p3 = 18-11 = 7

if p2+p3 is odd, then p4 (when p3 = -2) = (p2+p3). So p2 = 11 +2 = 13

if p2+p3 is even, then p4 (when p3 = -2) = (p2+p3)/2. so p2 = 22+2 = 24

if p2+p3 is odd, then p4 (when p3 = 7) = (p2+p3). So p2 = 11 -7 = 4

if p2+p3 is even, then p4 (when p3 = 7) = (p2+p3)/2. so p2 = 22-7 = 15

if p2+p1 is odd, then p3 (when p3 = -2 and p2 = 13) = (p2+p1). So p1 = -2-13=-15

if p2+p1 is even, then p3 (when p3 = -2 and p2 = 13) = (p2+p1)/2. so p1 = -4-13 = -17

if p2+p1 is odd, then p3 (when p3 = -2 and p2 = 24) = (p2+p1). Not applicable (NA)

if p2+p1 is even, then p3 (when p3 = -2 and p2 = 24) = (p2+p1)/2. so p1 = -4-24 = -28

if p2+p1 is odd, then p3 (when p3 = -2 and p2 = 4) = (p2+p1). NA.

if p2+p1 is even, then p3 (when p3 = -2 and p2 = 4) = (p2+p1)/2. so p1 = -4-4 = -8

if p2+p1 is odd, then p3 (when p3 = -2 and p2 = 15) = (p2+p1). So p1 = -2-15=-17

if p2+p1 is even, then p3 (when p3 = -2 and p2 = 15) = (p2+p1)/2. so p1 = -4-15 = -19

if p2+p1 is odd, then p3 (when p3 = 7 and p2 = 13) = (p2+p1). So p1 = -6

if p2+p1 is even, then p3 (when p3 = 7 and p2 = 13) = (p2+p1)/2. so p1 = 1

if p2+p1 is odd, then p3 (when p3 = 7 and p2 = 24) = (p2+p1). So p1 = -17

if p2+p1 is even, then p3 (when p3 = 7 and p2 = 24) = (p2+p1)/2. so p1 = 14-24 = -10

if p2+p1 is odd, then p3 (when p3 = 7 and p2 = 4) = (p2+p1). So p1 = -3

if p2+p1 is even, then p3 (when p3 = 7 and p2 = 4) = (p2+p1)/2. so p1 = 10

if p2+p1 is odd, then p3 (when p3 = 7 and p2 = 15) = (p2+p1). So p1 = -8

if p2+p1 is even, then p3 (when p3 = 7 and p2 = 15) = (p2+p1)/2. so p1 = -1

there are 16 values for p1, 4 values for p2 and 2 values for p3. the highest value is still 40.

will correct, if any.