In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5 ?
(1) t3 = 1/4
(2) t1 - t5 = 15/16
(1) t3 = 1/4
(2) t1 - t5 = 15/16
Trust but verify.
In this sequance, t(n+1) = t(n)/2
So,
t2 = (1/2)*t1,
t3 = (1/2)*t2 = (1/4)*t1
and so on…
t5 = (1/2)*t4 = (1/2)*(1/2)*t3 = (1/2)*(1/2)*(1/2)*t2 = (1/2)*(1/2)*(1/2)*(1/2)*t1
t5 = (1/16)*t1
Statement 1: t3 = 1/4
t5 = (1/2)*(1/2)*t3
t5 = (1/2)*(1/2)*(1/4)
t5 = 1/16
Sufficient.
Statement 2: t1 - t5 = 15/16
t1 - (1/16)t1 = 15/16
t1*(1 - 1/16) = 15/16
t1*(15/16) = 15/16
t1 = 1
So t5 = (1/16)*t1 = 1/16. Sufficient.
Choose D.
-BM-
