Question

Two positive real numbers, a and b, are expressed as the sum
of m positive real numbers and n positive real numbers respectively
as follows:
a = s1 + s2 + D..+ s m and
b = t1 + t2 + D..+ tn
If [a] = [s1] + [s2] + D.. + [sm] + 4 and [b] = [t1] + [t2] + D. + [tn] + 3,
where [x] denotes the greatest integer less than or equal to x, what
is the minimum possible value of m + n?
(1) 6
(2) 10
(3) 8
(4) 9

Answer 1

6
iS your answer
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Answer 2

Answer:

the minimum possible value of m + n = 9

Step-by-step explanation:

a = s1 + s2 + D..+ s m and

b = t1 + t2 + D..+ tn

If [a] = [s1] + [s2] + D.. + [sm] + 4 and [b] = [t1] + [t2] + D. + [tn] + 3,

for min m

m(0.9999) ≥ 4

=> m > 4

=> m = 5 ( as m is integer)

for min n

n(0.9999) ≥ 3

=> n > 3

=> n = 4 ( as n is integer)

m+n = 5 + 4 = 9

the minimum possible value of m + n = 9