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Statement 1: X < 3, Take 2 cases, 1 x=2, and one x=2.99, x=2 => Sqrt(x) = 1.414 is greater that 2.5*2 - 5, however x=2.99 => Sqrt(x) = 1.731 is less than 2.5*2.99 - 5 So this option is insufficient

Statement 2: X can be any prime number. Take 2 cases x=2, and x=3. Again it is insufficient.

Combining both statements: we get x<3 and is also a prime number, so only value x can have is 2.

for x = 2, Sqrt(x) = 1.414 is greater that 2.5*2 - 5

So question can be answered using both the statement together, Answer C.

If x is a positive integer, is \(\sqrt{x} \lt 2.5x - 5?\)

1. \(x \lt 3\) 2. \(x\) is a prime number

A

statement 1: if x is a positive integer less than 3, then x = 1 or 2 sqrt(x) is either 1 or ~1.4 if x = 1, then sqrt(x) > 2.5x - 5 , and if x = 2, then sqrt(x) > 2.5x - 5

statement 2: if x is a prime number, x could be 1 or 83 if x = 1, then sqrt(x) > 2.5x - 5 , BUT if x = 83, then sqrt(x) < 2.5x - 5

from stem, x is a postive integer, and so x=1 or 2. plug in x=1 you get 1<-2.5 ... plug in x=2 you get 1.4<0. in either case, the answer is 'no', so we can definitively answer the question

from stat 2, x=1 or x=3. for x=3 you have 1.7<2.5, which is true, but for x=1, the inequality isnt true. so insuff.

x could be 1 or 2 then plugging in 1 for we get -2.5 >+- 1 plugging in 2 we get 0> +- sqrt (2)

thus 1 is insufficient

using stmt -2 x could be 2,3,5,7.. for all the primes but for 2 the equation holds good but for 2 we run into the same problem as we did in plugging in 2 for x above thus insufficient

now combining both 1& 2 we still have the uncertainty about 0>+- sqrt(2) thus E for me
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