Question: A number, x is chosen at random from the set of positive integers less than 10. What is the probability that (9/x) > x?

(A) 1/5
(B) 2/9
(C) 1/3
(D) 2/3
(E) 7/9

Correct Answer: B

Solution and Explanation:

Approach Solution 1:
Number x has to be chosen from numbers 1-9

(9/x) > x
=> 9 > x^2
=>x^2 - 9 < 0
x can have 2 values only 1 , 2
Therefore , probability = 2 / 9
 

Approach Solution 2:
probability (9/x) > x?
rewrite - 9/x > x i.e. 9 > x^2
means x should be such a number which when squared is less than 9.
x is one of the integers 1 to 9.
only 1 & 2 would be less than 9 when squared. so 2 out of 9 are favorable.
Hence "probability that (9/x) > x" = 2/9
 

Approach Solution 3:
let x= 1
(9/x) = 9 >1...satisfy condition

let x= 2
(9/x) = 4.5>2...satisfy condition

let x= 3
(9/x) = 3 is not less than 3 ...not satisfying condition

Condition will not be satisfied for x>= 3, thus we can only select values 1 & 2
Thus probability = 2/9

“A number, x is chosen at random from the set of positive integers less”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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