If a number between 10 and 50 (inclusive) at random, what is the probability that the tens digit is greater than ones

[Gmat_mission]

If a number between 10 and 50 (inclusive) at random, what is the probability that the tens digit is greater than ones digit?

A. \(\dfrac{31}{41}\)

B. \(\dfrac{10}{41}\)

C. \(\dfrac{14}{41}\)

D. \(\dfrac{27}{41}\)

E. \(\dfrac{11}{41}\)

Answer: E

Source: GMAT Club Tests

[Scott@TargetTestPrep]

If a number between 10 and 50 (inclusive) at random, what is the probability that the tens digit is greater than ones digit?

A. \(\dfrac{31}{41}\)

B. \(\dfrac{10}{41}\)

C. \(\dfrac{14}{41}\)

D. \(\dfrac{27}{41}\)

E. \(\dfrac{11}{41}\)

Answer: E

Solution:

The numbers between 10 and 50, inclusive, with the tens digits greater than the ones digit are: 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, and 50. That is, there are 11 such numbers. Since there are 50 - 10 + 1 = 41 numbers in total, the probability of selecting a number with the tens digits greater than ones digit randomly is 11/41.

Answer: E