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The teacher asked a class of fifth grade students to find the average of 15 different two-digit numbers displayed on the blackboard. After the students finished the exercise, the teacher wrote the correct answer on the blackboard. Ankit, in an attempt to impress the teacher, claimed that he could reverse the digits of one of the numbers so that the new number also was a two-digit number, and the average he would get would be 2.4 more than the result displayed.
What is the probability of Ankit finding such a number on the blackboard?
  • a)
     10C15/ 90C15
  • b)
     5/ 90C 15
  • c)
    1/18
  • d)
    1 - 85C15/ 90C 15
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
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The teacher asked a class of fifth grade students to find the average ...
Since average of the fifteen numbers has been increased by 2.4, therefore the sum of the fifteen numbers Ankit has on his notebook must be greater than the actual sum by 15 x 2.4 = 36 Since, Ankit has left all the other fourteen numbers unaltered, that means that the new number formed by reversing the digits on the original number is greater than the original number by 36.
Let’s say that the original number was XY, therefore the new number will be YX.
Therefore, (10Y + X) - (10X+ Y) = 36 or, 9 ( Y - X ) = 36 or, Y - X = 4
Therefore, any number which does not have zero as one of its digits (the number cannot have zero since any number having zero when reversed will be turned to a one digit number) and where the difference of the digits is 4 will help Ankit to achieve his feat.
15, 26, 37, 48, 59 are the required numbers that can help Ankit.
Number of two digits numbers possible = 90 Number of ways in which 15 two digits number can be selected = 90C15
Number of ways in which 15 numbers can be selected such that the five numbers that can help Ankit in performing the mischief are not selected = 85C15 Hence, the probability that Ankit will find one of the given five numbers on the blackboard = 1 - (85C15/ 90C 15) Hence, option 4.
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The teacher asked a class of fifth grade students to find the average ...
To find the probability of Ankit finding a number on the blackboard that, when its digits are reversed, yields an average that is 2.4 more than the displayed result, we can follow these steps:

Step 1: Finding the Average
The average of 15 different two-digit numbers can be calculated by summing up all the numbers and then dividing the sum by 15.

Step 2: Reversing the Digits
Ankit needs to reverse the digits of one of the numbers on the blackboard and ensure that the new number is still a two-digit number.

Step 3: Calculating the Average with Reversed Digits
Ankit claims that if he reverses the digits of one number and recalculates the average using this new number, the result will be 2.4 more than the displayed average.

Step 4: Finding the Probability
To find the probability of Ankit finding such a number, we need to determine the number of favorable outcomes (numbers that satisfy Ankit's condition) and divide it by the total number of possible outcomes (all two-digit numbers displayed on the blackboard).

Now let's calculate the probability step by step:

Step 1: Finding the Average
Since the average is not provided in the question, we cannot calculate it. Therefore, we cannot proceed with the remaining steps.

Hence, the given information is insufficient to calculate the probability. Therefore, the correct answer is option 'E' (None of these).

Note: It is important to carefully read the question and understand the given information in order to solve it accurately. In this case, the average of the 15 two-digit numbers was not provided, making it impossible to find the probability.
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The teacher asked a class of fifth grade students to find the average of 15 different two-digit numbers displayed on the blackboard. After the students finished the exercise, the teacher wrote the correct answer on the blackboard. Ankit, in an attempt to impress the teacher, claimed that he could reverse the digits of one of the numbers so that the new number also was a two-digit number, and the average he would get would be 2.4 more than the result displayed.What is the probability of Ankit finding such a number on the blackboard?a)10C15/ 90C15b)5/ 90C 15c)1/18d)1 - 85C15/ 90C 15e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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The teacher asked a class of fifth grade students to find the average of 15 different two-digit numbers displayed on the blackboard. After the students finished the exercise, the teacher wrote the correct answer on the blackboard. Ankit, in an attempt to impress the teacher, claimed that he could reverse the digits of one of the numbers so that the new number also was a two-digit number, and the average he would get would be 2.4 more than the result displayed.What is the probability of Ankit finding such a number on the blackboard?a)10C15/ 90C15b)5/ 90C 15c)1/18d)1 - 85C15/ 90C 15e)None of theseCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The teacher asked a class of fifth grade students to find the average of 15 different two-digit numbers displayed on the blackboard. After the students finished the exercise, the teacher wrote the correct answer on the blackboard. Ankit, in an attempt to impress the teacher, claimed that he could reverse the digits of one of the numbers so that the new number also was a two-digit number, and the average he would get would be 2.4 more than the result displayed.What is the probability of Ankit finding such a number on the blackboard?a)10C15/ 90C15b)5/ 90C 15c)1/18d)1 - 85C15/ 90C 15e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The teacher asked a class of fifth grade students to find the average of 15 different two-digit numbers displayed on the blackboard. After the students finished the exercise, the teacher wrote the correct answer on the blackboard. Ankit, in an attempt to impress the teacher, claimed that he could reverse the digits of one of the numbers so that the new number also was a two-digit number, and the average he would get would be 2.4 more than the result displayed.What is the probability of Ankit finding such a number on the blackboard?a)10C15/ 90C15b)5/ 90C 15c)1/18d)1 - 85C15/ 90C 15e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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