Logical Reasoning2
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Question 1 of 7
1. Question
Consider all unique integral combinations of x^{y} and y^{x }for 2 ≤ x ≤ 5 and 2 ≤ y ≤ 7
Based on the above information, solve the following questions:If we arrange all the numbers in the ascending order, then what will the 7th number?
Correct
2^{2},2^{3}, …2^{7}, 3^{2},3^{3}…3^{7}, 4^{2},4^{3},…4^{7}, 5^{2},5^{3},…5^{7}, 6^{2},6^{3},…6^{5}, 7^{2},7^{3},…7^{5}
On arranging in ascending order
4, 8, 9, 16, 25, 27, 32, 36,…Incorrect
2^{2},2^{3}, …2^{7}, 3^{2},3^{3}…3^{7}, 4^{2},4^{3},…4^{7}, 5^{2},5^{3},…5^{7}, 6^{2},6^{3},…6^{5}, 7^{2},7^{3},…7^{5}
On arranging in ascending order
4, 8, 9, 16, 25, 27, 32, 36,… 
Question 2 of 7
2. Question
Consider all unique integral combinations of x^{y} and y^{x }for 2 ≤ x ≤ 5 and 2 ≤ y ≤ 7
Based on the above information, solve the following questions:What is the sum of all possible numbers forms of x^{y} ?
Correct
(2^{2}+2^{3}+…+2^{7})+( 3^{2}+3^{3}+…+3^{7})+( 4^{2}+4^{3}+…+4^{7})+(5^{2}+5^{3}+…+5^{7})
= {2^{2}(2^{6}1)}/21 + {3^{2}(3^{6}1)}/31 + {4^{2}(4^{6}1)}/41 + {5^{2}(5^{6}1)}/51
=252+3276+21840+97650
= 123018Incorrect
(2^{2}+2^{3}+…+2^{7})+( 3^{2}+3^{3}+…+3^{7})+( 4^{2}+4^{3}+…+4^{7})+(5^{2}+5^{3}+…+5^{7})
= {2^{2}(2^{6}1)}/21 + {3^{2}(3^{6}1)}/31 + {4^{2}(4^{6}1)}/41 + {5^{2}(5^{6}1)}/51
=252+3276+21840+97650
= 123018 
Question 3 of 7
3. Question
Consider all unique integral combinations of x^{y} and y^{x }for 2 ≤ x ≤ 5 and 2 ≤ y ≤ 7
Based on the above information, solve the following questions:What is sum of all the numbers in which either x or y is 5?
Correct
(5^{2}+5^{3}+…+5^{7})+2^{5}+3^{5}+4^{5}+6^{5}+7^{5}
=97650 + 32 + 243 + 1024 + 7776 + 16807
=123532Incorrect
(5^{2}+5^{3}+…+5^{7})+2^{5}+3^{5}+4^{5}+6^{5}+7^{5}
=97650 + 32 + 243 + 1024 + 7776 + 16807
=123532 
Question 4 of 7
4. Question
The number 197 is called a circular prime because all rotations of the digits: 197, 971 and 719 are themselves prime.
Note: Single digit prime numbers are also considered circular prime.
How many numbers less than 60 are circular prime?
Correct
Prime number below 60: 2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59.
Out of these 2, 3, 5, 7, 11, 13, 17, 31, 37.Incorrect
Prime number below 60: 2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59.
Out of these 2, 3, 5, 7, 11, 13, 17, 31, 37. 
Question 5 of 7
5. Question
The number 197 is called a circular prime because all rotations of the digits: 197, 971 and 719 are themselves prime.
Note: Single digit prime numbers are also considered circular prime.
Find the 12^{th} largest circular prime number?
Correct
2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.
Incorrect
2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.

Question 6 of 7
6. Question
The number 197 is called a circular prime because all rotations of the digits: 197, 971 and 719 are themselves prime.
Note: Single digit prime numbers are also considered circular prime.
What is the sum of the two smallest circular prime numbers greater than 100?
Correct
113 + 131 = 244
Incorrect
113 + 131 = 244

Question 7 of 7
7. Question
The number 197 is called a circular prime because all rotations of the digits: 197, 971 and 719 are themselves prime.
Note: Single digit prime numbers are also considered circular prime.
Find the sum of all circular prime numbers less than 50.
Correct
2+3+5+7+11+13+17+31+37 = 126
Incorrect
2+3+5+7+11+13+17+31+37 = 126