Problems And Answers PHIMO MOCK 2020 SECONDARY 2

6. Positive integers which read the same backwards as forwards are called palindromes; for example, 11, 252, and 31013 are palindromes. The number of palindromes less than \(10^6\), but greater than 10 is:

A. 999
B. 103
C. 1089
D. 1989
E. 2209

7. Jessie have just won 50 of 75 games on the computer. The number of games out of the next 30 games that Jessie must win in order to have won 60% overall is:
A. 10
B. 13
C. 15
D. 20
E. 25

8. If \(x\) is a positive integer, then \(x +\sqrt x\) cannot possibly equal:

A. 20
B. 30
C. 60
D. 90
E. 110

9. The number of dierent pairs of positive integers \((x,y)\) that satisfies \(x^y = 7^{20}\) is:

A. 4
B. 5
C. 6
D. 7
E. more than 7

10. A fair six-sided die, with faces numbered 1 to 6, is tossed two times. The probability that the two outcomes are in strictly ascending order, for example a 1 and then a 3, (equality is NOT allowed) is:

A.\(\frac{5}{12}\)
B.\(\frac{1}{2}\)
C.\(\frac{1}{3}\)
D.\(\frac{1}{4}\)
E.\(\frac{5}{6}\)