|
1. Is x^2 > x?
(1) If x is doubled, the result is less than 1.
(2) 0 is less than or equal to x; x<1
In order to satisfy x^2 > x, x has to be x <0 or x>1.
(1) says 2x < 1, or x < 1/2. This is not enough to limit the range of x.
(2) says that 0 =< x < 1. This is still not enough, because if 0<x<1, x^2>x, but if x=0, x^2 = x.
Combining (1) and (2) does not help, either. The answer is (E)
2. The symbol _ represents a digit in the 9-digit number 475,_23,202. What is the value of _?
(1) The missing digit is not a divisor of any other digit in the number.
(2) The sum of the 9 digits is equal to the square of an integer.
(1) says that the missing digit can be 0, 6, 8, 9.
(2) says that the missing digit plus 25 is a square of an integer.
However, the only possibility is 25, because the sum cannot be 36.
So (2) is the enough condition to determine the missing number.
|