1. If f(x) = x² – 3, where x is an integer, which of the following could be a value of f(x)?
A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III
Correct Answer: A
Choice I is correct because f(x) = 6 when x=3. Choice II is incorrect because to make f(x) = 0, x² would have to be 3. But 3 is not the square of an integer. Choice III is incorrect because to make f(x) = 0, x² would have to be –3 but squares cannot be negative. (The minimum value for x2 is zero; hence, the minimum value for f(x) = -3)
2. For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?
Correct Answer: C
1 < 4n + 7 < 200. n can be 0, or -1. n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1. The largest value for n will be an integer < (200 - 7) /4. 193/4 = 48.25, hence 48. The number of integers between -1 and 48 inclusive is 50
3. In the following correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?
Correct Answer: B
First you must realize that the sum of two 2-digit numbers cannot be more that 198 (99 + 99). Therefore in the given problem D must be 1. Now use trial and error to satisfy the sum 5A + BC = 143. A + C must give 3 in the units place, but neither can be 1 since all the digits have to be different. Therefore A + C = 13. With one to carry over into the tens column, 1 + 5 + B = 14, and B = 8. A + C + B + D = 13 + 8 + 1 = 22
4. 12 litres of water a poured into an aquarium of dimensions 50cm length , 30cm breadth, and 40 cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)
Correct Answer: B
Total volume of water = 12 liters = 12 x 1000 cm3. The base of the aquarium is 50 x 30 = 1500cm3. Base of tank x height of water = volume of water. 1500 x height = 12000; height = 12000 / 1500 = 8