Education Exams (Secondary Education (Mathematics)) – Page 8

#140. Which of the following is true about Vinogradov's theorem?
A all sufficiently large odd integers can be expressed as the sum of three prime numbers
B all sufficiently large even integers can be expressed as the sum of three prime numbers
C all sufficiently large odd integers can be expressed as the sum of three composite numbers
D all sufficiently large even integers can be expressed as the sum of three composite numbers
Answer: all sufficiently large odd integers can be expressed as the sum of three prime numbers
#141. If the linear system has no solution, it is said to be _____________.
A inconsistent
B consistent
C trivial
D nontrivial
Answer: inconsistent
#142. Two m x n matrices \( A = [a_{ij}]\) and \( B = [b_{ij}]\) are equal if \(\a_{ij}) = \( b_{ij}\), for \(i = 1, 2, 3, ..., m \) and \(j = 1, 2, 3, ..., n\)
A True
B False, not equal
C False, n x m matrices
D False, \(ji\)
Answer: True
#143. Diophantus spent 1/12 of his life in childhood, 1/6 in youth, and 1/7 as a bachelor. Five years after his marriage was born a son who died four years before him at half his final age. How old was Diophantus when he died?
A 84
B 72
C 108
D 94
Answer: 84
#144. A 100 kg salt solution originally 4% by weight NaCl in water is evaporated until the concentration is 5% by weight NaCl. What percentage of water in the original solution is evaporated?
A 20.83%
B 20%
C 80%
D 12.56%
Answer: 20.83%
#145. A jewelry craftsman needs 100 grams of gold alloy, of 75 % pure gold for his products. Only two alloys of gold are available from a supplier. The first is 80 % pure gold and the other is 60% pure gold. How many grams of 80% gold alloy must he use to suit his requirement?
A 75 grams
B 200 grams
C 80 grams
D 100 grams
Answer: 75 grams
#146. A container contains 40 liters of a wine which is 80% alcohol by volume. How much of the mixture should be removed and replace by an equal volume of water so that the resulting solution will be 70% alcohol by volume.
A 5 liters
B 10 liters
C 15 liters
D 20 liters
Answer: 5 liters