Question Number: 1
Which of the following sets below contains only prime numbers?
A) 7, 11, 49
B) 7, 37, 51
C) 7, 23, 47
D) 2, 29, 93
Question Number: 2
Which of the following statements is true?
A) Perpendicular lines must cross, but intersecting lines do not have to cross.
B) Perpendicular lines never cross, but intersecting lines always cross.
C) Perpendicular lines must cross to form ninety degree angles, but intersecting lines
cross to form angles of varying measures.
D) Perpendicular lines must cross to form obtuse angles, whereas intersecting lines
must cross to form acute angles.
Question Number: 3
Which of the following statements is not true?
A) The denominator is the bottom number in a fraction.
B) The multiples of 9 are 1, 3, and 9.
C) The factors of 12 are 1, 2, 3, 4, 6, and 12.
D) A mixed number consists of a whole number and a fraction.
Question Number: 4
Solve: x - 4 < 5
A) x > 9
B) x < 9
C) x > 1
D) x < 1
Page 2 of 3
Question Number: 5
Which one of these proportions is true?
A)
3
5
B)
9
6
C)
3
4
D)
2
5
Question Number: 6
When two fractions with different denominators are to be added using the standard
procedure, which of these must first be found?
A) The GCF (Greatest Common Factor) of the fractions
B) The prime factorization of the fractions’ numerators
C) The LCD (Least Common Denominator) of the fractions
D) The mean value of the denominators
Question Number: 7
Write an equivalent expression to 12x+3.
A) 12(x+1)
B) 3(4x + 1)
C) 6(2x-2)
D) 3(9x+1)
Question Number: 8
The city of Trenton hired a crew of 100 workers to clean up the streets of the city. The crew
worked for 14 days. Each worker was paid at a rate of $90 per day. What was the total labor
cost for the city?
A) $1,260
B) $126,000
C) $11,400
D) $9,000
Answers
Answer:
(a) (19, 21)
(b) (29, 31)
(c) (39, 41)
(d) (49, 51)
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Hint: First of all check if both the numbers are prime or not. If yes, then check if the difference between the numbers is 2 or not. If both conditions satisfy, then only two numbers are twin prime.
Complete step-by-step answer:
Here, we have to find which of the following pairs twin primes are: (19, 21), (29, 31), (39, 41), (49, 51).
Before proceeding with this question, we must know what twin prime numbers are. Two numbers are twin prime to each other when they both are prime and have a difference of 2 between them. For example, (5, 7) and (11, 13), etc. are twin prime numbers. Also, a prime number is a number that is divisible by 1 and itself only. For example, 2, 7, 17, etc. are prime numbers.
Now, we will check which of the pairs in options are twin prime.
(a) (19, 21)
In the above pair, 19 is a prime number, and the difference between 19 and 21 is 2, but 21 is not a prime number as it has factors like 3, 7, etc. So, we get that the pair (19, 21) is not a twin prime.
(b) (29, 31)
In the above pair, both 29 and 31 are prime numbers and the difference between 29 and 31 is 2. So, we get that the pair (29, 31) is twin prime.
(c) (39, 41)
In the above pair, 41 is a prime number but 39 is not a prime number as it has factors like 3, 13, etc. So we get that the pair (39, 41) is not a twin prime.
(d) (49, 51)
In the above pair, neither 49 nor 51 is a prime number because 49 has factors like 7, etc. and 51 has factors like 17, 3, etc. So, we get that the pair (49, 51) is not a twin prime.
So, we get only one pair that is twin prime and that pair is (29, 31).
Hence, option (b) is the right answer.
Note: Students must note that 2 is the smallest prime number and is the only even prime number. All other prime numbers are odd. Students often make this mistake of considering many odd numbers as prime. For example, many students consider 237, 147, 51, 91, etc. as prime by just looking at them, but they are not prime numbers. So, care must be taken while selecting numbers as prime or not.