The sum of three consecutive multiples of 3 is 72. What is the largest of the three numbers?
Answer: C
Let the three consecutive multiples of 3 be 3x, 3(x+1), and 3(x+2). A simpler way is to let them be n-3, n, n+3, where n is the middle number. Their sum is 3n = 72, so n=24.
The numbers are 21, 24, and 27.
The largest number is 27.
Please log in or register to report this question.
A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is the number?
Answer: B
Let the number be x. We work backward from the result.
Before being trebled, the number was 75 / 3 = 25.
This resultant (25) was obtained after doubling the number and adding 9. So, 2x + 9 = 25.
2x = 25 - 9 = 16.
x = 16 / 2 = 8.
Please log in or register to report this question.
What is 0.04% of 15000?
Answer: A
\[ 0.04\% = \frac{0.04}{100} = 0.0004 \]
\[ 0.0004 \times 15{,}000 = 6 \]
Treating 0.04% as 0.04 would give 600, a hundredfold error.
Please log in or register to report this question.
Find the value of \(999 \frac{995}{999} \times 999\).
Answer: A
The expression can be rewritten as \((999 + \frac{995}{999}) \times 999\).
Using the distributive property: \(999 \times 999 + \frac{995}{999} \times 999\)
= \(999^2 + 995\)
= \((1000 - 1)^2 + 995\)
= \((1000000 - 2000 + 1) + 995\)
= 998001 + 995 = 998996.
Please log in or register to report this question.
The sum of all prime numbers from 1 to 20 is:
Answer: B
The primes from 1 to 20 are
\[ 2,\ 3,\ 5,\ 7,\ 11,\ 13,\ 17,\ 19 \]
\[ 2+3+5+7+11+13+17+19 = 77 \]
1 is not prime, having only one divisor rather than two.
Please log in or register to report this question.
Find the value of \(0.3^2 + 0.1^2 - 2 \times 0.3 \times 0.1\).
Answer: A
The three terms are the expansion of a squared difference.
\[ a^{2} + b^{2} - 2ab = (a-b)^{2} \]
\[ (0.3 - 0.1)^{2} = 0.2^{2} = 0.04 \]
Please log in or register to report this question.
A number is divided into two parts in such a way that 80% of the first part is 3 more than 60% of the second part, and 80% of the second part is 6 more than 90% of the first part. The number is:
Answer: C
Let the parts be x and y.
1) 0.8x = 0.6y + 3 => 8x = 6y + 30 => 4x - 3y = 15
2) 0.8y = 0.9x + 6 => 8y = 9x + 60 => 9x - 8y = -60
Solving these two linear equations. Multiply (1) by 8 and (2) by 3:
32x - 24y = 120
27x - 24y = -180
Subtracting the second from the first gives: 5x = 300 => x = 60.
Substitute x=60 into (1): 4(60) - 3y = 15 => 240 - 3y = 15 => 225 = 3y => y = 75.
The number is the sum of the parts: x + y = 60 + 75 = 135.
Please log in or register to report this question.
What is the difference between the largest 4-digit number and the smallest 3-digit number?
Answer: A
The largest four-digit number is 9999 and the smallest three-digit number is 100.
\[ 9999 - 100 = 9899 \]
The smallest three-digit number is 100, not 99 - which would give 9900, the adjacent option.
Please log in or register to report this question.
\(1/4\) of a number subtracted from \(1/3\) of the number gives 12. The number is:
Answer: B
Let the number be x.
\(\frac{1}{3}x - \frac{1}{4}x = 12\).
To subtract the fractions, find a common denominator, which is 12.
\(\frac{4x - 3x}{12} = 12\).
\(\frac{x}{12} = 12\).
\(x = 144\).
Please log in or register to report this question.
Find the value of \(0.99^2\) using an algebraic identity.
Answer: A
Write 0.99 as \( 1 - 0.01 \) and use \( (a-b)^{2} \).
\[ (1 - 0.01)^{2} = 1 - 2(0.01) + (0.01)^{2} \]
\[ = 1 - 0.02 + 0.0001 = 0.9801 \]
Please log in or register to report this question.
