Mathematics

The expression as given is ambiguous, but interpreting it as (27 ÷ 32) + 4; 2 - 1 suggests two separate expressions: 27 divided by 32 plus 4, and 2 minus 1. The first evaluates to approximately 4.84375, and the second to 1, neither matching options A, B, or C. Therefore, 'None of these' is the correct choice.

An arithmetic sequence is defined as a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

Using the principle of inclusion-exclusion, the percentage reading at least one magazine is 45% + 55% + 40% - 30% - 15% - 25% + 10% = 80%. Therefore, the percentage not reading any magazine is 100% - 80% = 20%. However, since 20% is option C, the correct answer is C, not A. Recalculating carefully: 45 + 55 + 40 = 140; subtract pairs: 30 + 15 + 25 = 70; add triple: 10; total = 140 - 70 + 10 = 80%. So 20% do not read any magazine, which matches option C.

To find what percent 90 is of 120, divide 90 by 120 to get 0.75, which is 75%. Among the options, 0.75 corresponds to 75%, making option C correct.

If x, y, and z are in proportion, it means the ratio of x to y is equal to the ratio of y to z, which is expressed as x : y :: y : z. Option B correctly represents this proportion.

To express 1.14 as a percent of 1.9, divide 1.14 by 1.9 and multiply by 100: (1.14 / 1.9) × 100 ≈ 60%. Hence, option A is correct.

The nth term of an arithmetic progression (A.P.) is given by Tn = a + (n-1)d. Here, a = 3, d = 6, and n = 9, so T9 = 3 + (9-1)*6 = 3 + 48 = 51.

Rearranging the equation 4/x √(10x - 4) - 8 = 0 and solving for x yields x = 2 as the valid solution. Substituting x = 2 satisfies the equation, while x = 4 does not.

The population increased from 175,000 to 262,500 over 10 years, which is a total increase of 50%. The average annual percent increase is calculated as (50% ÷ 10) = 5%. However, since the question asks for average percent increase per year, it is more accurate to calculate the compound annual growth rate (CAGR): ((262500/175000)^(1/10) - 1) × 100 ≈ 4.75%. Therefore, option A is correct.

In an arithmetic progression (A.P.) with first term 3 and common difference 0, all terms are equal to the first term. Therefore, the 5th term is also 3.