Test: Arithmetic - GMAT MCQ

To find the least possible value of 0.7a / 0.08b, we need to consider the minimum values of a and b.

The hundredths digit, a, is nonzero. Since it is a digit, the minimum value for a is 1.

Similarly, the thousands digit, b, is nonzero. The minimum value for b is also 1.

Now, we can substitute the minimum values into the expression:

0.7(1) / 0.08(1) = 0.7 / 0.08

Dividing 0.7 by 0.08 gives us:

0.7 / 0.08 ≈ 8.75

The closest value to 8.75 among the given options is 8, which corresponds to option D.

Therefore, the closest value to the least possible value of 0.7a / 0.08b is 8, which corresponds to option D.

Sum of cubes of first n natural numbers = (n(n+1)/2)²
Sum of cubes of first 10 positive integers = (10(10+1)/2)² = (55)² 

Let's denote the initial number of men as x. In this case, the total man-hours needed to complete the task is x * 18 * 8.

After the increase, the revised number of men becomes 4x/3 (an increase of 1/3). Additionally, the time spent per day is reduced to 4 hours.

To find the number of days needed to complete the task in the revised scenario, we divide the total man-hours (x * 18 * 8) by the product of the revised number of men (4x/3) and the reduced time per day (4):

Number of days needed = (x * 18 * 8) / (4x/3 * 4)

Simplifying this expression, we can cancel out some terms:

Number of days needed = (x * 18 * 8 * 3) / (4x * 4)
Number of days needed = 27

Therefore, the same task will be completed in 27 days when the number of men is increased by 1/3 and the time spent per day is decreased by half.

To determine which of the given options is equal to 351/558, we can simplify the fraction 351/558 to its simplest form.

Both the numerator and denominator of the fraction can be divided by their greatest common divisor, which is 9:

351/558 = (351 ÷ 9) / (558 ÷ 9) = 39/62

Among the provided answer choices, option B: 39/62 is indeed equal to 351/558.

Therefore, the answer is B: 39/62.

To determine which of the given options is most nearly equal to √10, we can compare the values of each option to the actual value of √10.

Using a calculator, we find that √10 is approximately 3.16227766017.

Among the provided answer choices, the value that is closest to √10 is option B: 3.2.

Therefore, the answer is B: 3.2.

To calculate the amount of interest Nathan owed for the first 3 years, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:
A is the final amount (including principal and interest)
P is the principal amount (loan amount)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Nathan's loan amount (principal) is $1200, the annual interest rate is 10% (0.10 as a decimal), and the interest is compounded annually (n = 1). We want to calculate the interest owed for 3 years (t = 3).

Plugging in these values into the compound interest formula, we get:

A = 1200(1 + 0.10/1)^(1*3)
A = 1200(1 + 0.10)³
A = 1200(1.10)³
A = 1200(1.331)

Calculating this expression:

A ≈ 1597.20

To find the amount of interest owed, we subtract the principal amount from the final amount:

Interest owed = A - P
Interest owed = 1597.20 - 1200
Interest owed ≈ 397.20

Among the provided answer choices, the closest value to 397.20 is C: 400.

Therefore, the closest amount of interest Nathan owed for the first 3 years is approximately $400.

The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers.

Since kss is a three-digit number, it implies that k cannot be zero.

Now, let's consider the possibilities for the two-digit integers ks and rs:

If both ks and rs have a tens digit of 1, the sum would result in a three-digit number with a thousands digit of 2 (k = 2).
If both ks and rs have a ones digit of 9, the sum would result in a three-digit number with a hundreds digit of 9 (r = 9).
If both ks and rs have a ones digit of 5, the sum would result in a three-digit number with a ones digit of 0 or 1, which is not possible.
Based on the analysis, we can conclude that option II (r = 9) must be true, as it is the only valid and necessary condition for the sum of the two-digit integers to result in a three-digit integer kss.

Therefore, the correct answer is B: II only.

If Q is an odd number and the median of Q consecutive integers is 120, we can determine the largest of these integers using the properties of odd numbers.

Let's consider the median of Q consecutive integers. Since Q is an odd number, the median will be the middle number. In this case, the median is given as 120.

We know that the median is the average of the two middle numbers when Q is an odd number. Therefore, we can represent the two middle numbers as 120 and 120.

To find the largest integer, we need to determine the number that comes after the second middle number. Since the consecutive integers are evenly spaced, the difference between each integer is 1.

Therefore, the largest integer can be obtained by adding (Q - 1)/2 to the second middle number, which is 120.

Hence, the largest integer is (Q - 1)/2 + 120.

Therefore, the correct answer is A: (Q - 1)/2 + 120.