Test: Arithmetic - GMAT MCQ

To fringe the 3-inch-wide end of a streamer by making small cuts every 1/16 inch, we need to calculate the number of cuts required.

First, we need to convert the width of the streamer from inches to 1/16 inch units, since the cuts are made every 1/16 inch.

The width of the streamer is 3 inches, which is equal to 3 * (16/16) = 48/16 = 3 * 3 = 9/3 * 3 = 9 * 3/3 = 27/3 * 3/1 = 27 * 3/1 = 81/1 * 1/1 = 81/1 = 81/16 * 16/1 = 81/16 inches in terms of 1/16 inch units.

To fringe the end, we need to make cuts every 1/16 inch, so the number of cuts required is equal to the width of the streamer in 1/16 inch units.

Therefore, the number of cuts required is 81/16.

Among the given answer choices, the closest option is C: 47.

Given that x percent of the 1,150 people surveyed chose A as their favorite brand and rounding x to the nearest integer results in 3, we can set up the following equation:

Round(x) = 3

To determine the possible values of x, we need to consider the range within which x can fall when rounded to the nearest integer. Since x is given as a percentage, it must be between 0 and 100.

Let's calculate the upper and lower bounds for x:

Upper bound:
If x = 3, then x rounded to the nearest integer is already 3.

Lower bound:
If x = 2.5, rounding it to the nearest integer would result in 3.

Therefore, x can be any value between 2.5 and 3.5, inclusive.

Now, let's calculate the number of people who chose A using the lower and upper bounds:

Lower bound:
(2.5/100) * 1150 = 28.75

Upper bound:
(3.5/100) * 1150 = 40.25

The number of people who chose A can vary between approximately 28.75 and 40.25.

Among the given answer choices:

I. 30: This falls within the possible range (between 28.75 and 40.25).
II. 35: This falls within the possible range.
III. 45: This does not fall within the possible range.

Therefore, the correct answer is D. I and II only.

Suppose the present ages of the three friends are A, B and C respectively.
We know that A + B + C = 21.
Five years later, their ages would be (A + 5), (B + 5) and (C + 5) respectively.
So, (A + 5 + C + 5) / 2 = (B + 5) + 3/2, which on simplifying gives A + C + 10 = 2B + 13. From the first expression we know that A + C = 21 – B.
Substituting this value in the second expression,
we get 21 – B +10 = 2B + 13 or 3B = 18,
which yields B = 6 years.
Thus, 10 years hence, B will be 16 years old.
So, option 16 years is the correct answer.

According to the blueprint, 1 centimeter corresponds to 0.8 millimeters on the microchip. Since 1 centimeter is equal to 10 millimeters, we can set up the following proportion:

1 centimeter on blueprint = 0.8 millimeters on microchip
10 millimeters on blueprint = x millimeters on microchip

To find the diameter on the blueprint, we need to double the radius. Therefore, we can multiply the 10 millimeters on the blueprint by 2:

Diameter on blueprint = 2 * 10 millimeters = 20 millimeters.

Since 1 centimeter is equal to 10 millimeters, we can convert the diameter from millimeters to centimeters:

Diameter on blueprint = 20 millimeters = 2 centimeters.

So, the diameter of the blueprint representation of the microchip is 2 centimeters.

Among the given answer choices, the closest option is D: 50.

Therefore, the correct answer is D: 50.

We can let the time from Downtown to Beachside = t, and thus the time from Beachside to Downtown = t/2.

Since the average speed was ⅔, we have:

average speed = (total distance)/(total time)

2/3 = (1 + 1)/(t + t/2)

2/3 = 2/(3t/2)

3t = 6

t = 2

Since it takes 2 hours to go from Downtown to Beachside, a distance of 1 mile, the speed is 1/2 mph.

To find the 18th digit to the right of the decimal point in the decimal expansion of 1/37, we can perform the division and observe the pattern that emerges.

When we divide 1 by 37, the decimal expansion is 0.027027027027... with the repeating pattern being 027.

To determine the 18th digit to the right of the decimal point, we need to identify which digit from the repeating pattern corresponds to that position.

Since the repeating pattern has a length of 3 digits (027), we can divide 18 by 3 to determine the number of complete repetitions and the remainder to find the position within the repeating pattern.

18 ÷ 3 = 6 with no remainder

Since there is no remainder, the 18th digit corresponds to the third digit within the repeating pattern (027), which is 7.

Therefore, the 18th digit to the right of the decimal point in the decimal expansion of 1/37 is 7.

Hence, the correct answer is D) 7.

To find the average download speed of the dial-up connection, we need to convert the given data into a common unit (bits per second).

First, let's calculate the number of bits in 75,000,000 bytes. Since 1 byte is equal to 8 bits, we can multiply 75,000,000 by 8 to get the total number of bits:
75,000,000 bytes * 8 bits/byte = 600,000,000 bits

Now, we can calculate the download speed of the dial-up connection. We are given that this same task takes 3 hours, which is equal to 3 * 60 * 60 = 10,800 seconds.

To find the average download speed, we divide the total number of bits by the time in seconds:
Average download speed = 600,000,000 bits / 10,800 seconds

Calculating this value gives us approximately 55,555.56 bits per second.

Among the answer choices provided, the closest value to the calculated average download speed is 56,000 bits per second (option D).

Therefore, the correct answer is D) 56,000.

Given:
Distance = 100 feet
Time = 2 seconds

To convert feet to miles, we divide the distance by the conversion factor of 5280 feet per mile:
Distance in miles = 100 feet / 5280 feet per mile
Distance in miles ≈ 0.018939 miles

To convert seconds to hours, we divide the time by the conversion factor of 3600 seconds per hour:
Time in hours = 2 seconds / 3600 seconds per hour
Time in hours ≈ 0.000556 hours

Now, we can calculate the approximate speed in miles per hour by dividing the distance in miles by the time in hours:
Speed = Distance / Time
Speed ≈ 0.018939 miles / 0.000556 hours
Speed ≈ 34.062 miles per hour

Among the answer choices provided, the closest value to the calculated approximate speed is 34 miles per hour (option C).

Therefore, the correct answer is C) 34.

To estimate the number of microbes after 48 hours, we can use the formula provided: 70/t hours, where t is the rate of increase per hour expressed as a percent.

Given:
Rate of increase = 9 percent per hour
Number of microbes at the start = 60,000

Using the formula, we can calculate the approximate doubling time:
Doubling time (t) = 70 / 9
Doubling time (t) ≈ 7.78 hours

Now, we can calculate the number of doublings that occur in 48 hours:
Number of doublings = 48 hours / 7.78 hours ≈ 6.16 doublings

Since the population doubles approximately every 7.78 hours, after 6.16 doublings, the population will be approximately 2^6.16 times the initial population.

Approximate number of microbes after 48 hours = 60,000 * 2^6.16 ≈ 3,800,000

Among the answer choices provided, the closest value to the calculated approximate number of microbes is 3,800,000 (option E).

Therefore, the correct answer is E) 3,800,000.

The rate of 24 machines is 1/10.

On a certain day 16 machines first ran for 2 hours.

The rate of the 16 machines is:

16/n = 24/(1/10)

16/n = 240

16 = 240n

n = 16/240 = 1/15

Thus, when 16 machines work for 2 hours, the fraction of the job completed is 1/15 x 2 = 2/15.

Thus, 13/15 of the job needs to be completed by 24 machines. The time it will take to complete the job is:

(13/15)/(1/10) = 130/15 = 26/3 hours

Therefore, the total time spent on the job is 2 + 26/3 = 32/3 hours = 10 ⅔ hours = 10 hours 40 minutes, which is 40 minutes more than on a normal day.