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Test: Arithmetic - GMAT MCQ


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10 Questions MCQ Test - Test: Arithmetic

Test: Arithmetic for GMAT 2024 is part of GMAT preparation. The Test: Arithmetic questions and answers have been prepared according to the GMAT exam syllabus.The Test: Arithmetic MCQs are made for GMAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Arithmetic below.
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Test: Arithmetic - Question 1

If a is the hundredths digit in the decimal 0.7a and if b is the thousands digit in the decimal 0.08b, where a and b are nonzero digit, which of the following is closest to the least possible value of 0.7a/0.08b ?

Detailed Solution for Test: Arithmetic - Question 1

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.

Test: Arithmetic - Question 2

What is the sum of the cubes of the first ten positive integers?

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Test: Arithmetic - Question 3

It is known that 1.117 is approximately equal to 5.05. What is the approximate value of 1.150 ?

Detailed Solution for Test: Arithmetic - Question 3

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 

Test: Arithmetic - Question 4

A certain number of men can do a piece of work in 18 days working 8 hours a day. If the number of men is increased by 1/3 and the time spent per day is decreased by half, in how many days will the same work be completed?

Detailed Solution for Test: Arithmetic - Question 4

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.

Test: Arithmetic - Question 5

Which of the following is equal to 351/558 ?

Detailed Solution for Test: Arithmetic - Question 5


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.

Test: Arithmetic - Question 6

Which of the following can be the number of integers between 3x and 9x, both inclusive, if x is a positive integer?

Test: Arithmetic - Question 7

Of the following, which is most nearly equal to √10?

Detailed Solution for Test: Arithmetic - Question 7

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.

Test: Arithmetic - Question 8

Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.

Detailed Solution for Test: Arithmetic - Question 8

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.

Test: Arithmetic - Question 9

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. Which of the following must be true?

I. k = 2
II. r = 9
III. s = 5

Detailed Solution for Test: Arithmetic - Question 9

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.

Test: Arithmetic - Question 10

If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

Detailed Solution for Test: Arithmetic - Question 10

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.

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