Arithmetic - GMAT Quantitative
Card 0 of 4488
Subtract nine hundred six ten-thousandths from four tenths.
Subtract nine hundred six ten-thousandths from four tenths.
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Nine hundred six ten-thousandths = 0.0906
Four tenths = 0.4, or 0.4000
The difference:
This is three thousand ninety-four ten-thousandths.
Nine hundred six ten-thousandths = 0.0906
Four tenths = 0.4, or 0.4000
The difference:
This is three thousand ninety-four ten-thousandths.
If 
and 
are positive integers such that 
= 4.46, which of the following numbers could be the remainder when 
is divided by 
?
If
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Given that
it follows that 
.
We don't need to know 
or 
, the only important information is that:
Where the remainder is any one of the answer choices. This is because the remainder for any divisor/dividend pair is the product of the decimal portion of the quotient and the divisor.
Since we don't know y, our answer choice for the remainder is any answer that satisfies the above equation for a positive interger, since 
is specified as such in the problem.
The only answer choice that satisfies the constraints on 
is 184:
==> 
==> 
Given that
it follows that
We don't need to know
Where the remainder is any one of the answer choices. This is because the remainder for any divisor/dividend pair is the product of the decimal portion of the quotient and the divisor.
Since we don't know y, our answer choice for the remainder is any answer that satisfies the above equation for a positive interger, since
The only answer choice that satisfies the constraints on
Rewrite as a fraction in lowest terms: 
Rewrite as a fraction in lowest terms:
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Add one hundred seven ten-thousandths to seventeeen one-hundredths.
Add one hundred seven ten-thousandths to seventeeen one-hundredths.
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One hundred seven ten-thousandths = 0.0107
Seventeeen one-hundredths = 0.17, or 0.1700
The sum:
This is one thousand eight hundred seven ten-thousandths.
One hundred seven ten-thousandths = 0.0107
Seventeeen one-hundredths = 0.17, or 0.1700
The sum:
This is one thousand eight hundred seven ten-thousandths.
Multiply seventy-seven one-hundredths by sixty-six one-thousandths.
Multiply seventy-seven one-hundredths by sixty-six one-thousandths.
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Seventy-seven one-hundredths = 0.77
Sixty-six one-thousandths = 0.066
The product:
0.77 and 0.066 have a total of five digits to the right of their decimal points, so position the decimal point in the answer so that there are five digits to its right.
This is five thousand eighty-two hundred-thousandths.
Seventy-seven one-hundredths = 0.77
Sixty-six one-thousandths = 0.066
The product:
0.77 and 0.066 have a total of five digits to the right of their decimal points, so position the decimal point in the answer so that there are five digits to its right.
This is five thousand eighty-two hundred-thousandths.
Divide eight hundred eighty-eight thousandths by sixty-four ten-thousandths.
Divide eight hundred eighty-eight thousandths by sixty-four ten-thousandths.
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Eight hundred eighty-eight thousandths = 0.888
Sixty-four ten-thousandths = 0.0064
Set up a long division:
Move the decimal point four places right in both numbers so that the divisor will be a whole number. Note that this will require the use of placeholder zeroes in the dividend.
(Note that leading zeroes have been removed.)
Carry out the long division, making sure you align the decimals:
The quotient of this division is that of the original problem, so the correct choice is 138.75.
Eight hundred eighty-eight thousandths = 0.888
Sixty-four ten-thousandths = 0.0064
Set up a long division:
Move the decimal point four places right in both numbers so that the divisor will be a whole number. Note that this will require the use of placeholder zeroes in the dividend.
(Note that leading zeroes have been removed.)
Carry out the long division, making sure you align the decimals:
The quotient of this division is that of the original problem, so the correct choice is 138.75.
Which of the following is the square of twenty seven one-thousandths?
Which of the following is the square of twenty seven one-thousandths?
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Twenty-seven one-thousandths = 0.027
Its square is
Multiply without regard to the decimals first:
0.027 and 0.027 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.
This is seven hundred twenty-nine one-millionths.
Twenty-seven one-thousandths = 0.027
Its square is
Multiply without regard to the decimals first:
0.027 and 0.027 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.
This is seven hundred twenty-nine one-millionths.
Which of the following is the cube of fifteen one-hundredths?
Which of the following is the cube of fifteen one-hundredths?
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Fifteen one-hundredths = 0.15
Its cube is 
Multiply without regard to the decimals first:
0.15, 0.15, and 0.15 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.
This is three thousand three hundred seventy-five one-millionths.
Fifteen one-hundredths = 0.15
Its cube is
Multiply without regard to the decimals first:
0.15, 0.15, and 0.15 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.
This is three thousand three hundred seventy-five one-millionths.
Which of these equations is not correct?
Which of these equations is not correct?
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Although tempting, a calculator is not required to spot the correct answer.
is equal to 
as it is 
parts of 
. And therefore 
must be slightly different. (It's it actually 
)
Although tempting, a calculator is not required to spot the correct answer.
If we divide 10 by 3, what is the 10th digit after the decimal point of the quotient?
If we divide 10 by 3, what is the 10th digit after the decimal point of the quotient?
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The tenth digit after the decimal point is 3.
When dividing 1 by 3 or 10 by 3, we get repeating 3s. So, there must be a 3 in the tenths digit.
The tenth digit after the decimal point is 3.
When dividing 1 by 3 or 10 by 3, we get repeating 3s. So, there must be a 3 in the tenths digit.
Given the sets A = {2, 3, 4, 5} and B = {3, 5, 7}, what is A bigcup B ?
Given the sets A = {2, 3, 4, 5} and B = {3, 5, 7}, what is A bigcup B ?
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We are looking for the union of the sets. That means we want the elements of A OR B.
So A bigcup B = {2, 3, 4, 5, 7}.
We are looking for the union of the sets. That means we want the elements of A OR B.
So A bigcup B = {2, 3, 4, 5, 7}.
Define three sets as follows:
How many elements does the set 
have?
Define three sets as follows:
How many elements does the set
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comprises the set of elements common to all three sets. However, since 
is the set of all even integers and 
comprises the set of all odd integers, no element can be common to all three sets. The correct response is 0.
Define two sets as follows:
. Which is a possible value of 
?
Define two sets as follows:
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comprises the set of all odd integers except 1; 
comprises the set of all integers of the form 
, 
a natural number. Therefore, any number that is not in the union of these two sets must be in neither one.
, so 
is even or 1 (although 1 is not a choice). We can eliminate odd choices 147, 149, and 151 immediately.
, so we determine which number cannot be expressed as 
, 
a natural number.
148 is elminated, since it is two less than a multiple of 3. 150 is the correct choice.
148 is elminated, since it is two less than a multiple of 3. 150 is the correct choice.
There exists two sets 
and 
. 
= {1, 4} and 
= {3, 4, 6}. What is 
?
There exists two sets
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Add each element of 
to each element of 
.
= {1 + 3, 1 + 4, 1 + 6, 4 + 3, 4 + 4, 4 + 6} = {4, 5, 7, 8, 10}
Add each element of
Let 
be the set 
, and 
be the set 
.
What are the elements in the set 
?
Let
What are the elements in the set
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is the set of all elements that are in both 
and 
. So in this case the elements that are the same for both sets are 
, Note that the order that you present the elements in your set doesn't matter. What matters is that you don't exclude any necessary elements, or add any that don't belong.
How many functions map from 
to 
?
How many functions map from
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There are three choices for 
(1, 2, and 3), and similarly there are three choices for 
(also 1, 2, and 3). Together there are 
possible functions from 
to 
. Remember to multiply, NOT add.
There are three choices for
Let the univeraal set 
be the set of all positive integers.
Define the sets
,
,
.
If the elements in 
were ordered in ascending order, what would be the fourth element?
Let the univeraal set
Define the sets
If the elements in
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are the sets of all positive integers that are one greater than a multiple of five, four, and three, respectively. Therefore, for a number to be in all three sets, and subsequently, 
, the number has to be one greater than a number that is a multiple of five, four, and three. Since 
, the number has to be one greater than a multiple of 60. The first four numbers that fit this description are 1, 61, 121, and 181, the last of which is the correct choice.
Define three sets as follows:
How many elements does the set 
have?
Define three sets as follows:
How many elements does the set
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comprises the set of elements common to all three sets. Only 5 fulfills that condition, so the correct choice is 1.
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
and 
are both numbers in Region I; also, 
. In how many of the five regions could the number 
possibly fall?
Examine the above diagram, which shows a Venn diagram representing the sets of real numbers.
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The numbers in Region I are exactly the natural numbers 
. All natural numbers are integers, and the integers are closed under subtraction, so 
cannot fall in Region IV or Region V. Also, since it is given in the problem that 
, it follows that 
, so the difference cannot be in Region II (the only whole number that is not a natural number is 
).
It is possible for 
to be in Region I. Example:
It is possible for to be in Region III (the integers that are not whole numbers, or the negative integers). Example:
can fall in either of two different regions.
The numbers in Region I are exactly the natural numbers
It is possible for
It is possible for
Given five sets 
, you are given that:
All of the following must be true if 
except:
Given five sets
All of the following must be true if
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The subset relation is transitive, so 
and 
together imply that 
.
Since all three of 
are subsets of 
, then any element of any of those four sets is an element of 
. Contrapositively, any nonelement of 
cannot be an element of any of 
.
However, it is possible for a nonelement of 
to be an element of 
if 
. A simple example:
and 
.
, 
, and 
.
The subset relation is transitive, so
Since all three of
However, it is possible for a nonelement of