How to make non-geometric comparisons - HSPT Quantitative
Card 1 of 416
$\frac{1}{3}$ of what number is equal to 2 times 4?
$\frac{1}{3}$ of what number is equal to 2 times 4?
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Set up the following equation.
$\frac{1}{3}$x=2cdot 4
$\frac{1}{3}$x=8
3cdot $\frac{1}{3}$x=8cdot 3
x=24
Set up the following equation.
$\frac{1}{3}$x=2cdot 4
$\frac{1}{3}$x=8
3cdot $\frac{1}{3}$x=8cdot 3
x=24
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Examine (A), (B), and (C) and find the best answer.
(A) .75
(B) $\frac{1}{2}$ of 1.5
(C) $\frac{3}{4}$
Examine (A), (B), and (C) and find the best answer.
(A) .75
(B) $\frac{1}{2}$ of 1.5
(C) $\frac{3}{4}$
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All of these choices are equal.
$\frac{3}{4}$ is .75 in fraction form, and .75 is $\frac{3}{4}$ in decimal form.
$\frac{1}{2}$ of 1.5 is the same as $\frac{1}{2}$cdot $\frac{3}{2}$=\frac{3}{4}$.
All of these choices are equal.
$\frac{3}{4}$ is .75 in fraction form, and .75 is $\frac{3}{4}$ in decimal form.
$\frac{1}{2}$ of 1.5 is the same as $\frac{1}{2}$cdot $\frac{3}{2}$=\frac{3}{4}$.
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Examine (A), (B), and (C) and find the best answer if both 
and 
are less than zero.
(A) -2x
(B) -2(x+y)
(C) -3(x+y)
Examine (A), (B), and (C) and find the best answer if both
(A) -2x
(B) -2(x+y)
(C) -3(x+y)
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This is a difficult problem. Since x and y are both negative, then x+y must be less than x.
In (A), (B), and (C) the variables (which are negative) are all multiplied by a negative number, so the ultimate values for each is positive.
Thus, since this is negative times negative=positive, the larger the absolute value of the variables AND the coefficient, the larger the answer will be.
x+y has an absolute value that is greater than x.
-3 has an absolute value that is greater than -2.
Combine these two and we realize that -3(x+y) must be the greatest of the three choices.
This is a difficult problem. Since x and y are both negative, then x+y must be less than x.
In (A), (B), and (C) the variables (which are negative) are all multiplied by a negative number, so the ultimate values for each is positive.
Thus, since this is negative times negative=positive, the larger the absolute value of the variables AND the coefficient, the larger the answer will be.
x+y has an absolute value that is greater than x.
-3 has an absolute value that is greater than -2.
Combine these two and we realize that -3(x+y) must be the greatest of the three choices.
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Examine (a), (b), and (c) and find the best answer.
a) the square root of 
b) 
of 
c) the average of 
& 
Examine (a), (b), and (c) and find the best answer.
a) the square root of
b)
c) the average of
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a) The square root of 
is 
, because 
.
b) 
of 
is 
, because 
.
c) The average of 
and 
is 
, because 
.
Therefore (b) and (c) are equal, and they are both smaller than (a).
a) The square root of
b)
c) The average of
Therefore (b) and (c) are equal, and they are both smaller than (a).
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Examine (a), (b), and (c) and find the best answer.
a) 
percent of 
b) 
percent of 
c) 
percent of 
Examine (a), (b), and (c) and find the best answer.
a)
b)
c)
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a) 
percent of 
is 
because 
.
b) 
percent of 
is 
because 
.
c) 
percent of 
is 
because 
.
Therefore (b) is smaller than (a) which is smaller than (c).
a)
b)
c)
Therefore (b) is smaller than (a) which is smaller than (c).
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Examine (a), (b), and (c) and find the best answer.
a) 
b) 
c) 
Examine (a), (b), and (c) and find the best answer.
a)
b)
c)
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a) 
b) 
c) 
Therefore (a) is larger than (b) which is larger than (c).
a)
b)
c)
Therefore (a) is larger than (b) which is larger than (c).
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Examine (a), (b), and (c) and find the best answer.
a) 
b) 
c) 
Examine (a), (b), and (c) and find the best answer.
a)
b)
c)
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a) 
b) 
c) 
Therefore (a) and (b) are equal, and they are larger than (c).
a)
b)
c)
Therefore (a) and (b) are equal, and they are larger than (c).
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Examine (a), (b), and (c) and find the best answer.
a) 
b) 
c) 
Examine (a), (b), and (c) and find the best answer.
a)
b)
c)
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This question tests your understanding of the order of operations. First complete operations in parentheses, then multiplication and division, and finally addition and subtraction.
a) 
b) 
c) 
Therefore (a) is smaller than (c) which is smaller than (b).
This question tests your understanding of the order of operations. First complete operations in parentheses, then multiplication and division, and finally addition and subtraction.
a)
b)
c)
Therefore (a) is smaller than (c) which is smaller than (b).
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Examine (a), (b), and (c) and find the best answer.
a) 
b) 
percent of 
c) 
Examine (a), (b), and (c) and find the best answer.
a)
b)
c)
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a) 
b) 
percent of 
c) 
Therefore (a) and (c) are the same, and they are both larger than (b).
a)
b)
c)
Therefore (a) and (c) are the same, and they are both larger than (b).
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Examine (a), (b), and (c) and choose the best answer.
a) 
percent of 
percent of 
b) 
percent of 
percent of 
c) 
percent of 
percent of 
Examine (a), (b), and (c) and choose the best answer.
a)
b)
c)
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a) 
percent of 
percent of 
b) 
percent of 
percent of 
c) 
percent of 
percent of 
Therefore (a), (b), and (c) are all equal.
a)
b)
c)
Therefore (a), (b), and (c) are all equal.
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Examine (a), (b), and (c) to find the best answer:
a) 
b) 
c) 
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
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a) 
This expression is already simplified.
b) 
This expression simplifies to 
.
c) 
This expression also simplifies to 
.
Clearly (b) and (c) are equal, but (a) is smaller because it has a smaller numerator.
a)
This expression is already simplified.
b)
This expression simplifies to
c)
This expression also simplifies to
Clearly (b) and (c) are equal, but (a) is smaller because it has a smaller numerator.
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Examine (a), (b), and (c) to find the best answer:
a) 
b) The smallest prime number larger than 
c) 
percent of 
Examine (a), (b), and (c) to find the best answer:
a)
b) The smallest prime number larger than
c)
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a) 
b) The smallest prime number larger than 
is 
.
c) 
percent of 
Therefore (b) is smaller than (c) which is smaller than (a).
a)
b) The smallest prime number larger than
c)
Therefore (b) is smaller than (c) which is smaller than (a).
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Examine (a), (b), and (c) to find the best answer:
a) 
b) 
c) 
*
is a non-zero integer
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
*
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a) 
b) 
c) 
Therefore (a) and (b) are equal. For all non-zero integers (whole numbers other than zero), 
will be smaller than 
, so (c) is smaller than (a) and (b).
a)
b)
c)
Therefore (a) and (b) are equal. For all non-zero integers (whole numbers other than zero),
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Examine (a), (b), and (c) to find the best answer:
a) 
percent of 
b) 
percent of 
c) 
percent of 
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
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In each of these scenarios, if the percentage increases, the number decreases by the same factor. All cases are the same value:
a) 
percent of 
b) 
percent of 
c) 
percent of 
In each of these scenarios, if the percentage increases, the number decreases by the same factor. All cases are the same value:
a)
b)
c)
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Examine (a), (b), and (c) to find the best answer:
a) 
b) 
c) 
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
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Always do the operations in parantheses first, then multiplication, then addition.
a) 
b) 
c) 
Therefore (a) is greater than (b), which is greater than (c) .
Always do the operations in parantheses first, then multiplication, then addition.
a)
b)
c)
Therefore (a) is greater than (b), which is greater than (c) .
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Examine (a), (b), and (c) to find the best answer:
a) 
of 
b) 
of 
c) 
of 
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
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Multiply each fraction by the number to find each value:
a) 
of 
b) 
of 
c) 
of 
Therefore (a) is less than (c), which is less than (b).
Multiply each fraction by the number to find each value:
a)
b)
c)
Therefore (a) is less than (c), which is less than (b).
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Examine (a), (b), and (c) to find the best answer:
a) 
b) 
c) 
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
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Simplify each expression to see if they are equal:
a) 
(already simplified)
b) 
c) 
Therefore (a) and (c) are equal, but (b) is different.
Simplify each expression to see if they are equal:
a)
b)
c)
Therefore (a) and (c) are equal, but (b) is different.
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Examine (a), (b), and (c) to find the best answer:
a) 
b) 
percent
c) 
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
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Convert each expression into a decimal in order to compare them:
a) 
b) 
c)
Therefore (a) is the largest.
Convert each expression into a decimal in order to compare them:
a)
b)
c)
Therefore (a) is the largest.
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Examine (a), (b), and (c) to find the best answer:
a) 
of 
b) 
of 
c) 
of 
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
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Calculate each expression in order to compare them:
a) 
of 
b) 
of 
c) 
of 
(b) and (c) are equal, and (a) is greater than both.
Calculate each expression in order to compare them:
a)
b)
c)
(b) and (c) are equal, and (a) is greater than both.
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Examine (a), (b), and (c) to find the best answer:
a) 
b) 
c) 
Examine (a), (b), and (c) to find the best answer:
a)
b)
c)
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Rewrite the first fraction with a denominator of 
in order to compare more easily:
a) 
b) 
c) 
It becomes clear that (b) is the greatest, followed by (a), then (c).
Rewrite the first fraction with a denominator of
a)
b)
c)
It becomes clear that (b) is the greatest, followed by (a), then (c).
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