HSPT Quantitative : How to make non-geometric comparisons

Study concepts, example questions & explanations for HSPT Quantitative

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Example Questions

Example Question #81 : Non Geometric Comparison

 

 

Compare the values of (a), (b), and (c):

(a) 

(b) 

(c) 

Possible Answers:

(a), (b), and (c) are all unequal

(a) is equal to (c), but not (b)

(a), (b), and (c) are all equal

(b) is equal to (c), but not (a)

Correct answer:

(a), (b), and (c) are all equal

Explanation:

(a), (b), and (c) are all different ways of writing the same mathematical expression. By simplifying (a), we would obtain (b) and (c). You can test that these expressions are equal by substituting a number for  and solving each expression.

Example Question #82 : Non Geometric Comparison

Compare the values of (a), (b), and (c):

(a)  of 

(b)  of 

(c)  of 

Possible Answers:

Correct answer:

Explanation:

Find the values by multiplying each set of numbers together:

(a) 

(b) 

(c) 

(a) is smaller than (c), which is smaller than (b)

Example Question #83 : Non Geometric Comparison

Examine (a), (b), and (c) to find the best answer:

a) 

b) 

c) 

Possible Answers:

(a) is equal to (c) but not (b)

(a) is equal to (b) but not (c)

(a), (b), and (c) are all unequal

(a), (b), and (c) are all equal

Correct answer:

(a), (b), and (c) are all unequal

Explanation:

Follow the order of operations in this problem and compute the exponents before the multiplication.

a)  

b)  

c)  

It is now evident that the three are not equal.

Example Question #84 : Non Geometric Comparison

Examine (a), (b), and (c) to find the best answer, for all values  of , and :

a)  

b) 

c) 

Possible Answers:

(a), (b), and (c) are all equal

(a) is equal to (c) but not (b)

(a), (b), and (c) are all unequal

(a) is equal to (b) but not (c)

Correct answer:

(a) is equal to (b) but not (c)

Explanation:

To get (b) from (a), simply distribute the  to each term within the parantheses. In (c), it looks like the  has been distributed, but actually the exponent has jumped to the other variables. This is no longer equal.

Example Question #85 : Non Geometric Comparison

Examine (a), (b), and (c) to find the best answer:

a) 

b) 

c) 

Possible Answers:

(c) is greater than (a) and (b).

(a) is greater than (b) or (c).

(b) is equal to (c).

(a) is equal to (b).

Correct answer:

(c) is greater than (a) and (b).

Explanation:

Remember to follow the order of operations for this problem: first parantheses, then exponents, then addition.

a)  

b) 

c)  

Therefore (c) is the greatest number.

Example Question #81 : Non Geometric Comparison

Examine (A), (B), and (C) and find the best answer if both  and  are less than zero.

(A)  \dpi{100} -2x

(B) \dpi{100} -2(x+y)

(C) \dpi{100} -3(x+y)

Possible Answers:

\dpi{100} A<B<C

\dpi{100} A>B>C

\dpi{100} A>B=C

\dpi{100} A=B=C

Correct answer:

\dpi{100} A<B<C

Explanation:

This is a difficult problem.  Since \dpi{100} x and \dpi{100} y are both negative, then \dpi{100} x+y must be less than \dpi{100} 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 \dpi{100} negative \times negative=positive, the larger the absolute value of the variables AND the coefficient, the larger the answer will be. 

\dpi{100} x+y has an absolute value that is greater than \dpi{100} x.

\dpi{100} -3 has an absolute value that is greater than \dpi{100} -2.

Combine these two and we realize that \dpi{100} -3(x+y) must be the greatest of the three choices.

Example Question #87 : Non Geometric Comparison

Examine (a), (b), and (c) to find the best answer:

a)  

b)  

c)  

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #88 : Non Geometric Comparison

Examine (a), (b), and (c) to find the best answer:

a)  of 

b)  of 

c)  of 

Possible Answers:

Correct answer:

Explanation:

Calculate each expression to compare the values:

a) 

b) 

c) 

It is now evident that (a) is smaller than (b), which is smaller than (c).

Example Question #89 : Non Geometric Comparison

Examine (a), (b), and (c) to find the best answer:

a)  of 

b)  of 

c)  of 

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #90 : Non Geometric Comparison

Examine a, b, and c and find the best answer.

a. percent of

b. percent of

c. percent of

Possible Answers:

Correct answer:

Explanation:

Find the values of a, b, and c.

With these values, .

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