Call Now to Set Up Tutoring:

(888) 888-0446

HSPT Quantitative : Non-Geometric Comparison

Study concepts, example questions & explanations for HSPT Quantitative

Create An Account

All HSPT Quantitative Resources

6 Diagnostic Tests 55 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #81 : Non Geometric Comparison

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

(a) -3(x-14)

(b) -(3x-42)

Possible Answers:

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

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

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

(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.

Report an Error

Example Question #82 : Non Geometric Comparison

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

(a) $\frac{4}{10}$ of

(b) $\frac{4}{9}$ of

Possible Answers:

a=c<b

a=c>b

a<c<b

a>c>b

Correct answer:

a<c<b

Explanation:

Find the values by multiplying each set of numbers together:

(a) $\frac{4}{10}\cdot 16=6.4$

(b) $\frac{4}{9}\cdot 16=7.1$

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

Report an Error

Example Question #83 : Non Geometric Comparison

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

a) $5\cdot6.5^2$

b) $25\cdot6.5^2$

c) $25\cdot6.5$

Possible Answers:

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

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

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

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

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) $5\cdot6.5^2$ $=5\cdot42.25=211.25$

b) $25\cdot6.5^2$ $=25\cdot42.25=1056.25$

c) $25\cdot6.5$ =162.5

It is now evident that the three are not equal.

Report an Error

Example Question #84 : Non Geometric Comparison

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

a) z^2(x+y)

b) z^2x+z^2y

c) zx^2+zy^2

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

To get (b) from (a), simply distribute the z^2 to each term within the parantheses. In (c), it looks like the z^2 has been distributed, but actually the exponent has jumped to the other variables. This is no longer equal.

Report an Error

Example Question #85 : Non Geometric Comparison

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

a) (2+4)^2

b) 2^2+4^2

c) $2^{2+4}$

Possible Answers:

(b) is equal to (c).

(a) is equal to (b).

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

Correct answer:

Explanation:

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

a) (2+4)^2 =6^2=36

b) 2^2+4^2 =4+16=20

c) $2^{2+4}$ =2^6=64

Therefore (c) is the greatest number.

Report an Error

Example Question #86 : 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) $\dpi{100} -2(x+y)$

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.

Report an Error

Example Question #87 : Non Geometric Comparison

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

a) $\frac{3}{x^{2}}$

b) $\left(\frac{3}{x}\right)^{2}$

c) $\frac{3^{2}}{x^{2}}$

Possible Answers:

a>b=c

a<b=c

a=b=c

a<b<c

Correct answer:

a<b=c

Explanation:

a) $\frac{3}{x^{2}}$

This expression is already simplified.

b) $\left(\frac{3}{x}\right)^{2}$

This expression simplifies to $\left(\frac{3}{x}\right)^{2}=\frac{3^{2}}{x^{2}}=\frac{9}{x^{2}}$ .

c) $\frac{3^{2}}{x^{2}}$

This expression also simplifies to $\frac{3^{2}}{x^{2}}=\frac{9}{x^{2}}$ .

Clearly (b) and (c) are equal, but (a) is smaller because it has a smaller numerator.

Report an Error

Example Question #88 : Non Geometric Comparison

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

a) $\frac{5}{6}$ of

b) $\frac{6}{5}$ of

c) $\frac{6}{5}$ of

Possible Answers:

a>b>c

a<b<c

a<c<b

a=b<c

Correct answer:

a<b<c

Explanation:

Calculate each expression to compare the values:

a) $\frac{5\cdot30}{6}=25$

b) $\frac{6\cdot25}{5}=30$

c) $\frac{6\cdot30}{5}=36$

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

Report an Error

Example Question #89 : Non Geometric Comparison

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

a) $\frac{1}{2}$ of

b) $\frac{1}{3}$ of

c) $\frac{3}{4}$ of

Possible Answers:

a>b=c

a=b=c

a < b=c

a < b < c

Correct answer:

a>b=c

Explanation:

Calculate each expression in order to compare them:

a) $\frac{1}{2}$ of

$\frac{32}{2}=16$

b) $\frac{1}{3}$ of

$\frac{45}{3}=15$

c) $\frac{3}{4}$ of

$\frac{3\cdot20}{4}=15$

(b) and (c) are equal, and (a) is greater than both.

Report an Error

Example Question #131 : Hspt Quantitative Skills

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

a. percent of

b. percent of

c. percent of

Possible Answers:

a>b=c

a>b>c

a=b<c

a=b=c

a<b=c

Correct answer:

a=b<c

Explanation:

Find the values of a, b, and c.

$a=\tfrac{20}{100}*50=\tfrac{1000}{100}=10$

$b=\tfrac{50}{100}*20=\tfrac{1000}{100}=10$

$c=\tfrac{30}{100}*90=\tfrac{2700}{100}=27$

With these values, a=b<c .

Report an Error

View Tutors

Kevin
Certified Tutor

St. Johns University, Bachelors, Math/Coaching.

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

All HSPT Quantitative Resources

6 Diagnostic Tests 55 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in Philadelphia, SSAT Tutors in Miami, LSAT Tutors in Chicago, Statistics Tutors in San Diego, English Tutors in Dallas Fort Worth, ACT Tutors in Philadelphia, French Tutors in Miami, Reading Tutors in Chicago, Statistics Tutors in Houston, MCAT Tutors in Los Angeles

Popular Courses & Classes

LSAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Houston, ACT Courses & Classes in Atlanta, GRE Courses & Classes in Boston, GRE Courses & Classes in New York City, SAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Atlanta, SSAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Houston

Popular Test Prep

SAT Test Prep in Washington DC, LSAT Test Prep in Miami, LSAT Test Prep in Atlanta, SAT Test Prep in Chicago, MCAT Test Prep in Denver, SSAT Test Prep in Miami, ACT Test Prep in Atlanta, ISEE Test Prep in San Diego, MCAT Test Prep in Dallas Fort Worth, GRE Test Prep in Miami

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

HSPT Quantitative : Non-Geometric Comparison

Study concepts, example questions & explanations for HSPT Quantitative

All HSPT Quantitative Resources

Example Questions

Example Question #81 : Non Geometric Comparison

Example Question #82 : Non Geometric Comparison

Example Question #83 : Non Geometric Comparison

Example Question #84 : Non Geometric Comparison

Example Question #85 : Non Geometric Comparison

Example Question #86 : Non Geometric Comparison

Example Question #87 : Non Geometric Comparison

Example Question #88 : Non Geometric Comparison

Example Question #89 : Non Geometric Comparison

Example Question #131 : Hspt Quantitative Skills

All HSPT Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: