Hi Folks

We start a new project: the GRE prep Club mini tests series. In our mind, we will release every other Monday a mini GRE test composed of 10 quant questions and 10 verbal questions. Moreover, based on the feedback received, we will release mini-tests per area of content, for example a mini-test of 20 questions quant on absolute value and inequality, a verbal test using only TC , and so forth.

What are the main benefits of a mini-exam taken on a regular basis:

• increase your stamina
• reinforce your confidence in the area tested and, as such, increase your time management to solve questions, and, in the end, improve your score
• improve your quant and verbal skills in every area tested during the GRE exam.

What are the characteristics of the MINI-Tests:

• they are usually composed of brand-new questions never released on the board. However, from time to time they could be made using questions from our vast database.
• usually are on the mid-hardest side. Our goal is to challenge the students. Therefore, take these tests in the second half of your preparation. What I mean by that: suppose that your study plan is three months span, then you should take the tests after at least one month of study and practice.
• the questions will be contained in a single post. This way, you can time yourself, going straight from the first one to the last one question
• very important: for a full solution just reply to the topic asking for example, I need the explanation for the MINI-Test #X, quant or verbal question #Y.
  BrushMyQuant & Carcass / GeminiHeat will be quite happy to provide you with them

My humble suggestion to you is to do the following:

Open this simple tab in your browser https://www.timer-tab.com/, set the time to 35 minutes for each section or 70 minutes for both, and test your skills.





Mini-Test #1 - 01/30/2023 Difficult level: medium
Mini-Test #2 - 02/13/2023 Difficult level: hard
Mini-Test #3 - 02/27/2023 Difficult level: hard


Enjoy



_________________

MINI-Test #1

QQ #1

The ratio of the number of male and female workers in a company in 2002 was 3 : 4. The ratio of the number of male and female workers in 2003 was 10 : 7.

Quantity A	Quantity B
Percent increase in the number of males from 2002 to 2003	Percent increase in the number of females from 2002 to 2003

Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105296


QQ #2

In a particular professional club, exactly 75 percent of the female members are engineers, and, of them, 1/3 are mechanical engineers. Exactly 30 percent of the male members are engineers. It is known that, only those who are engineers can be mechanical engineers.

Quantity A	Quantity B
Fraction of the members who are mechanical engineers in the club	\(\frac{1}{3}\)

Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105297


QQ #3




In the figure above, the triangle ABC is inscribed in the circle; the ratio of the sides BC, AC, and AB is 3 : 4 : 5 and the perimeter of the triangle is 48.

Quantity A	Quantity B
Circumference of the circle	20 \(\pi\)

Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105298


QQ #4

\(0 < x < 1\)

Quantity A	Quantity B
\(x-x^5\)	\(x^2-x^3 \)

Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105299


QQ #5


If \(r < 0\) and \(0 <\frac{pq}{r }< 1\), which of the following must be true?

A. p < 0
B. q < 0
C. p > q
D. p < q
E. pq > 0
F. pq < 0
G. pq < r
H. pq > r





Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105300


QQ #6

\(\sqrt{3 \sqrt{80} + \frac{3}{9+ 4 \sqrt{5}} }\)

A. \(3\)
B. \(3 \sqrt{2}\)
C. \(2 \sqrt{3}\)
D. \(3 \sqrt{3}\)
E. \(4 \sqrt{3}\)





Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105301


QQ #7


A sports apparel company makes basketball shirts in 15 sizes. For each of the 14 sizes, the ratio of the length of a shirt to that of its next larger size shirt is a fixed constant.
The sizes are ordered by increasing the length of the shirts. If the length of the smallest size shirt is 20 inches, and the length of the largest size shirt is 40 inches, then what is the length of the 8th size shirt?

A. \(20 \sqrt{2}\)
B. \(20 \sqrt[14]{2^5}\)
C. \(20 \sqrt[4]{2^7}\)
D. \(20 \sqrt[2]{2^8}\)
E. \(20 \sqrt[2]{2^{14}}\)





Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105303


QQ #8


If k is a two-digit positive integer with tens digit x and units digit y, then \(k^2 −(x+y)^2\) must be divisible by which of the following?

(A) 2
(B) 6y
(C) 9x
(D) 9xy
(E) 27





Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105304


QQ #9


A machine can be repaired for $1,200 and will last for one year, while the new machine would cost for $2,800 and will last for two years. The average cost per year of the new machine is what percent greater than the cost of repairing the current machine ?

(A) 7%
(B) 10%
(C) 16.67%
(D) 18.83%
(E) 20%




Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105306


QQ #10

In 2001, Joe paid 5.1 percent of his income in taxes. If from 2001 to 2002, Joe’s income increased by 10 percent, and taxes paid in 2002 are equivalent to 3.4 percent of Joe’s income in 2001, what percent of his income did Joe pay in taxes, in 2002?





Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105307



VQ #1


Consolidating memory is not instantaneous or even _____: every memory must be encoded and moved from short-term to long-term storage, and some of these memories are, for whatever reason, more vividly imprinted than others.

Blank (i)
A. salutary
B. deliberate
C. sequential
D. momentary
E. inevitable

Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105282


VQ #2

The politician’s record while in office, though (i)_____, hardly accounts for her high standard three decades later—a standing all the more (ii)_____ because of continuing assaults on her reputation during those years.

Blank (i)	Blank (ii)
A. bewildering	D. unusual
B. admirable	E. regrettable
C. unappreciated	F. persistent

Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105284


VQ #3


When a new scientific model emerges, research studies (i)_____ that paradigm tend to dominate in the scientific literature: the process of selecting articles for publication is tilted towards positive results. But once the paradigm (ii)_____, the academic incentives shift in the opposite direction: research results are more considered worthy publication when they (iii)_____ what has become the established view.

Blank (i)	Blank (ii)	Blank (iii)
A. tweaking	D. is initially articulated	G. bolster
B. affirming	E. has become entrenched	H. circumvent
C. controverting	F. is about to be attacked	I. undermine

Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105285



VQ #4/5/6





Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105295

VQ #7


The initial, widely shared pessimism turned out to be _____, because it ignored the many things that could be done with resources left behind.

Two Answers
A. unintelligible
B. unfathomable
C. unfounded
D. unimaginative
E. unjustified
F. unimportant

Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105289


VQ #8


Despite a tendency to be overtly _____, her poetry does not consist solely of pious sentiments: it often sparks the imagination and provides lively entertainment.

Two Answers
A. preachy
B. querulous
C. insincere
D. sanctimonious
E. plaintive
F. disingenuous

Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105290


VQ #9


Although in his new book he tends to repeat himself like a _____ uncle, McHughen makes a persuasive case for the safety of tinkering with genes to create new foods.

Two Answers
A. taciturn
B. reserved
C. prototypical
D. cantankerous
E. loquacious
F. garrulous

Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105291

VQ #10




Solution: https://gre.myprepclub.com/forum/gre-mi ... ml#p105287
_________________

Mini-test #1 VQ #1 Solution


Consolidating memory is not instantaneous or even _____: every memory must be encoded and moved from short-term to long-term storage, and some of these memories are, for whatever reason, more vividly imprinted than others.

Tricky question because we do not have so many clues even though the sentence is pretty clear and not convoluted that much.

Here what we do have: we do have a clear process that happens in our brain. Consolidated memory means all our memories are gathered and arranged in a clear and systematic way AND moved from one place to another. In this process, some memories are more vivid or clear - we could imagine how they are highlighted and others do not - and on top of that , this process doe snot happen neither in a snap or immediately nor

A. salutary - means good or healthy. OFF

B. deliberate - means consciously or that we do know the exact reason why the process takes place. However, during the process for some reasons that we do not know some memories are in a certain way and others in another fashion. So this word is OFF

C. sequential - we do not have any information how the process is conducted and how the memories are arranged. We do know only that they are moved from one spot to another. OFF

D. momentary - we do know that memories are moved and some are more vivid than others. Therefore, the memories are imprinted permanently and moved in LONG-TERM storage. OFF

E. inevitable - Correct

The correct answer is E
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Mini-test #1 VQ #2 Solution


The politician’s record while in office, though (i)_____, hardly accounts for her high standard three decades later—a standing all the more (ii)_____ because of continuing assaults on her reputation during those years.

The sentence in a nutshell tells us that even though the politician's record is somehow important (so it is admirable) does not explain to us why when she was in that specific position she had weird/strange - therefore unusual - attacks during her tenure.

B and D are the correct choices
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Mini-test #1 VQ #3 Solution


When a new scientific model emerges, research studies (i)_____ that paradigm tend to dominate in the scientific literature: the process of selecting articles for publication is tilted towards positive results. But once the paradigm (ii)_____, the academic incentives shift in the opposite direction: research results are more considered worthy publication when they (iii)_____ what has become the established view.

When a new scientific model emerges then this becomes a new standard, The studies related to this new model reinforce and so affirming this model in a pervasive way as a result, all the studies that gravitate around this new model tend to push for it even more and somehow become biased towards it.

However, once this same new model is well established or eradicated or entrenched we have a shift in the scientific world, instead, the studies conducted are made to reinforce even more the model, moving to undermine it
_________________

Mini-test #1 VQ #10 Solution


Argument 1 (argument from a psychologist)

Prerequisite: People who lack social will be depressed + time online cannot be used for social

Conclusion: going online can cause depression

Argument 2 (the author's argument)

Prerequisite: The study found that people who use the Internet more have a higher rate of depression

Conclusion: going online can cause depression

Reverse option A: The reason why those people in the experiment increased online was because they had experienced a decrease in social before. In this case, it means that these people are not depressed because of surfing the Internet, but because there is no social, and social causes both surfing and depression, but there is no correlation between surfing the Internet and depression! ! ! (They are more prone to depression before going online. Depression is not to blame on the Internet!) After being reversed, it played a role in weakening the original conclusion. Therefore, it shows that this option is a necessary premise that the author relies on in the reasoning process.

Reverse option C:After this option is reversed, it becomes, there is actually a chance to be social when surfing the Internet. In this case, there will be no depression, so the conclusion is overturned. Isn't this an assumption? This thinking process seems reasonable, but!!! To be clear about the author's argumentation process, don't be disturbed by the psychologist's argumentation! This option is hypothesized by the "psychologist", but not by the author. After this option is reversed, there is still no way to explain why those who surf the Internet are more depressed.


IMO A
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Mini-test #1 VQ #7 Solution

The initial, widely shared pessimism turned out to be _____, because it ignored the many things that could be done with resources left behind.

At the end of the day many things turned to be useful. Therefore, the initial sadness turned to be a joy because it was unfunded and unjustified.

There was no reason to be concerned

The answers are C and E
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Mini-test #1 VQ #8 Solution


Despite a tendency to be overtly _____, her poetry does not consist solely of pious sentiments: it often sparks the imagination and provides lively entertainment.

The keywords here - luckily we do have a strong clue in this sentence - is pious sentiments coupled with the contrast word despite

This means: even though her poetry is directly of a quality or characteristic that is preachy and sanctimonious, her poetry is more than that

A and D are the correct choices
_________________

Mini-test #1 VQ #9 Solution


Although in his new book he tends to repeat himself like a _____ uncle, McHughen makes a persuasive case for the safety of tinkering with genes to create new foods.


Here we do have a clue: to repeat. Or verbose. The rest of the sentence is just a filler

loquacious and garrulous are the correct options for this sentence.

E and F are the correct choices
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Mini-test #1 VQ #4/5/6 Solution


African American drama has, until recently, been rooted in the mimetic tradition of modern American naturalism.

The drama has a strong bond with the tradition of modern American naturalism. So far we do know what we will have ahead of this first statement.

The most distinctive attribute of this tradition is the mechanistic, materialistic conception of humanity.

The tradition of modern American naturalism has a key feature: that humanity and maybe as a consequence human beings see or care a lot of the material side: cars, houses , and so on.


Naturalism sees each individual as inextricably bound to the environment and depicts each person as someone controlled by, instead of controlling, concrete reality.

every human being is controlled and is strongly related to his/her environment and the reality around them


As long as African American drama maintained naturalism as its dominant mode, it could only express the “plight of African American people”.

If the American naturalism is related and maintains a bond with the material things that forge the life of those people, then we can only express the difficulties of the African American people

Its heroes might declare the madness of reality, but reality inevitably triumphed over them.

The heroes - I am not sure who are these heroes but I believe prominent figures - African American people can only denote or report that the reality around them is crazy and this is unfair. However, this will win. No matter what.

The surrealistic plays of Adrienne Kennedy mark one of the first departures from naturalism by an African American dramatist.

I believe the theatrical piece of Adrienne Kennedy is a shift from the configuration depicted above

The overall goal of her work has been to depict the world of the soul and the spirit, not to mirror concrete reality.

As can we easily infer, Kennedy narrates about the soul and the spirit and how they are important in contrast to a tyrannic reality

Within this framework, Kennedy has been able to portray African American minds and souls liberated from their connections to the external environment.

The important goal Kennedy achieved was that African American can be free from the chains of reality, elevating and - most important - freeing them.


1. Which of the following best states the central idea of the passage?

A. African American drama has been primarily influenced by naturalisms emphasis on the materialistic.

This is in the first part of the passage but is NOT the main point. It serve as a sort of framing of what is important later on in the passage. Tricky

B. African American drama has traditionally acknowledged the relationship between the individual and the environment.

NO, it has a key feature about but we do not know if it USUALLY recognizes that

C. African American drama, traditionally naturalistic, has been little influenced by dramatist Kennedy’s spiritual and psychological approach to drama.

Not so much information about that

D. The work of Kennedy suggests a shift away from a commitment to strict naturalism in African American drama.

Yes. It is mentioned clearly in the last part of the passage and it is the main goal of the passage itself

E. The work of Kennedy best exemplifies the current interest of African American artists in the spiritual and psychological worlds.

No mention about that




2. According to the passage, Kennedy is concerned with depicting the

A. internal rather than the external life of her characters
B. madness of reality rather than the effects of reality
C. effects of materialism on African American minds and souls
D. relationship between naturalism and the human spirit
E. effects that her characters have on the environment


Pretty straight question: Kennedy is concerned mainly of minds and souls of African American rather than the reality around them



3. Which of the following statements, if true, would most strengthen the authors assertion that Kennedy’s work marks a serious departure from the tradition described in the first paragraph?

A. Kennedy places the action in a real-life setting that is nevertheless unfamiliar to the average viewer or reader.

Kennedy's play never mentions real-life setting

B. Kennedy movingly portrays the lives and struggles of prominent African Americans in the United States.

No mention of this in the passage: she depicts prominent personalities


C. Kennedy uses characters found only in ancient African legends and mythology.

The heroes. Keep this for now

D. Kennedy provides insights into American mimetic tradition and dramatic convention.

No She narrated about minds and souls

E. Kennedy depicts the events in a style reminiscent of a television documentary.

Completely out of scope

By POE C is the best answer
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Mini-test #1 QQ #1 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




The ratio of the number of male and female workers in a company in 2002 was 3 : 4. The ratio of the number of male and female workers in 2003 was 10 : 7.

\(\frac{M_2002 }{ F_2002}\) = \(\frac{3}{4}\) = \(\frac{3x}{4x}\)

\(\frac{M_2003 }{ F_2003}\) = \(\frac{10}{7}\) = \(\frac{10y}{7y}\)

Quantity A : Percent increase in the number of males from 2002 to 2003

= \(\frac{M_2003 - M_2002}{M_2002}\) * 100 = \(\frac{10y - 3x}{3x}\) * 100 = (\(\frac{10}{3} * \frac{y}{x}\) - 1 ) * 100 ~ (3.33 * \(\frac{y}{x}\) - 1 ) * 100 = 333 * \(\frac{y}{x}\) - 100

Quantity B : Percent increase in the number of females from 2002 to 2003

= \(\frac{F_2003 - F_2002}{F_2002}\) * 100 = \(\frac{7y - 4x}{4x}\) * 100 = (\(\frac{7}{4} * \frac{y}{x}\) - 1 ) * 100 ~ (1.75 * \(\frac{y}{x}\) - 1 ) * 100 = 175 * \(\frac{y}{x}\) - 100

Clearly, Quantity A > Quantity B

So, Answer will be A
Hope it helps!
_________________

Mini-test #1 QQ #2 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




In a particular professional club, exactly 75 percent of the female members are engineers, and, of them, 1/3 are mechanical engineers. Exactly 30 percent of the male members are engineers. It is known that, only those who are engineers can be mechanical engineers.

Let number of Females be 100 and Number of Males be 200
There can be three types of Males and Females: Mechanical Engineer (ME), Other Engineers (OE), Non-Engineers(NE)

Female Mechanical Engineer, Other Engineers and Non-Engineers are denoted as FME, FOE, FNE
Male Mechanical Engineer, Other Engineers and Non-Engineers are denoted as MME, MOE, MNE

Exactly 75 percent of the female members are engineers, and, of them, 1/3 are mechanical engineers

=> FME = \(\frac{75}{100}\) * 100 * \(\frac{1}{3}\) = 25

Exactly 30 percent of the male members are engineers

=> MME + MOE = \(\frac{30}{100}\) * 200 = 60
=> Maximum value of MME = 60

Quantity A: Fraction of the members who are mechanical engineers in the club

Maximum value of this = \(\frac{FME + MME }{ 100 + 200}\) = \(\frac{25 + 60 }{ 300}\) < \(\frac{100}{300}\) => < \(\frac{1}{3}\)

Clearly, Quantity A < Quantity B

So, Answer will be B
Hope it helps!
_________________

Mini-test #1 QQ #3 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




In the figure above, the triangle ABC is inscribed in the circle; the ratio of the sides BC, AC, and AB is 3 : 4 : 5 and the perimeter of the triangle is 48.

BC : AC : AB = 3 : 4 : 5 = 3x : 4x : 5x

The perimeter of the triangle is 48

=> 3x + 4x + 5x = 12x = 48
=> x = \(\frac{48}{12}\) = 4

Given that BC : AC : AB = 3 : 4 : 5
=> ABC is a Right angled triangle right angled at C
=> AB becomes a diameter and its length = 5x = 5*4 = 20

Quantity A: Circumference of the circle

Circumference of the circle = πD = π * 20 = 20π

Clearly, Quantity A = Quantity B

So, Answer will be C
Hope it helps!

Watch the following video to Learn Basics of Circles


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Mini-test #1 QQ #4 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




Given that 0 < x < 1

Assume x = 0.1

Quantity A: \(x - x^5\)

Now, when x is a positive fraction between 0 and 1 then as we increase power of x then value of the numbers starts decreasing
Ex: x = 0.1 , \(x^2\) = \(0.1^2\) = 0.01

So, \(x^5\) will be a very small number and will be less than x but will be positive
=> \(x - x^5\) ~ x > 0

Quantity A: \(x^2 - x^3\) = 0

Clearly, Quantity A > Quantity B

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Inequalities


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Mini-test #1 QQ #5 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




Given that r < 0 and 0 < \(\frac{pq}{r}\) < 1 and we need to find which of the following is true

0 < \(\frac{pq}{r}\)
=> \(\frac{pq}{r}\) > 0

As r is negative so if we take r to the right hand side the sign of the inequality will reverse, we get
=> pq< r*0
=> pq < 0

\(\frac{pq}{r}\) < 1
As r is negative so if we take r to the right hand side the sign of the inequality will reverse, we get

=> pq > r

There is no other way to prove other options correct for sure
pq < 0
=> Either p > 0, q < 0 or p < 0, q > 0
But we cannot say for sure if any other option choice will be true.

So, Answer will be F, H
Hope it helps!

Watch the following video to learn the Basics of Inequalities


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Mini-test #1 QQ #6 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




We need to simplify \(\sqrt{3 \sqrt{80} + \frac{3}{9 + 4 \sqrt{5}} }\)

To Simplify \(\sqrt{3 \sqrt{80} + \frac{3}{9 + 4 \sqrt{5}} }\) we need to multiply the numerator and the denominator of \(\frac{3}{9 + 4 \sqrt{5}}\) with the Conjugate of \(9 + 4 \sqrt{5}\)

Conjugate of \(9 + 4 \sqrt{5}\) can be found by just reversing the middle sign => \(9 - 4 \sqrt{5}\). So, we will multiply the numerator and the dominator of \(\frac{3}{9 + 4 \sqrt{5}}\) with \(9 - 4 \sqrt{5}\)

=> \(\sqrt{3 \sqrt{80} + \frac{3}{9 + 4 \sqrt{5}} }\) = \(\sqrt{3 \sqrt{80} + \frac{3}{9 + 4 \sqrt{5}} * \frac{9 - 4 \sqrt{5} }{ 9 - 4 \sqrt{5}} }\)

Now the denominator is of the form (a-b) * (a+b) and will be equal to \(a^2 - b^2\)

= \(\sqrt{3 \sqrt{4^2 * 5} + \frac{27 - 12\sqrt{5} }{9^2 - 4^2 * 5} }\)
= \(\sqrt{12\sqrt{5} + \frac{27 - 12\sqrt{5} }{81 - 80} }\)
= \(\sqrt{27}\) = 3\(\sqrt{3}\)

So, Answer will be D
Hope it helps!

Watch the following video to learn How to Rationalize Roots


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Mini-test #1 QQ #7 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




A sports apparel company makes basketball shirts in 15 sizes. For each of the 14 sizes, the ratio of the length of a shirt to that of its next larger size shirt is a fixed constant. The sizes are ordered by increasing the length of the shirts. If the length of the smallest size shirt is 20 inches, and the length of the largest size shirt is 40 inches, then what is the length of the 8th size shirt?

The problem is based on Geometric Progression(GP) with first term (a) as 20 and number of terms (n) as 15.
Size of \(15^{th}\) shirt, \(T_{15}\) = 40.
Let r be the ratio between consecutive sizes.
We need to find the size of \(8^{th}\) shirt, \(T_8\)

Using, GP formula for \(T_n\) we get
\(T_n = a*r^{n-1}\)
=> \(T_{15} = a*r^{15-1}\) = 20 * \(r^{14}\)
=> \(r^{14}\) = \(\frac{40}{20}\) = 2

\(T_8 = a*r^{8-1}\) = 20 * \(r^7\)

We know that \(r^{14}\) = 2
Taking square root on both the sides we will get
\(r^7\) = \(\sqrt{2}\)

=> \(T_8\) = 20 * \(\sqrt{2}\)

So, Answer will be A
Hope it helps!

Watch the following video to learn How to Solve Sequence problems


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Mini-test #1 QQ #8 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




If k is a two-digit positive integer with tens digit x and units digit y, then \(k^2−(x+y)^2\) must be divisible by which of the following?

k is a 2-digit number with tens digit as x and units digit as y
=> k = xy = 10x + y

=> \(k^2−(x+y)^2\) = \((10x + y)^2−(x+y)^2\) = \(100x^2 + 20xy + y^2−(x^2 + 2xy + y^2)\) = \(99x^2 + 18xy\) = 9x*(11x + 2y)

=> Divisible by 9x

So, Answer will be C
Hope it helps!
_________________

Mini-test #1 QQ #9 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




A machine can be repaired for $1,200 and will last for one year, while the new machine would cost for $2,800 and will last for two years. The average cost per year of the new machine is what percent greater than the cost of repairing the current machine ?

Per Year cost of repair = $1,200
Cost of New machine with life of two years = $2,800
=> Per Year cost of new machine = \(\frac{$2,800}{2}\) = $1,400

The average cost per year of the new machine is what percent greater than the cost of repairing the current machine = ( (Per Year Cost of New Machine - Per Year Cost of Old Machine) / Per Year Cost of Old Machine) * 100 = \(\frac{1400 - 1200}{1200}\) * 100 = \(\frac{200}{1200}\) * 100 = \(\frac{100}{6}\) = \(\frac{50}{3}\) = 16.67%

So, Answer will be C
Hope it helps!
_________________

Mini-test #1 QQ #10 Solution

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




In 2001, Joe paid 5.1 percent of his income in taxes. If from 2001 to 2002, Joe’s income increased by 10 percent, and taxes paid in 2002 are equivalent to 3.4 percent of Joe’s income in 2001, what percent of his income did Joe pay in taxes, in 2002?

2001
Let his Income in 2001 = 100
=> Tax paid = 5.1% of Income = \(\frac{5.1}{100}\) * 100 = 5.1

2002
Income increased by 10%
=> Income in 2002 = 100 + 10% * 100 = 110
Tax paid in 2002 = 3.4% of Income in 2001 = \(\frac{3.4}{100}\) * 100 = 3.4

% of Income paid in taxes in 2002 = \(\frac{Tax}{Income}\) * 100 = \(\frac{3.4}{110}\) * 100 = \(\frac{34}{11}\) = 3.09%

So, Answer will be 3.09%
Hope it helps!
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