GMAT Verbal : Strengthen/Weaken Critical Reasoning

Study concepts, example questions & explanations for GMAT Verbal

varsity tutors app store varsity tutors android store

Example Questions

Example Question #21 :Strengthen/Weaken Critical Reasoning

UCLA Sociologist:Between 1962 and 2012, the marriage rate (that is the percentage of adult women over 16 who get married for the first time each year) fell from 110 marriages a year per 1,000 unmarried women to just 37, a stunning 66 percent decline. Given this trend, there will likely be no women getting married for the first time by 2050!

Which of the following, if true, exposes a flaw in the sociologist’s reasoning?

Possible Answers:

Many women are deciding to simply live with their partners rather than get married.

The average age of marriage has increased dramatically in the past 20 years.

Marriage is much less likely to occur today for the first time than it was in the 1960’s.

Today’s divorce rates are expected to rise dramatically over the next 40 years.

More women are expected to get married for a second and third time in the next 40 years.


Correct answer:

The average age of marriage has increased dramatically in the past 20 years.

Explanation:

The key in this problem is to consider some flaw with the trend that the sociologist cites. In other words, what might indicate that the trend will not continue? Consider the following scenario: 10 years ago, most women who would normally have married at 22 start waiting to get married until they are forty. Over the next twenty years, the marriage rate would go down dramatically because women are waiting to get married (and the average marriage age is going up). However, when they do decide to get married, the rate will go back up again. If this were true it would show a huge flaw in the sociologist’s reasoning so "The average age of marriage has increased dramatically in the past 20 years." is correct. For "Today’s divorce rates are expected to rise dramatically over the next 40 years." and "More women are expected to get married for a second and third time in the next 40 years." divorce rates and second/third time marriages are unimportant because the argument is only about first time marriages. "Many women are deciding to simply live with their partners rather than get married." and "Marriage is much less likely to occur today for the first time than it was in the 1960’s." would not indicate a flaw as they both seem to support the sociologist (that is the trend that marriage is disappearing). Answer is "The average age of marriage has increased dramatically in the past 20 years."

Example Question #22 :Strengthen/Weaken Critical Reasoning

Epidemiologist: The cancer death rate (number of deaths from cancer per 1,000 people) in the city of Maple Grove is 30% percent higher now than it was ten years ago. The corresponding increase in Fernland, where a major anti-smoking initiative was introduced a decade ago, is only 10%. These figures support the conclusion that residents of Maple Grove are more likely to die from cancer than residents of Fernland.

The epidemiologist’s conclusion is flawed because it fails to consider __________________

Possible Answers:

Whether the population in Maple Grove has increased dramatically in the past decade.

Whether most cancer victims in Maple Grove survive more than 10 years.

Whether Fernland and Maple Grove had similar cancer death rates 10 years ago.

Whether Maple Grove has ever introduced an anti-smoking initiative.

Whether smoking is the primary cause of cancer in Fernland.


Correct answer:

Whether Fernland and Maple Grove had similar cancer death rates 10 years ago.

Explanation:

The epidemiologist’s argument improperly assumes that the cancer death rates were similar in the two towns ten years ago. While the rates in Maple Grove have INCREASED much more than in Fernland, what if they were much lower to begin with. Just because the rate has increased more in Maple Grove, it could easily be lower today than in Fernland. Answer choice "Whether Fernland and Maple Grove had similar cancer death rates 10 years ago." properly points out this assumption and is thus the correct answer. For "Whether the population in Maple Grove has increased dramatically in the past decade.", population growth is unimportant because it is a per capita rate. The smoking issue is a red herring in this problem (tries to steal your attention from the major data problem), so "Whether smoking is the primary cause of cancer in Fernland." and "Whether Maple Grove has ever introduced an anti-smoking initiative." are both wrong. For "Whether most cancer victims in Maple Grove survive more than 10 years.", the length of survival is also immaterial to the major data problem isolated above. Answer is "Whether Fernland and Maple Grove had similar cancer death rates 10 years ago.".

Example Question #23 :Strengthen/Weaken Critical Reasoning

As far back as the 1950s, research has shown that adults who participate in over 30 minutes of aerobic exercise at least three times a week have a significantly lower prevalence of respiratory illness than those who do not. In recent years, studies have consistently confirmed these same statistics. It can be concluded, therefore, that regular aerobic exercise can be helpful in preventing respiratory illness.

Which of the following, if true, would most weaken the argument above?

Possible Answers:

Some respiratory illnesses are hereditary and therefore minimally affected by lifestyle choices.

Recent studies have debunked the conventional wisdom that aerobic exercise is an effective preventer of heart disease.

The lengths of the average workday and commute have increased markedly since the 1950s, leaving the average person with less time for aerobic exercise.

People with respiratory illnesses are generally told by doctors that they must limit or cease their aerobic exercise routines.

The amount of air pollution, a common cause of respiratory illness, has increased dramatically since the 1950s.

Correct answer:

People with respiratory illnesses are generally told by doctors that they must limit or cease their aerobic exercise routines.

Explanation:

As you deconstruct this argument, you should notice a classic case of mistaking correlation (two things occur together) for causation (one causes the other). Here you're told that people who exercise regularly have a lower incidence of respiratory illness, and then the conclusion is that regular exercise helps prevent respiratory illness.

But why can't that be the other way around? Whenever a question is structured as "X and Y happen together, so X likely causes Y" you should be on the lookout for an answer choice that suggests that, actually, Y is the thing that causes X.

Answer choice "People with respiratory illnesses are generally told by doctors that they must limit or cease their aerobic exercise routines." here supplies exactly that: if people who have respiratory illness are unable to exercise, that's a possible reason for the statistics (exercise and respiratory health occur together) to be true. So by providing an alternate explanation for the premises, "People with respiratory illnesses are generally told by doctors that they must limit or cease their aerobic exercise routines." shows that the conclusion is not necessarily true. "People with respiratory illnesses are generally told by doctors that they must limit or cease their aerobic exercise routines." is correct.

"Some respiratory illnesses are hereditary and therefore minimally affected by lifestyle choices." is incorrect because the conclusion is so soft, that exercise "can be helpful in preventing" respiratory illness. Even if some respiratory illnesses cannot be prevented, choice "Some respiratory illnesses are hereditary and therefore minimally affected by lifestyle choices." does not prohibit exercise from preventing other respiratory illnesses. Note also that "Some respiratory illnesses are hereditary and therefore minimally affected by lifestyle choices." says that the hereditary respiratory illnesses areminimally affectedby lifestyle choices. "Minimally affected" still allows for lifestyle choices to have an impact, which is consistent with "can be helpful" in preventing these illnesses.

"The amount of air pollution, a common cause of respiratory illness, has increased dramatically since the 1950s." and "The lengths of the average workday and commute have increased markedly since the 1950s, leaving the average person with less time for aerobic exercise." are wrong for similar reasons: they are each overruled by the facts, which state that exercise and a lack of respiratory illness have remained correlated over time, even if respiratory illness is increasing due to pollution "The amount of air pollution, a common cause of respiratory illness, has increased dramatically since the 1950s." or people in general are exercising less "The lengths of the average workday and commute have increased markedly since the 1950s, leaving the average person with less time for aerobic exercise.". You still have facts from the argument that those who do find time to exercise have less respiratory illness than those who do not, so "The amount of air pollution, a common cause of respiratory illness, has increased dramatically since the 1950s." and "The lengths of the average workday and commute have increased markedly since the 1950s, leaving the average person with less time for aerobic exercise." are countered by the given information.

"Recent studies have debunked the conventional wisdom that aerobic exercise is an effective preventer of heart disease." misses the specific scope of the conclusion, which is only about respiratory illness. The fact that exercise doesn't prevent heart disease doesn't factor in to a discussion about respiratory issues. Because heart issues and respiratory issues are two completely different categories, "Recent studies have debunked the conventional wisdom that aerobic exercise is an effective preventer of heart disease." does not directly address the conclusion about respiratory issues.

Example Question #24 :Strengthen/Weaken Critical Reasoning

If a package isn’t scanned by the parcel company by 4:30pm, it will not be included for overnight delivery. James is responsible for shipping prototypes to a client, who has expressed that if they do not receive the prototypes - which were delayed by over a week because of production issues - by Thursday morning, the client will cancel its account with the company. Fortunately, James dropped off the prototypes at the parcel company at 4:00pm on Wednesday, so the company will not lose the client’s account.

Which of the following, it true, most justifies the reasoning above?

Possible Answers:

The client does not currently have other vendors who can perform the same service as James’s company.

The client was satisfied by the company’s explanations of the production issues that delayed the prototypes.

James has proven to be trustworthy with expedited shipments to clients in the past.

Any parcel dropped off before the overnight shipping deadline will be scanned prior to the deadline.

The prototypes being sent to the client are of reasonably high quality.

Correct answer:

Any parcel dropped off before the overnight shipping deadline will be scanned prior to the deadline.

Explanation:

An important gap in logic on this question exists between premises: we’re told that if a parcel isn’t SCANNED by 4:30, it will not be included for overnight delivery. And we’re told that if the prototypes in the package are not received by the next day, the client will cancel its account. The concluding sentence says that because James DROPPED OFF the package by 4:00, ahead of the 4:30 SCANNING deadline, the company will not lose the account.

Now, notice the big gap here between “DROPPED OFF” and “SCANNED” - is it sufficient to say that because James dropped off the package it will definitely be scanned in time? Dropped off and scanned are two different things. So the answer “Any parcel dropped off before the overnight shipping deadline will be scanned prior to the deadline” is important to connect those dots.

Recognize that the argument contains other gaps, too: the client wants the prototypes by the next morning, but does “scanned for overnight delivery” guarantee “received by morning?” It does not, but no answer choices deal with that gap in logic.

Example Question #25 :Strengthen/Weaken Critical Reasoning

电脑制造商,为了增加ales, often include at no additional charge a number of utility software programs. Since these programs take care of tasks such as virus protection, disk defragmentation, and application updating, they are of considerable savings to the computer manufacturers as well.

The argument above would be most strengthened by which of the following, assuming that it is true?

Possible Answers:

Disk defragmentation is an important routine task that should be performed at least once per month.

Many anti-virus programs offer little, if any, real protection.

Even though computer manufacturers buy these utility programs in bulk, they are still a significant cost to the manufacturer.

Computer viruses, disk fragmentation, and out-of-date applications are three major sources of warranty claims against computer manufacturers.

Surveys indicate that free software packages are very important to consumers.

Correct answer:

Computer viruses, disk fragmentation, and out-of-date applications are three major sources of warranty claims against computer manufacturers.

Explanation:

The argument jumps from the idea that these utilities are included for sales reasons to suggesting that they save the computer manufacturer money. Something to link the function of these programs to savings is necessary -- and that is exactly what answer choice "Computer viruses, disk fragmentation, and out-of-date applications are three major sources of warranty claims against computer manufacturers." offers. It is the correct answer. Answer choice "Surveys indicate that free software packages are very important to consumers." may initially appear attractive because of the original statement that free software is included to drive sales, but the argument focuses on cost savings to the manufacturer. Answer choices "Many anti-virus programs offer little, if any, real protection." and "Disk defragmentation is an important routine task that should be performed at least once per month." offer interesting but irrelevant information. Answer choice "Even though computer manufacturers buy these utility programs in bulk, they are still a significant cost to the manufacturer." would, if anything, weaken the argument.

Example Question #26 :Strengthen/Weaken Critical Reasoning

Type 1a supernovae, caused by the detonation of matter accreted onto white dwarf stars, explode with a highly predictable brightness. Since the brightness of these explosions fades over distance in a highly predictable way, scientists have long used images measuring the brightness of type 1a supernovae to determine the distance to distant galaxies.

Which of the following discoveries, if true, would most jeopardize scientists' reliance on images of type 1a supernovae as tools for measuring distances to distant galaxies?

Possible Answers:

Some supernovae exhibit very unusual spectral classifications and changes in brightness, and do not fit into the existing categories.

A new telescope is able to measure the brightness of several thousand type 1a supernovae with an unprecedented level of precision.

Large clouds of interstellar dust and ionized hydrogen can absorb the light emitted by type 1a supernovae.

Models explaining the causes of type 1a supernovae are altered to include an updated understanding of the role played by carbon fusion.

Type 2 supernovae are discovered to be even more dramatically variable in their brightness than previously thought.

Correct answer:

Large clouds of interstellar dust and ionized hydrogen can absorb the light emitted by type 1a supernovae.

Explanation:

在这种弱化的问题,结论是:泰pe 1a supernovae are an effective way of measuring distances. The reason is that they have a predictable brightness that fades over distance in a predictable way. Observing and measuring this brightness then allows the distance to be reconstructed. If answer choice "Large clouds of interstellar dust and ionized hydrogen can absorb the light emitted by type 1a supernovae.", the correct answer, were true, however, external factors could create significant variations in the way that the light is observed from Earth, and the use of the brightness observations to gauge distance would seem to be unreliable. Answer choices "Type 2 supernovae are discovered to be even more dramatically variable in their brightness than previously thought." and "Some supernovae exhibit very unusual spectral classifications and changes in brightness, and do not fit into the existing categories." talk about other sorts of supernovae which are not the type we are considering and are, therefore, out of scope. Answer choice "Models explaining the causes of type 1a supernovae are altered to include an updated understanding of the role played by carbon fusion." discusses the model explaining how the supernova works but says nothing about modifying the predictions of how bright the explosion is. Answer choice "A new telescope is able to measure the brightness of several thousand type 1a supernovae with an unprecedented level of precision." does not say anything about the results of the telescope and therefore has no effect on the assumption.

Example Question #61 :Critical Reasoning

Oil executive:While it is true that the number of reported oil spills per year has increased steadily over the last three decades, this is much more a function of how easy it is to detect small oil spills than of an increase in frequency of oil spills overall. In the past the only spills reported were those large enough to be detected by environmentalists and journalists. Nowadays analytics will report to the authorities even the smallest fissures in pipelines and tankers.

Which of the following, if true, best supports the executive’s argument?

Possible Answers:

The size of the average oil spill has decreased over the last three decades.

Because of improved logistics, the average distance a barrel of oil travels to its destination has decreased by 40% over the last three decades.

The average oil company spends nearly twice as much today on anti-spill equipment as it spent three decades ago.

The number of large and medium oil spills has remained roughly constant over the last three decades.

The cost required to clean up the average oil spill has decreased by over 20% over the last three decades.


Correct answer:

The number of large and medium oil spills has remained roughly constant over the last three decades.

Explanation:

In this strengthen question, take careful note of the oil executive's conclusion, which is that the increase in reported oil spills (he concedes this is a fact) has occurred because it is easier to detectsmalloil spills, not because there are more oil spills. In other words, the total number of oil spills is the same, and the increased number of reports of them is due to the more-frequent reporting of small spills.

Note how correct answer "The number of large and medium oil spills has remained roughly constant over the last three decades." directly strengthens that: if you know (from the argument) that there are more reported spills overall, and you know (from choice "The number of large and medium oil spills has remained roughly constant over the last three decades.") that the number of large and medium spills is unchanged, then the increase has to have come from the reporting of those small spills. "The number of large and medium oil spills has remained roughly constant over the last three decades." limits the increase to the smaller spills, and therefore furthers the executive's argument.

Note that with choice "The size of the average oil spill has decreased over the last three decades.", the conclusion isn't that there are more small oil spills total but that there have been more reported. So the fact that the average spill is smaller doesn't directly relate to the executive's argument. Furthermore, even if the average reported spill were smaller, that doesn't necessarily mean that there are more small spills being reported - it could just be that each of the larger and medium spills reported have been smaller (maybe they were better-controlled than in the past, for example).

选择”因为物流的改善,平均水平distance a barrel of oil travels to its destination has decreased by 40% over the last three decades." might seem to suggest a reason that there are fewer spills (there is less time/space that each barrel spends in transit) but this misses the general purpose of the argument, which relates to the detection of small spills. The argument isn't that there are fewer transportation-related spills, but that the increase in reported spills comes primarily from the detection of smaller spills.

选择“需要清理的平均成本oil spill has decreased by over 20% over the last three decades." and "The average oil company spends nearly twice as much today on anti-spill equipment as it spent three decades ago." each attempt to use cost as proxy for safety - "The cost required to clean up the average oil spill has decreased by over 20% over the last three decades." wants you to think that because the cost of cleanup is down, the spills must be less frequent or smaller, but that's not necessarily the reason. Perhaps cleanup technology has just gotten less expensive. Similarly "The average oil company spends nearly twice as much today on anti-spill equipment as it spent three decades ago." wants you to think that because companies are spending more to prevent spills, spills have decreased or stayed the same. But that's not necessarily the case: what if inflation is higher and the companies are spending less in "real" terms and more nominally because of the currency, for example?

Only choice "The number of large and medium oil spills has remained roughly constant over the last three decades.", which is correct, directly relates to the detection of small spills.

Example Question #28 :Strengthen/Weaken Critical Reasoning

Senator:Between 1950 and present, the number of women diagnosed with postpartum depression each year in the country of Heranita has increased by a factor of ten. We must improve our systems for supporting women after childbirth to stem this increase in the number of new mothers experiencing postpartum depression.

Which of the following, if true, would most call the argument above into question?

Possible Answers:

The amount of spending on women’s health has increased since 1950.

It is likely that cases of postpartum depression are underreported in Heranita.

Until 1970, most doctors were not specific in their diagnoses but instead grouped all types of depression together.

The minimum threshold of symptoms women experience before they can be diagnosed has increased since 1950.

Rates of postpartum depression are not included in official government statistics.

Correct answer:

Until 1970, most doctors were not specific in their diagnoses but instead grouped all types of depression together.

Explanation:

Whenever you are asked for an answer choice that will weaken a given argument or conclusion, remember that you should first seek to understand the argument and then you should look to find the gap between the premises of the argument and its conclusion.

You are told here that since 1950 the number of women diagnosed with postpartum depression in Heranita has increased. Because of this, the advocate suggests that the country improve the women's health care system so that women do not have to experiencethe symptoms of postpartum depression.Already you should see that there are a few gaps here - what if women have symptoms but aren't diagnosed? What differentiates postpartum depression from regular depression?

Only "Until 1970, most doctors were not specific in their diagnoses but instead grouped all types of depression together." addresses one of those gaps. If cases of postpartum depression were once described under the general umbrella of "depression", then it is impossible to know if postpartum depression is in fact on the rise.

Among the other answers, "The amount of spending on women’s health has increased since 1950." can be eliminated since just because women's health has increased, there is no telling whether spending to prevent postpartum depression has increased. "Rates of postpartum depression are not included in official government statistics." can be eliminated since another agency outside the government might keep track of rates of postpartum depression so this doesn't affect the argument. "The minimum threshold of symptoms women experience before they can be diagnosed has increased since 1950." can be eliminated since just because the minimum severity of symptoms required for diagnosis has increased doesn't mean that the rate has not increased. "It is likely that cases of postpartum depression are underreported in Heranita." can be eliminated because it would in fact strengthen the argument posed.

Example Question #29 :Strengthen/Weaken Critical Reasoning

Ecological studies have shown that the current landfill that serves Sturgeon County is responsible for the vast majority of the county's groundwater pollution problem. Surprisingly, however, Sturgeon County's leading environmentalists support a ballot initiative that will invest in the expansion of the current landfill, as opposed to another initiative that will invest the same amount of money in creating a new landfill that would have zero impact on the county's groundwater.

Which of the following, if true, serves as the best justification for the environmentalists' position?

Possible Answers:

Polling data indicates that the new landfill proposal is unlikely to pass without support from prominent environmental activists.

Several recent ecological studies suggest that the rate of pollution from the current landfill is lower than had initially been reported.

The site of the proposed new landfill is privately-owned land that the county would have to purchase during a period of high real estate values.

Without continued operation and maintenance, the current landfill's groundwater pollution rate would more than double.

Groundwater pollution is less of a concern in Sturgeon County than is air pollution from the county's coal-fired power plants.


Correct answer:

Without continued operation and maintenance, the current landfill's groundwater pollution rate would more than double.

Explanation:

Your goal in this "Explain the Paradox" question is to find a reason why environmentalists would support the expansion of a landfill that comes with groundwater pollution problems over the construction of a new landfill that would come with no groundwater pollution problems. As you anticipate what you would want to see from a correct answer, you might think about:

-What if the new landfill doesn't havegroundwaterpollution problems, but instead creates other pollution problems?

-What is leaving the old landfill would create even bigger problems than staying there?

Choice "Without continued operation and maintenance, the current landfill's groundwater pollution rate would more than double. " works well with the second option: if leaving the current landfill would create a much bigger environmental problem than staying there would, that is a reason that those who care about the environment would vote to stay. Choice "Without continued operation and maintenance, the current landfill's groundwater pollution rate would more than double. " is correct.

选择“最近的一些生态研究表明that the rate of pollution from the current landfill is lower than had initially been reported." and "Groundwater pollution is less of a concern in Sturgeon County than is air pollution from the county's coal-fired power plants." may be tempting, but each comes with a significant flaw. Note that "Several recent ecological studies suggest that the rate of pollution from the current landfill is lower than had initially been reported.", while reducing the impact of the pollution problem with the current landfill, still leaves the ballot proposals as a comparison between "some pollution" and "no pollution," so you still don't have a reason that the environmentalists would pick "some" when "none" is an option. And while choice "Groundwater pollution is less of a concern in Sturgeon County than is air pollution from the county's coal-fired power plants." may seem to hit the standard of "what about other types of pollution other than just groundwater?" note that the argument doesn't provide any reason to suspect that the new landfill would create more air pollution. With all known information, it's still a comparison between "some pollution" and "no pollution."

Choice "Polling data indicates that the new landfill proposal is unlikely to pass without support from prominent environmental activists. " is irrelevant - what the polls suggest is no reason for the environmentalists to choose pollution over no pollution. And choice "The site of the proposed new landfill is privately-owned land that the county would have to purchase during a period of high real estate values." is carefully invalidated by the phrase "same amount" in the argument - if each plan costs the same amount, then the expense of the land for the new landfill isn't a reason to not choose it.

Example Question #62 :Critical Reasoning

Research studies on albatrosses and other soaring birds have found that the least intrusive geolocation tag placement, defined as the placement that minimizes interference with movement, is close to the center of the bird's back. While the placement increases drag when the birds dive into the water, it does not affect the birds’ ability to stay aloft for days at a time because the feathers of the back aren’t used for lift during soaring. However, the majority of studies on birds in general indicate that the least intrusive geolocation tag placement is under the tailfeathers, a placement that would cause great instability during flight but that doesn’t interfere with underwater movement

Which of the following, if true, most helps to explain the exception noted above?

Possible Answers:

Albatrosses are much larger than other soaring birds, so geolocation tags make up less of their total body weight.

Soaring doesn’t involve the tailfeathers, so geotag placement there will not affect movement.

Geolocation tagging practices have changed over time to include smaller devices.

Albatrosses tend to expend less energy than other birds while soaring because of their large wingspan.

The majority of studies were done on penguins, which don’t fly but do spend much of their time hunting underwater.

Correct answer:

The majority of studies were done on penguins, which don’t fly but do spend much of their time hunting underwater.

Explanation:

In this “explain the paradox” question, you are told that for albatrosses, placing geolocation tags in the middle of the back of the bird interferes less with bird movement than does placing geolocation tags under the tail feathers. However most studies on birds in general show the opposite to be true. In looking to resolve this paradox, you should ask yourself - what makes albatrosses and soaring birds special compared to other birds studied?

Choice "Albatrosses are much larger than other soaring birds, so geolocation tags make up less of their total body weight." makes a distinction between albatrosses and other soaring birds. Since both albatrosses and soaring birds are addressed together, this doesn’t given information as to why these birds are more affected by one geolocation tag placement and other birds are more affected by another. Eliminate "Albatrosses are much larger than other soaring birds, so geolocation tags make up less of their total body weight.".

Choice "Geolocation tagging practices have changed over time to include smaller devices." can be eliminated because it deals with change over time - something that isn’t addressed within the question. All the studies referenced could have been in the last year or they could have been over the course of 20 years. There’s no way of knowing, so there’s no way of knowing whether this would have an affect on placement.

If choice "Soaring doesn’t involve the tailfeathers, so geotag placement there will not affect movement." was true, then soaring birds would be less affected by placing the geolocation tags than would other flying birds, not more.

Choice "Albatrosses tend to expend less energy than other birds while soaring because of their large wingspan." can also be eliminated. The question deals with relative interference with movement, not the absolute amount of energy expended.

Choice "The majority of studies were done on penguins, which don’t fly but do spend much of their time hunting underwater." is correct. You are told that geolocation tags can affect drag (which occurs in the water) and lift (which occurs in the air). Since you are told that penguins can’t fly but that they do swim, you can conclude that only drag matters, so if the majority of studies were done on penguins, then the majority of studies would say that the ideal placement is under the tailfeathers.

Tired of practice problems?

Try live online GMAT prep today.

1-on-1 Tutoring
Live Online Class
1-on-1 + Class
Learning Tools by Varsity Tutors