Tüm alıştırma soruları

If $x$ and $y$ are real numbers, what is the value of $x^3 - y^3$?

(1) $x - y = 2$
(2) $x^2 + y^2 = 10$

Fill in the blank to logically complete the passage based on the premises provided.

Premises: A technology firm requires all software engineers who work on cybersecurity infrastructure to complete an advanced cryptography certification. Marcus is a software engineer at the firm who has not completed the advanced cryptography certification.

Based solely on the premises above, evaluate the following statement:
Marcus does not work on cybersecurity infrastructure at the technology firm.

If $a$ and $b$ are real numbers, what is the value of $a^2 - b^2$?

(1) $a + b = 7$
(2) $a - b = 3$

For all non-zero real numbers $m$ and $n$ with $m \neq n$, the Data Sufficiency target question "Is $\frac{m^2 + n^2}{2mn} > 1$?" is algebraically equivalent to the simplified target question "Are $m$ and $n$ of opposite signs?".

A regional electric utility company launched a program offering residential customers subsidized smart thermostats designed to lower household electricity usage during peak demand hours. Over the three years following the program's rollout, total peak-period electricity demand on the regional grid increased by 12 percent, even though more than 80 percent of households in the region installed the smart thermostats and each participating household successfully reduced its peak-period power consumption by an average of 15 percent.

Which of the following, if true, most helps to explain the apparent discrepancy described above?

A municipal energy commission released a report containing the following facts regarding regional energy infrastructure:

• In any municipality where smart meters were installed in more than 80 percent of residential units, peak-hour electricity demand decreased by at least 15 percent during summer months.
• In every municipality where peak-hour electricity demand decreased by at least 15 percent during summer months, municipal electricity tax revenues fell unless local utility rates were increased.
• Last summer, District X had smart meters installed in 90 percent of its residential units, while its local utility rates were held constant.

If the statements above are true, which of the following must also be true regarding District X last summer?

If $x$ and $y$ are positive integers, is the product $xy$ divisible by 4?

(1) $x$ is divisible by 4.
(2) $x + y$ is an odd integer.

What is the value of the real number $k$?

(1) $4k - 8 = 12$
(2) $k^2 = 25$

In Data Sufficiency analysis, for any non-zero real numbers $x$ and $y$ with $|x| \neq |y|$, the target question 'Is $\frac{x^2 - y^2}{xy} > 0$?' is algebraically equivalent to the rephrased target question 'Do $x$ and $y$ have opposite signs if and only if $|x| < |y|$?'

In an effort to lower fleet fuel costs and carbon emissions, a commercial beverage distributor replaced its traditional single-use glass bottles with ultra-lightweight aluminum cans. Although the aluminum cans weighed significantly less per unit than the glass bottles, the company's total annual fleet fuel consumption increased by 14 percent during the year following the transition. This increase occurred despite the company delivering the exact same total volume of beverage product across identical distribution routes, with no changes to vehicle fuel efficiency, delivery schedules, or driver performance. Which of the following, if true, most helps to resolve the apparent discrepancy described above?

If $m$ is a real number, is $m$ an even integer?

(1) $2m$ is an even integer.
(2) $m + 1$ is an odd integer.

In a GMAT Data Sufficiency 'Yes/No' question asking whether a real variable $x > 0$, a statement that establishes definitively that $x < 0$ is considered INSUFFICIENT because it yields a negative answer to the question stem.

If $p$ and $q$ are real numbers such that $p \neq 0$, is $p^2 q < 0$?

(1) $|q - 5| = q - 5$ and $q \neq 5$
(2) $p + q = 2$

To reduce agricultural nitrate pollution in local river systems, a regional water district plans to install floating artificial wetlands across its primary collection reservoirs. Critics argue that because the wetland plants enter dormancy during the winter—the season when agricultural runoff peaks—the system will fail to reduce nitrate levels when treatment is most needed. Nevertheless, environmental engineers maintain that installing these floating wetlands will substantially reduce the total annual amount of nitrates reaching the rivers. Which of the following, if true, provides the strongest support for the environmental engineers' prediction?

A local coffee shop owner plans to increase total monthly profits by raising the price of all specialty espresso drinks by 10 percent. The owner reasons that because demand for specialty drinks has remained steady over the past year, customers will continue to buy the exact same quantity of drinks despite the price increase.

Which of the following would be most useful to evaluate the validity of the coffee shop owner's argument?

In GMAT Data Sufficiency logic, if a statement determines a single unique numerical value for a variable $x$, that statement is sufficient to answer a 'Value' question asking for the exact value of $x$, but is insufficient to answer a 'Yes/No' question asking whether $x > 5$.

Hospitals in competitive metropolitan areas frequently suffer substantial revenue loss when surgical procedures are delayed due to sterilizer equipment failure. To eliminate these losses, a regional hospital network plans to replace all of its steam-autoclave sterilizers with modern hydrogen peroxide gas plasma units. Because gas plasma units complete a sterilization cycle in one-third the time required by steam autoclaves, hospital administrators conclude that adopting gas plasma units will virtually eliminate surgical delays caused by equipment unavailability.

Which of the following, if true, most seriously undermines the hospital administrators' conclusion?

A major commercial airline plans to retrofit its long-haul passenger fleet with lightweight carbon-fiber seating frames to reduce overall aircraft weight and lower fuel expenditures over the next five years. Management reasons that because jet fuel represents over thirty percent of total operating expenses, achieving a ten percent reduction in cabin weight will generate substantial net financial savings, even after accounting for the initial capital costs of purchasing and installing the new seats.

Which of the following, if true, most seriously undermines the reasoning behind the airline management's plan?

In 2024, a major city launched a public transit initiative that made bus travel entirely free for all residents. Transportation officials expected this program to significantly reduce traffic congestion on city roads by encouraging drivers to leave their personal vehicles at home. However, six months after the policy took effect, traffic congestion on major roadways remained virtually unchanged, despite municipal transit data showing a fifty percent increase in total bus ridership.

Which of the following, if true, most helps to explain the apparent discrepancy described above?