Tüm alıştırma soruları

A renewable energy facility stores electricity in three separate battery modules: Module $X$, Module $Y$, and Module $Z$. The ratio of the initial energy stored in Module $X$ to Module $Y$ is $2 : 3$, and the ratio of the initial energy stored in Module $Y$ to Module $Z$ is $5 : 8$. Each module discharges its stored energy at a constant individual rate. Operating alone, Module $Y$ can completely discharge its initial stored energy in $5$ hours. Module $X$ discharges energy at a rate $33\frac{1}{3}\%$ greater than Module $Y$, and Module $Z$ discharges energy at a rate $25\%$ less than the combined discharge rate of Modules $X$ and $Y$. If all three modules begin discharging simultaneously, how many hours will it take to completely discharge the total initial energy stored across all three modules?

Fill in the blanks in the passage below to maintain logical coherence and inter-blank structural dependency. What words best complete {{blank_1}} and {{blank_2}}?

The greatest common divisor of a positive integer $n$ and $120$ is $24$, and their least common multiple is $2520$. How many positive divisors does $n$ have?

Although the minimalist sculptor claimed her stark geometric installations were entirely devoid of narrative intent, recent archival discoveries reveal that her choices were surprisingly __________, deeply rooted in the political turmoil of her era. Which of the following options, when inserted into the blank, produce completed sentences that are equivalent in meaning? Select two choices.

A logistics company operates a fleet of $14$ vans consisting solely of Model $X$ and Model $Y$ vans.

- The ratio of the cargo volume capacity of one Model $X$ van to one Model $Y$ van is $3 : 5$.
- The ratio of the energy consumption rate (in kWh per mile) of one Model $X$ van to one Model $Y$ van is $4 : 5$.
- When fully loaded, a Model $X$ van carries $30\text{ m}^3$ of cargo and a Model $Y$ van carries $50\text{ m}^3$ of cargo.
- The entire fleet of $14$ vans, when fully loaded, transports a total of $620\text{ m}^3$ of cargo in one trip.
- A Model $X$ van consumes $2\text{ kWh}$ of energy per mile.

Which of the following statements must be true? Select all such statements.

In the $xy$-plane, line $L$ passes through the origin $(0, 0)$ and the point $P(a, b)$, where $a > 0$ and $b > 0$. Line $M$ is perpendicular to line $L$ at point $P$. If line $M$ has a $y$-intercept at $(0, 10)$ and $b = 2$, what is the value of $a$?

Two events $E$ and $F$ in a sample space have probabilities $P(E) = 0.40$ and $P(F) = 0.50$. Which of the following statements must be true? Select all such statements.

A sequence $a_1, a_2, a_3, \dots$ is defined by $a_1 = 3$ and $a_{n+1} = \sqrt{a_n + 12}$ for all integers $n \geq 1$. If $S_{100} = \sum_{k=1}^{100} a_k$, what is the value of $S_{100}$ rounded to the nearest integer?

In a convex polygon, the sum of the measures of all interior angles except one is $1,200^\circ$. If the measure of the remaining interior angle is an integer degree, what is the number of sides of the polygon?

Read the passage below and determine the contextual meaning of the highlighted word.

A manufacturing facility produces precision metal components. Each component has a mass of $8.4 \times 10^{-4}$ kilograms. If a shipment container holds a batch of these components with a total mass of $1.05$ kilograms, how many components are in the container?

In GRE Sentence Equivalence items, test-takers must evaluate structural contrast clues to eliminate false synonym traps and topically related distractors. Consider the following sentence context:

"Far from presenting an entirely __________ ecosystem, the hydrothermal vent community exhibited an extraordinary degree of biodiversity that defied early marine biological models."

Match each candidate option pair below with its correct functional distractor classification.

A commercial property was purchased at an initial value of $V$ dollars. In its first year, the value of the property increased by $25\%$. In its second year, the property's value decreased by $20\%$ relative to its value at the end of the first year. In its third year, the value of the property increased by $15\%$ relative to its value at the end of the second year. If the value of the property at the end of the third year was $\$276,000$, what was the initial purchase value $V$, in dollars, of the property?

At an automated agricultural sorting facility, harvested apples are inspected for two independent quality conditions: surface bruising and internal core rot. The probability that a randomly chosen apple has surface bruising is $\frac{1}{6}$, and the probability that it has internal core rot is $\frac{1}{5}$. What is the probability that a randomly chosen apple has at least one of these two quality conditions?

A chemical synthesis plant uses two reaction vessels, Vessel 1 and Vessel 2, to produce a liquid solution composed entirely of Compound X, Compound Y, and water.

- Vessel 1 produces the solution at a constant rate of $60$ liters per hour, with Compound X, Compound Y, and water in the volume ratio $2 : 1 : 3$, respectively.
- Vessel 2 produces the solution at a constant rate of $90$ liters per hour, with Compound X, Compound Y, and water in the volume ratio $1 : 3 : 2$, respectively.

If both vessels operate simultaneously to fill an initially empty storage tank, which of the following statements must be true regarding the mixture in the storage tank after operating for any duration $H$ hours ($H > 0$)? Select all such statements.

Read the passage below:

Although early art conservators viewed the anomalous chemical compounds detected in the Renaissance painting as unequivocal evidence of modern (i)________, recent non-destructive spectroscopic analyses demonstrated that these compounds resulted from gradual ambient degradation over centuries, thereby (ii)________ long-standing allegations of deliberate forgery.

Which of the following word pairs best completes the blanks in the passage so that the text maintains logical coherence and proper inter-blank structural dependency?

In the $xy$-plane, line $k$ passes through the points $(-3, 5)$ and $(3, 1)$. Line $m$ is perpendicular to line $k$ and passes through the point $(1, -1)$. Which of the following statements must be true? Indicate all such statements.