Tüm alıştırma soruları

Soru 1Soru →

For over a century, European paleoecology was dominated by the closed-canopy paradigm, which posited that post-glacial Europe prior to early agriculture was covered by an unbroken, dense primeval forest. Proponents of this view relied primarily on pollen diagrams from peat bogs, which showed high proportions of arboreal pollen relative to herbaceous species. However, ecologist Frans Vera recently challenged this orthodox reconstruction, arguing that heavy grazing and browsing by now-extinct or decimated megaherbivores—such as aurochs, wisents, and wild horses—maintained a dynamic, open mosaic of woodlands, scrub, and pastures. Vera suggested that high arboreal pollen percentages were an artifact of wind-pollinated trees over-representing forest cover compared to insect-pollinated or browsed open-habitat flora. While some palynologists have criticized Vera for underestimating the shade tolerance of climax forest species and over-extrapolating from modern wood-pasture analogues, his work has nonetheless forced a fundamental re-evaluation of primeval ecosystem dynamics, demonstrating that herbivore disturbance was an integral driver of landscape architecture rather than a minor, localized factor.

Which of the following best states the primary purpose of the passage?

To evaluate a challenge to a longstanding ecological model and assess its impact on primeval ecosystem studies.

To explain why wind-pollinated trees produce higher percentages of pollen in peat bogs than insect-pollinated flora.

To argue that megaherbivore reintroduction is the only viable method for restoring Europe's prehistoric biodiversity.

To demonstrate that traditional palynology successfully disproved Vera's wood-pasture hypothesis regarding shade-tolerant climax forests.

To denounce twentieth-century paleoecologists for deliberately falsifying pollen data to support closed-canopy models.

Cevabı ve açıklamayı göster

Cevap: To evaluate a challenge to a longstanding ecological model and assess its impact on primeval ecosystem studies.

Cevap

To evaluate a challenge to a longstanding ecological model and assess its impact on primeval ecosystem studies.

The passage outlines the traditional closed-canopy forest paradigm, explains Frans Vera's alternative megaherbivore grazing model, notes the points of debate raised by critics, and concludes by explaining how Vera's work compelled a major re-examination of prehistoric ecological dynamics. Thus, the main purpose is to evaluate this theoretical challenge and summarize its impact on the field.

Adım Adım Çözüm

1

Identify the structural trajectory of the passage.

The text begins by establishing an established consensus (closed-canopy paradigm), presents a major counter-theory (Vera's wood-pasture hypothesis), acknowledges counterarguments/criticisms, and summarizes the ultimate impact of the debate.

Determining how the passage is organized helps isolate the author's overarching objective.

2

Distinguish the main claim from supporting details and evidence.

Specific details like pollen collection mechanics or shade tolerance are subordinate points that support the broader intellectual shift described in the final sentence.

Primary purpose questions require selecting an answer choice that encompasses the scope of the entire text rather than isolated paragraphs or facts.

3

Evaluate the choices against the passage scope and author tone.

The statement summarizing the evaluation of a challenge to a established model accurately captures both the presentation of Vera's hypothesis and its significance in paleoecology.

The correct primary purpose option must capture the author's neutral-to-analytical stance and overall thematic objective.

Anahtar Kavram

Identifying Main Idea and Primary Purpose in Reading Comprehension

Soru 2Soru →

A study of high-growth technology startups established over the past decade revealed that every company that achieved a valuation exceeding one billion dollars was co-founded by an executive with prior experience in enterprise software. Based on this finding, a venture capital analyst argued that in order to ensure a newly launched biotechnology startup achieves a billion-dollar valuation, the founding team must simply hire a former enterprise software executive.

Which of the following best describes the flaw in the venture capital analyst's reasoning?

Treats a factor that was present in successful past cases as though it were a sufficient condition to guarantee future success.

Ignores potential differences in regulatory compliance costs between biotechnology firms and enterprise software companies.

Assumes without justification that no biotechnology startup lacking an enterprise software executive can ever become profitable.

Provides additional empirical evidence that reinforces the assertion that executive leadership directly determines market valuation.

Relies on the unstated premise that the financial valuation metrics collected across the ten-year period were completely free of reporting bias.

Cevabı ve açıklamayı göster

Cevap: Treats a factor that was present in successful past cases as though it were a sufficient condition to guarantee future success.

Cevap

The argument flaw is best described as treating a factor observed in past successful cases as a sufficient condition to guarantee future success.

The argument observes that a specific factor (having an enterprise software executive) was present in all past billion-dollar startups. However, assuming that introducing this single factor into a new company will guarantee a billion-dollar valuation mistakes a correlated or historical feature for a sufficient cause.

Adım Adım Çözüm

1

Identify the premise and conclusion of the argument.

Premise: All billion-dollar startups studied in the past decade had a co-founder with enterprise software experience. Conclusion: Hiring a former software executive will ensure a new biotech startup achieves a billion-dollar valuation.

Isolating the core structure reveals the logical gap between the factual evidence and the recommendation.

2

Analyze the logical gap in the inference.

Even if every successful past startup possessed this characteristic, possessing it does not guarantee success. The analyst mistakes a co-occurring trait for a sufficient condition that automatically produces the outcome.

Identifying the misuse of conditional logic (confusing necessary or correlated conditions with sufficient conditions) pins down the flaw.

3

Select the option that accurately describes this conditional logic error.

The option stating that the argument treats a factor present in past success as a sufficient condition for future success precisely captures this reasoning vulnerability.

This directly matches the identified logical flaw without bringing in irrelevant external scope.

Anahtar Kavram

Evaluating Reasoning Flaws: Confusing Necessary/Correlated Conditions with Sufficient Conditions

Soru 3Soru →

Consider the following excerpt regarding paleoclimate methodology:

Rather than providing a (i)________ rebuttal to the hypothesis of abrupt climate change during the Younger Dryas, the newly extracted ice core samples offered remarkably (ii)________ evidence; while the isotopic ratios initially appeared to confirm rapid cooling, subsequent trace-gas analyses revealed complex fluctuations that ultimately (iii)________ any definitive conclusion.

Which of the following combinations of terms correctly completes the blanks in the passage?

(i) decisive; (ii) equivocal; (iii) precluded

(i) decisive; (ii) incontrovertible; (iii) sanctioned

(i) tentative; (ii) equivocal; (iii) sanctioned

(i) convoluted; (ii) incontrovertible; (iii) precluded

(i) decisive; (ii) equivocal; (iii) adumbrated

Cevabı ve açıklamayı göster

Cevap: (i) decisive; (ii) equivocal; (iii) precluded

Cevap

The combination '(i) decisive; (ii) equivocal; (iii) precluded' logically completes the passage by properly resolving inter-blank dependencies and structural transitions.

The correct choice establishes total logical coherence across all three blanks. The introductory transition 'Rather than' requires Blank (i) and Blank (ii) to stand in contrast: a 'decisive' (conclusive) rebuttal is contrasted with 'equivocal' (uncertain or ambiguous) evidence. The second clause elaborates on this ambiguity by noting that while one metric suggested cooling, another revealed complex fluctuations; such contradictions naturally 'precluded' (ruled out) any definitive conclusion.

Adım Adım Çözüm

1

Analyze structural contrast clues governing Blank (i) and Blank (ii).

The opening structure 'Rather than providing a (i)________ rebuttal... samples offered remarkably (ii)________ evidence' signals an antonymous or opposing relationship between Blank (i) and Blank (ii).

Resolving either blank in isolation is impossible without ensuring that Blank (i) and Blank (ii) express contrasting levels of certainty.

2

Examine the context following the semicolon to determine the polarity of Blank (ii) and Blank (iii).

The phrase 'while isotopic ratios initially appeared to confirm... subsequent trace-gas analyses revealed complex fluctuations' indicates that the overall findings are ambiguous and conflicting.

Ambiguous evidence requires Blank (ii) to mean open to interpretation ('equivocal') and Blank (i) to mean conclusive ('decisive').

3

Determine the semantic fit for Blank (iii) based on the outcome of the complex fluctuations.

Data containing 'complex fluctuations' prevents or rules out a firm conclusion, requiring a verb meaning prevented ('precluded').

The word 'precluded' completes the causal chain showing how data complexity thwarted definitive closure.

Anahtar Kavram

Multi-Blank Dependency Tracking

Tahmini Süre:2m 0s

Soru 4Soru →

Dendrochronological analysis of oak panels used by seventeenth-century Dutch master painters demonstrates that all timber imported from the Baltic region between 1620 and 1650 was derived from slow-growing old-growth trees. Oak felled in the Baltic during these three decades consistently exhibits narrow growth rings containing high structural density. Panels crafted from this Baltic oak resist warping significantly better than panels made from domestic Dutch oak. Historical records confirm that Rembrandt van Rijn painted exclusively on wooden panels made from Baltic oak between 1630 and 1645. However, after 1645, trade blockades completely halted Baltic timber shipments to Amsterdam for over ten years.

If the statements above are true, which of the following must also be true on the basis of them?

Rembrandt was forced to switch to canvas for all of his paintings produced immediately following the 1645 timber trade blockades.

Any wooden panel on which Rembrandt painted between 1630 and 1645 was constructed from timber that possessed high structural density.

Domestic Dutch oak was never utilized by Dutch master painters prior to the implementation of the 1645 trade blockades.

The superior warp resistance of Baltic oak panels caused Dutch painters to prefer them over all other artistic media in the seventeenth century.

Baltic oak imported after 1650 lacked the narrow growth rings characteristic of Baltic timber imported between 1620 and 1650.

Cevabı ve açıklamayı göster

Cevap: Any wooden panel on which Rembrandt painted between 1630 and 1645 was constructed from timber that possessed high structural density.

Cevap

Any wooden panel on which Rembrandt painted between 1630 and 1645 was constructed from timber that possessed high structural density.

The correct answer combines two explicit facts: Rembrandt painted exclusively on Baltic oak between 1630 and 1645, and all Baltic oak imported between 1620 and 1650 possessed high structural density. Because the 1630–1645 timeframe is entirely contained within 1620–1650, any wooden panel Rembrandt painted on during that period must have high structural density.

Adım Adım Çözüm

1

Identify the given premises in the passage

Premise 1: All Baltic timber imported between 1620 and 1650 came from old-growth trees with narrow growth rings and high structural density. Premise 2: Rembrandt painted exclusively on wooden panels made from Baltic oak between 1630 and 1645.

Establishing the explicit facts provided in the text defines the strict boundaries of what can be logically inferred.

2

Connect the premises logically

Because 1630–1645 falls entirely within the 1620–1650 window, any Baltic oak used by Rembrandt during 1630–1645 must have been imported during the 1620–1650 period.

Valid inferences require combining premises without introducing outside assumptions.

3

Deduce the necessary conclusion

Every wooden panel Rembrandt used between 1630 and 1645 necessarily possessed high structural density.

Since all timber from that source and timeframe had high structural density, any panel sourced from it must share that property.

Anahtar Kavram

Drawing Valid Inferences via Categorical Syllogism

Soru 5Soru →

In her reevaluation of early industrial urban planning, Dr. Aris Thorne challenges the prevailing scholarly consensus that municipal leaders acted out of pure altruism. While acknowledging that newly constructed public parks provided crucial green space for working-class families, Thorne highlights internal memoranda revealing that city officials primarily viewed these spaces as calculated buffer zones to contain urban unrest. Rather than celebrating these civic additions as simple expressions of benevolence, Thorne characterizes the administration's intentions as decidedly pragmatic. Consequently, her analysis portrays the municipal strategy not as a noble crusade for public health, but as a sober exercise in social management.

In the context of the passage, the word 'calculated' as used by Thorne conveys a tone of which of the following?

Utilitarian self-interest aimed at strategic risk mitigation

Malicious hostility intended to actively suppress working-class movements

Mathematical precision derived from quantitative empirical measurements

Unqualified praise for the administration's visionary public policy

Spontaneous altruism triggered by sudden urban health crises

Cevabı ve açıklamayı göster

Cevap: Utilitarian self-interest aimed at strategic risk mitigation

Cevap

Utilitarian self-interest aimed at strategic risk mitigation

The correct answer accurately reflects the passage's structural framing. Thorne explicitly contrasts 'expressions of benevolence' with 'pragmatic' intentions, using 'calculated' to convey that city officials acted out of deliberate, utilitarian self-interest to mitigate political risk rather than out of pure altruism.

Adım Adım Çözüm

1

Analyze the structural pivots and surrounding vocabulary in the passage.

The text contrasts 'pure altruism' and 'expressions of benevolence' with terms like 'pragmatic', 'sober exercise', and 'contain urban unrest'.

Structural signals establish that 'calculated' describes a shift from idealist motives to practical self-preservation.

2

Evaluate the contextual connotation of 'calculated'.

The word modifies 'buffer zones' and aligns with the author's portrayal of officials conducting a 'sober exercise in social management'.

This indicates that 'calculated' signifies deliberate, self-interested planning designed to control risk rather than numerical computation or outright malice.

3

Match the derived tone to the options.

The phrase describing utilitarian self-interest for strategic risk mitigation precisely captures the measured, pragmatic tone of the passage.

It captures both the deliberate strategy ('calculated') and the non-altruistic motive ('pragmatic buffer zones').

Anahtar Kavram

Contextual Tone and Polarity Identification

Soru 6Soru →

Read the passage below and answer the question that follows.

While early historiographies of early modern science portrayed Isaac Newton’s esoteric laboratory notes as an embarrassing aberration that was deliberately (i)_______ by Enlightenment commentators, recent archival analyses suggest that eighteenth-century natural philosophers did not view these manuscripts with (ii)_______. Far from signaling a secret (iii)_______ of rationalist principles, Newton’s alchemical inquiries were deeply intertwined with his overarching search for a unified active principle in nature.

Which set of words, when inserted into the blanks in order, best completes the passage so that it maintains cross-sentence contextual coherence throughout?

(i) expunged, (ii) derision, (iii) repudiation

(i) lauded, (ii) reverence, (iii) confirmation

(i) expunged, (ii) reverence, (iii) repudiation

(i) publicized, (ii) derision, (iii) affirmation

(i) expunged, (ii) derision, (iii) vindication

Cevabı ve açıklamayı göster

Cevap: (i) expunged, (ii) derision, (iii) repudiation

Cevap

The correct completion is the set containing 'expunged', 'derision', and 'repudiation'.

The correct set of words maintains logical, thematic, and rhetorical coherence across both sentences. 'Expunged' aligns with the portrayal of the notes as an 'embarrassing aberration', 'derision' fits the contrast showing natural philosophers did not hold the notes in contempt, and 'repudiation' establishes the concession needed before explaining that Newton's alchemical work was integrated into his broader rationalist pursuits.

Adım Adım Çözüm

1

Analyze Blank (i) using the initial contrast clue 'While' and the phrase 'embarrassing aberration'.

The word in blank (i) must reflect negative treatment or removal. 'Expunged' (erased/removed) logically fits the idea that historians portrayed the notes as deliberately suppressed.

An 'embarrassing aberration' would historically be covered up or omitted rather than celebrated.

2

Analyze Blank (ii) using the shift introduced by 'recent archival analyses suggest that... did not view these manuscripts with...'.

The word in blank (ii) must represent negative judgment or contempt, which the recent analyses refute. 'Derision' (contemptuous ridicule) fits seamlessly.

Saying contemporary scholars 'did not view these manuscripts with derision' directly contrasts with the old historiographical view that they were seen as an embarrassing aberration.

3

Analyze Blank (iii) using the concessionary shift 'Far from signaling a secret... of rationalist principles, Newton’s alchemical inquiries were deeply intertwined with...'.

The word in blank (iii) must denote a rejection or abandonment of rationalism. 'Repudiation' (rejection/disavowal) completes the thought that his work was not a rejection of rationalism, but part of it.

The structure 'Far from X, [statement of Y]' requires X to represent the opposite of Y.

Anahtar Kavram

Cross-Sentence Contextual Coherence in Multi-Blank Text Completion

Soru 7Soru →

How many positive integers $n$ less than $30$ satisfy the condition that $n^2 - 1$ is divisible by $24$ ?

5

8

9

10

15

Cevabı ve açıklamayı göster

Cevap: 10

Cevap

10

For

n^2 - 1

to be divisible by

24 = 8 \times 3

,

n

must be an odd integer that is not divisible by 3, which means

\gcd(n, 6) = 1

. The positive integers less than 30 coprime to 6 are 1, 5, 7, 11, 13, 17, 19, 23, 25, and 29, totaling 10 integers.

Adım Adım Çözüm

1

Factor the expression and analyze divisibility requirements for 24.

n^2 - 1 = (n - 1)(n + 1)

. Since

24 = 8 \times 3

with

\gcd(8, 3) = 1

,

n^2 - 1

must be divisible by both

8

and

3

.

Decompose 24 into coprime prime-power factors to evaluate modular conditions independently.

2

Determine the condition for

n^2 - 1

to be divisible by 8.

If

n

is even,

n^2 - 1

is odd and cannot be divisible by 8. If

n

is odd, let

n = 2k + 1

; then

n^2 - 1 = 4k(k + 1)

. Since one of

k

or

k + 1

is always even,

4k(k + 1)

is divisible by 8. Thus,

n

must be odd.

Analyze parity requirements for the power of 2.

3

Determine the condition for

n^2 - 1

to be divisible by 3.

If

n

is a multiple of 3,

n^2 - 1 \equiv -1 \pmod 3

, which is not divisible by 3. If

n

is not a multiple of 3,

n \equiv 1

or

2 \pmod 3

, so

n^2 \equiv 1 \pmod 3

and

n^2 - 1

is divisible by 3. Thus,

n

cannot be a multiple of 3.

Analyze remainder properties modulo 3.

4

Combine the conditions and count valid positive integers

n < 30

.

The combined requirement is

\gcd(n, 6) = 1

(

n

is odd and not a multiple of 3). The positive integers less than 30 satisfying this are 1, 5, 7, 11, 13, 17, 19, 23, 25, and 29. Counting these yields 10 integers.

Enumerate all integers meeting the coprime condition within the specified domain.

Anahtar Kavram

Modular arithmetic properties of quadratic expressions and coprimality constraints

Soru 8Soru →

Let $K = 2^5 \times 3^4 \times 5^3 \times 11^2$ . How many positive integer factors of $K$ are divisible by $300$ but are not divisible by $900$ ?

16

24

36

48

96

Cevabı ve açıklamayı göster

Cevap: 24

Cevap

24

The correct answer 24 is obtained by analyzing the prime factorizations

300 = 2^2 \times 3^1 \times 5^2

and

900 = 2^2 \times 3^2 \times 5^2

. Any factor

f = 2^a \times 3^b \times 5^c \times 11^d

must satisfy

a \in \{2, 3, 4, 5\}

(4 choices),

b = 1

(1 choice, since

b \ge 1

for 300 but

b < 2

for 900),

c \in \{2, 3\}

(2 choices), and

d \in \{0, 1, 2\}

(3 choices). Multiplying these choices gives

4 \times 1 \times 2 \times 3 = 24

.

Adım Adım Çözüm

1

Express any factor of

K

in terms of prime factor exponent constraints.

Any factor

f

of

K

has the form

f = 2^a \times 3^b \times 5^c \times 11^d

, where

0 \le a \le 5

,

0 \le b \le 4

,

0 \le c \le 3

, and

0 \le d \le 2

.

The prime factors of

f

must be subsets of the prime factors of

K

with exponents not exceeding those in

K

.

2

Find the prime factorizations of

300

and

900

.

300 = 2^2 \times 3^1 \times 5^2

and

900 = 2^2 \times 3^2 \times 5^2

.

Divisibility criteria correspond to minimum exponent requirements for each prime factor.

3

Apply the divisibility conditions to determine constraints on each exponent.

For

f

to be divisible by

300

, we need

a \ge 2

,

b \ge 1

, and

c \ge 2

. For

f

to NOT be divisible by

900

, we must have

b < 2

. Thus,

b = 1

.

Combining

b \ge 1

and

b < 2

uniquely restricts

b

to

1

.

4

Count the number of valid choices for each exponent.

a \in \{2, 3, 4, 5\}

(

4

choices),

b \in \{1\}

(

1

choice),

c \in \{2, 3\}

(

2

choices), and

d \in \{0, 1, 2\}

(

3

choices).

The exponent

d

is unrestricted by

300

or

900

, so it can take any valid power present in

K

.

5

Multiply the number of independent choices using the fundamental counting principle.

4 \times 1 \times 2 \times 3 = 24

.

Each exponent choice can be paired independently to form a unique factor.

Anahtar Kavram

Counting Divisors Using Prime Exponent Constraints

Soru 9Soru →

In circle $O$ , sector $AOB$ has a central angle of $60^\circ$ and a radius of $12$ . A smaller circle $C$ is inscribed within sector $AOB$ such that it is tangent to radii $OA$ and $OB$ , as well as to arc $AB$ . What is the area of the region inside sector $AOB$ that lies outside circle $C$ ?

4\pi

8\pi

12\pi

16\pi

18\pi

Cevabı ve açıklamayı göster

Cevap: $8\pi$

Cevap

The area of the region inside sector

AOB

outside circle

C

is

8\pi

.

The correct answer is derived by first finding the area of sector

AOB

using

\frac{60}{360} \pi (12^2) = 24\pi

. Then, analyzing the geometry of the inscribed circle reveals that the line from

O

to the center of circle

C

bisects the

60^\circ

angle. In the resulting

30^\circ-60^\circ-90^\circ

right triangle, the hypotenuse length is

2r

, making the total radius of sector

AOB

equal to

2r + r = 3r = 12

, which yields

r = 4

. The area of circle

C

is

\pi (4^2) = 16\pi

. Subtracting the circle area from the sector area gives

24\pi - 16\pi = 8\pi

.

Adım Adım Çözüm

1

Calculate the area of sector

AOB

Sector area

= \frac{60^\circ}{360^\circ} \times \pi (12^2) = \frac{1}{6} \times 144\pi = 24\pi

The area of a sector with central angle

\theta

and radius

R

is

\frac{\theta}{360^\circ} \pi R^2

.

2

Find the radius

r

of the inscribed circle

C

Distance from

O

to center of circle

C

is

OP = 2r

, so total radius

R = OP + r = 3r = 12 \implies r = 4

The line segment connecting center

O

to center

P

of circle

C

bisects the

60^\circ

angle into two

30^\circ

angles. A perpendicular dropped from

P

to radius

OA

forms a

30^\circ-60^\circ-90^\circ

right triangle where

\sin(30^\circ) = \frac{r}{OP} = \frac{1}{2}

, giving

OP = 2r

.

3

Calculate the area of circle

C

Area of circle

C = \pi r^2 = \pi (4^2) = 16\pi

The area of a circle with radius

r

is

\pi r^2

.

4

Subtract the area of circle

C

from the area of sector

AOB

24\pi - 16\pi = 8\pi

The desired region is the difference between the full sector area and the enclosed circle's area.

Anahtar Kavram

Inscribed circles in sectors and central angle sector area calculations

Tahmini Süre:2m 30s

Soru 10Soru →

While early botanists viewed plant responses to pest attacks as mere passive physiological reactions, recent ecological studies indicate that flora actively emit volatile organic compounds to signal neighboring plants of impending threats. To test this phenomenon in controlled environments, researchers synthesized synthetic compounds mimicking plant distress signals and exposed healthy crops to them. Remarkably, the uninjured crops responded by preemptively synthesizing defensive enzymes. This finding strongly supports the hypothesis that plants communicate through chemical signaling, though further field trials are necessary to verify whether such interactions occur with equal efficacy in complex, unmonitored ecosystems.

Which of the following best describes the primary rhetorical function of the sentence beginning with 'Remarkably'?

It describes an empirical finding that serves as evidence supporting the hypothesis being tested.

It presents a counterargument intended to refute the early botanists' traditional perspective.

It summarizes the ultimate conclusion established by both laboratory tests and natural field observations.

It demonstrates conclusively that chemical communication functions with equal efficacy across all natural habitats.

It qualifies the author's primary hypothesis by pointing out a flaw in the researchers' initial setup.

Cevabı ve açıklamayı göster

Cevap: It describes an empirical finding that serves as evidence supporting the hypothesis being tested.

Cevap

The sentence describes an empirical finding that serves as evidence supporting the hypothesis being tested.

The sentence starting with 'Remarkably' reports the observed outcome of the researchers' experiment—namely, that uninjured crops responded to distress signals by producing defensive enzymes. In the broader rhetorical structure of the passage, this observed outcome serves as empirical evidence supporting the idea that plants communicate via chemical signals.

Adım Adım Çözüm

1

Analyze the context surrounding the target sentence.

The preceding sentence outlines an experimental setup (exposing healthy crops to synthetic signals). The target sentence reports what happened next (uninjured crops responded by producing enzymes).

Understanding the surrounding context clarifies how the target sentence relates to the passage's argument structure.

2

Determine the functional role of the target sentence.

The observation that uninjured crops responded demonstrates a concrete experimental result, providing empirical backing for the communication hypothesis mentioned in the subsequent sentence.

Identifying what role the sentence plays within the argument chain is key to choosing the correct description.

Anahtar Kavram

Identifying sentence function and evidence structure within an argument.

Soru 11Soru →

If $x$ is a real number that satisfies the inequality $|5 - 2x| \le 7$ , what is the minimum possible value of the expression $3 - 4x$ ?

-21

-1

7

27

-27

Cevabı ve açıklamayı göster

Cevap: $-21$

Cevap

-21

Solving

|5 - 2x| \le 7

yields

-7 \le 5 - 2x \le 7

. Subtracting

5

gives

-12 \le -2x \le 2

. Dividing by

-2

and flipping the inequality direction gives

-1 \le x \le 6

. To minimize

3 - 4x

, we choose the maximum value of

x

because the term

-4x

decreases as

x

increases. Substituting

x = 6

yields

3 - 4(6) = -21

.

Adım Adım Çözüm

1

Unpack the absolute value inequality into a compound inequality

-7 \le 5 - 2x \le 7

For any real constant

k \ge 0

,

|u| \le k

is equivalent to

-k \le u \le k

.

2

Isolate the variable term by subtracting

5

from all parts of the inequality

-12 \le -2x \le 2

Subtracting a constant from all parts preserves inequality direction.

3

Divide all parts by

-2

and reverse the inequality signs

6 \ge x \ge -1

, which is equivalent to

-1 \le x \le 6

Dividing an inequality by a negative number reverses the direction of the inequality signs.

4

Find the minimum value of

3 - 4x

over the interval

[-1, 6]

The minimum value occurs at

x = 6

:

3 - 4(6) = 3 - 24 = -21

Because the linear expression

3 - 4x

has a negative coefficient for

x

, it is a decreasing function; its minimum occurs at the largest allowed value of

x

.

Anahtar Kavram

Linear Inequalities and Absolute Value Bounds

Tahmini Süre:1m 30s

Soru 12Soru →

A vertical flagpole stands on flat, horizontal ground. An observer at point $S$ on the ground measures the angle of elevation to the top of the flagpole to be $60^\circ$ . A second observer at point $P$ on the ground, located $30$ feet further from the base of the flagpole along the same line extending from the base through $S$ , measures the angle of elevation to the top of the flagpole to be $30^\circ$ . What is the height of the flagpole, in feet?

15\sqrt{3}

30\sqrt{3}

45

30

15

Cevabı ve açıklamayı göster

Cevap: $15\sqrt{3}$

Cevap

The height of the flagpole is

15\sqrt{3}

feet.

Let

B

be the base and

T

be the top of the flagpole. The right triangle

TBS

has angles

30^\circ

,

60^\circ

, and

90^\circ

at

B

. If

BS = x

, then the height

TB = x\sqrt{3}

. In right triangle

TBP

, the angle at

P

is

30^\circ

, so the base

BP = TB\sqrt{3} = (x\sqrt{3})\sqrt{3} = 3x

. Since

BP = BS + 30

, we set up

3x = x + 30

, yielding

x = 15

. Therefore, the height

TB = 15\sqrt{3}

feet.

Adım Adım Çözüm

1

Model the scenario using right triangles.

Let

B

be the base of the flagpole and

T

be the top. Triangle

TBS

is a

30^\circ-60^\circ-90^\circ

right triangle at

B

, and triangle

TBP

is also a

30^\circ-60^\circ-90^\circ

right triangle at

B

.

The flagpole is perpendicular to the horizontal ground.

2

Express side lengths in terms of base distance

x = BS

.

In

30^\circ-60^\circ-90^\circ

triangle

TBS

,

TB = x\sqrt{3}

and

ST = 2x

.

The side opposite the

60^\circ

angle is

\sqrt{3}

times the side opposite the

30^\circ

angle.

3

Set up the equation for triangle

TBP

.

In

30^\circ-60^\circ-90^\circ

triangle

TBP

, the side opposite the

30^\circ

angle is

TB = x\sqrt{3}

, so the adjacent side

BP = (x\sqrt{3})\sqrt{3} = 3x

.

The side opposite the

60^\circ

angle (

BP

) is

\sqrt{3}

times the side opposite the

30^\circ

angle (

TB

).

4

Solve for

x

using the given distance

SP = 30

.

Since

BP = BS + SP

, we have

3x = x + 30

, which simplifies to

2x = 30

, so

x = 15

.

The total horizontal distance

BP

is the sum of segments

BS

and

SP

.

5

Calculate the height

TB

.

TB = 15\sqrt{3}

.

Substitute

x = 15

into

TB = x\sqrt{3}

.

Anahtar Kavram

Special Right Triangle Ratios (

30^\circ-60^\circ-90^\circ

)

Tahmini Süre:1m 30s

Soru 13Soru →

A beverage mixture is prepared by combining apple juice, orange juice, and grape juice in a ratio of $3 : 4 : 5$ by volume. If a pitcher contains a total of $48$ fluid ounces of this mixture, how many fluid ounces of orange juice are in the pitcher?

12

fluid ounces

16

fluid ounces

20

fluid ounces

24

fluid ounces

36

fluid ounces

Cevabı ve açıklamayı göster

Cevap: $16$ fluid ounces

Cevap

16

fluid ounces

The ratio

3 : 4 : 5

indicates that the total mixture is divided into

3 + 4 + 5 = 12

equal parts. Orange juice accounts for

4

of these

12

parts, representing

\frac{4}{12} = \frac{1}{3}

of the total volume. Taking

\frac{1}{3}

of

48

fluid ounces gives

16

fluid ounces.

Adım Adım Çözüm

1

Calculate the total number of ratio parts.

Total parts =

3 + 4 + 5 = 12

.

To find the fraction of each ingredient in the mixture, we must sum all parts of the ratio.

2

Determine the fraction of the total volume that represents orange juice.

Orange juice fraction =

\frac{4}{12} = \frac{1}{3}

.

Orange juice corresponds to

4

parts out of the

12

total parts.

3

Multiply the orange juice fraction by the total volume.

\frac{1}{3} \times 48 = 16

fluid ounces.

Multiplying the part-to-whole fraction by the total volume yields the exact volume of orange juice.

Anahtar Kavram

Part-to-Whole Ratio Relationships

Tahmini Süre:45s

Soru 14Soru →

If $x$ and $y$ are real numbers such that $|2x - 5| \le 9$ and $|y + 3| \le 4$ , what is the maximum possible value of $|x - 2y + 1|$ ?

22

20

14

13

6

Cevabı ve açıklamayı göster

Cevap: $22$

Cevap

The maximum possible value of

|x - 2y + 1|

is 22.

The correct answer is 22 because solving the absolute value inequalities gives

-2 \le x \le 7

and

-7 \le y \le 1

. To maximize

x - 2y + 1

, we take the largest possible value of

x

(

7

), the smallest possible value of

y

(

-7

, making

-2y = 14

), and add

1

, obtaining

7 + 14 + 1 = 22

. Since the lower bound of

x - 2y + 1

is

-3

, the maximum absolute value is

|22| = 22

.

Adım Adım Çözüm

1

Find the range of possible values for

x

from the inequality

|2x - 5| \le 9

.

-9 \le 2x - 5 \le 9 \implies -4 \le 2x \le 14 \implies -2 \le x \le 7

.

An absolute value inequality

|A| \le B

unwraps to

-B \le A \le B

.

2

Find the range of possible values for

y

from the inequality

|y + 3| \le 4

.

-4 \le y + 3 \le 4 \implies -7 \le y \le 1

.

Unwrapping the absolute value inequality gives the upper and lower bounds for

y

on the real number line.

3

Determine the range of possible values for

-2y

.

Multiplying

-7 \le y \le 1

by

-2

and reversing the inequality signs yields

-2(1) \le -2y \le -2(-7) \implies -2 \le -2y \le 14

.

Multiplying an inequality by a negative number reverses the direction of the inequality signs.

4

Combine the ranges to find the minimum and maximum bounds for

z = x - 2y + 1

.

Minimum

z = (-2) + (-2) + 1 = -3

; Maximum

z = 7 + 14 + 1 = 22

. Thus,

-3 \le x - 2y + 1 \le 22

.

Adding the individual minimums gives the absolute minimum, and adding the individual maximums gives the absolute maximum.

5

Calculate the maximum value of the absolute value

|x - 2y + 1|

.

\\max(|x - 2y + 1|) = \\max(|-3|, |22|) = 22

.

The absolute value of a quantity ranging from

-3

to

22

reaches its maximum distance from zero at

22

.

Anahtar Kavram

Properties of Real Numbers, Number Line Inequalities, and Absolute Value Operations

Tahmini Süre:2m 30s

Soru 15Soru →

In analyzing the ecological impact of rapid industrial development, environmental scientists note that expanding infrastructure continues to exact a heavy toll on local biodiversity, demanding sacrifices from surrounding ecosystems that cannot easily be recovered.

Which of the following words is closest in meaning to the word 'exact' as it is used in the passage above?

impose

precise

measure

lessen

isolate

Cevabı ve açıklamayı göster

Cevap: impose

Cevap

impose

In the context of the passage, 'exact' is used as a verb meaning to demand, inflict, or levy (e.g., 'to exact a toll'). Substituting 'impose' preserves the intended meaning that infrastructure expansion forces or inflicts a severe cost on biodiversity.

Adım Adım Çözüm

1

Identify the target word and its grammatical role in the sentence

The word 'exact' follows the infinitive marker 'to' ('to exact a heavy toll'), indicating it functions as a verb, not an adjective.

Determining the part of speech filters out primary adjective definitions that do not fit the syntactical structure.

2

Analyze surrounding contextual clues

The clause 'demanding sacrifices from surrounding ecosystems' directly clarifies what 'exact a heavy toll' means.

The surrounding text provides an explicit restatement of the secondary verb meaning.

3

Substitute options to find the semantic match

Replacing 'exact' with 'impose' yields 'continues to impose a heavy toll', maintaining the exact meaning of demanding or inflicting a cost.

'Impose' correctly captures the secondary verb definition of requiring or inflicting something burdensome.

Anahtar Kavram

Secondary verb meanings of polysemous words in academic contexts

Soru 16Soru →

Although early biographers depicted the diplomat’s private journal as a purely (i)________ account designed to settle old scores, subsequent historical analysis reveals that the entries were surprisingly (ii)________, offering an extraordinarily balanced and objective record of the negotiations.

Which of the following pairs of terms best completes the passage in a logically coherent manner?

(i) rancorous, (ii) dispassionate

(i) rancorous, (ii) tendentious

(i) meticulous, (ii) dispassionate

(i) scrupulous, (ii) tendentious

(i) rancorous, (ii) superficial

Cevabı ve açıklamayı göster

Cevap: (i) rancorous, (ii) dispassionate

Cevap

The pair '(i) rancorous, (ii) dispassionate' correctly completes the text by establishing the required contrast between a bitter early portrayal and a balanced historical reality.

The sentence relies on a concessive transition ('Although') paired with internal elaboration clues. The descriptive phrase 'designed to settle old scores' points to Blank (i) needing a word meaning resentful or bitter ('rancorous'). In contrast, the second clause describes the entries as an 'extraordinarily balanced and objective record', requiring Blank (ii) to mean impartial or unbiased ('dispassionate'). Only the pair featuring 'rancorous' for Blank (i) and 'dispassionate' for Blank (ii) satisfies both semantic requirements concurrently.

Adım Adım Çözüm

1

Analyze the clue for Blank (ii)

The phrase 'offering an extraordinarily balanced and objective record' directly describes the second blank.

Blank (ii) must be a synonym or positive attribute corresponding to 'balanced' and 'objective', pointing to 'dispassionate'.

2

Identify structural transition and clue for Blank (i)

The initial contrast word 'Although' indicates that early biographers held a view opposite to the 'balanced and objective' reality, while 'designed to settle old scores' provides a specific negative clue for Blank (i).

Blank (i) requires a term indicating bitterness or hostility, pointing to 'rancorous'.

3

Verify inter-blank dependency and overall sentence coherence

Combining 'rancorous' and 'dispassionate' completes the contrast smoothly: early biographers saw it as a bitter account, but later analysis revealed it to be surprisingly objective.

Both blanks must work simultaneously to satisfy both the internal clause clues and the overarching concession structure ('Although...').

Anahtar Kavram

Multi-Blank Dependency Tracking

Soru 17Soru →

A laboratory mixture is created by combining two solutions containing a specific tracer compound. Solution X has a volume of $2.5 \times 10^3$ milliliters and a tracer concentration of $4.8 \times 10^{-7}$ grams per milliliter. Solution Y has a volume of $7.5 \times 10^3$ milliliters and a tracer concentration of $1.6 \times 10^{-6}$ grams per milliliter. What is the total mass, in grams, of the tracer compound present in the combined mixture?

1.32 \times 10^{-2}

2.4 \times 10^{-3}

1.32 \times 10^{-5}

2.4 \times 10^{-2}

1.32 \times 10^{-1}

Cevabı ve açıklamayı göster

Cevap: $1.32 \times 10^{-2}$

Cevap

1.32 \times 10^{-2}

grams

The mass in Solution X is

(2.5 \times 10^3) \times (4.8 \times 10^{-7}) = 1.2 \times 10^{-3}

grams, and the mass in Solution Y is

(7.5 \times 10^3) \times (1.6 \times 10^{-6}) = 1.2 \times 10^{-2}

grams. Rewriting

1.2 \times 10^{-3}

as

0.12 \times 10^{-2}

allows direct addition:

(0.12 + 1.2) \times 10^{-2} = 1.32 \times 10^{-2}

grams.

Adım Adım Çözüm

1

Calculate the mass of the tracer in Solution X

M_X = (2.5 \times 10^3) \times (4.8 \times 10^{-7}) = 12.0 \times 10^{-4} = 1.2 \times 10^{-3}

grams

Mass equals volume multiplied by concentration.

2

Calculate the mass of the tracer in Solution Y

M_Y = (7.5 \times 10^3) \times (1.6 \times 10^{-6}) = 12.0 \times 10^{-3} = 1.2 \times 10^{-2}

grams

Mass equals volume multiplied by concentration.

3

Sum the tracer masses and adjust to scientific notation

M_{\text{total}} = 1.2 \times 10^{-3} + 1.2 \times 10^{-2} = 0.12 \times 10^{-2} + 1.2 \times 10^{-2} = 1.32 \times 10^{-2}

grams

To add terms in scientific notation, convert them to have matching exponents before adding coefficients.

Anahtar Kavram

Arithmetic operations with Scientific Notation and Decimals

Tahmini Süre:1m 30s

Soru 18Soru →

If $x + y = 8$ and $2x - y = 7$ , what is the value of $x$ ?

5

3

1

15

11

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

5

Adding the two equations yields

(x + y) + (2x - y) = 8 + 7

, which simplifies to

3x = 15

. Dividing both sides by 3 gives the correct value,

x = 5

.

Adım Adım Çözüm

1

Add the two equations together to eliminate the variable

y

.

(x + y) + (2x - y) = 8 + 7 \implies 3x = 15

Since the coefficients of

y

are

+1

and

-1

, adding the equations eliminates

y

directly.

2

Solve for

x

by dividing both sides of the equation by 3.

x = \frac{15}{3} = 5

Isolating

x

gives the required solution.

Anahtar Kavram

Elimination Method in Systems of Linear Equations

Soru 19Soru →

If $\frac{2x - 3}{4} - \frac{x - 5}{3} = \frac{x + 15}{12}$ , what is the value of $3x - 2$ ?

10

4

37

55

130

Cevabı ve açıklamayı göster

Cevap: 10

Cevap

The value of

3x - 2

is

10

.

Multiplying the given linear equation by the least common denominator 12 yields

3(2x - 3) - 4(x - 5) = x + 15

. Expanding both sides gives

6x - 9 - 4x + 20 = x + 15

, which simplifies to

2x + 11 = x + 15

, leading to

x = 4

. Substituting

x = 4

into

3x - 2

gives

3(4) - 2 = 10

.

Adım Adım Çözüm

1

Clear the denominators by multiplying both sides of the equation by the least common multiple of 4, 3, and 12, which is 12.

12 \cdot \left(\frac{2x - 3}{4}\right) - 12 \cdot \left(\frac{x - 5}{3}\right) = 12 \cdot \left(\frac{x + 15}{12}\right) \implies 3(2x - 3) - 4(x - 5) = x + 15

Eliminating fractions simplifies the algebraic manipulation.

2

Distribute the coefficients through the terms in parentheses, paying careful attention to the negative sign on the second term.

6x - 9 - 4x + 20 = x + 15

Distributing

-4

across

(x - 5)

yields

-4x + 20

.

3

Combine like terms on the left side of the equation.

2x + 11 = x + 15

Grouping variable terms

(6x - 4x = 2x)

and constant terms

(-9 + 20 = 11)

.

4

Isolate the variable

x

by subtracting

x

and

11

from both sides.

x = 4

Solves the linear equation for

x

.

5

Substitute

x = 4

into the target expression

3x - 2

.

3(4) - 2 = 12 - 2 = 10

Calculates the final answer requested in the stem.

Anahtar Kavram

Linear Equations with Fractional Coefficients

Soru 20Soru →

A sequence $a_1, a_2, a_3, \dots$ is defined by $a_n = \frac{1}{\sqrt{n} + \sqrt{n+2}}$ for all positive integers $n$ . If $S = \sum_{n=1}^{98} a_n$ , which of the following is closest to the value of $S$ when rounded to the nearest tenth?

8.8

4.5

9.0

9.9

17.5

Cevabı ve açıklamayı göster

Cevap: 8.8

Cevap

The value of

S

rounded to the nearest tenth is 8.8.

The term

a_n

simplifies to

\frac{\sqrt{n+2} - \sqrt{n}}{2}

upon rationalizing the denominator. Summing from

n=1

to

98

causes all middle terms to cancel out, leaving

\frac{\sqrt{99} + \sqrt{100} - \sqrt{1} - \sqrt{2}}{2}

. Substituting

\sqrt{100} = 10

,

\sqrt{1} = 1

,

\sqrt{99} \approx 9.95

, and

\sqrt{2} \approx 1.41

gives approximately

8.77

, which rounds to 8.8.

Adım Adım Çözüm

1

Rationalize the general term

a_n

a_n = \frac{1}{\sqrt{n} + \sqrt{n+2}} \cdot \frac{\sqrt{n+2} - \sqrt{n}}{\sqrt{n+2} - \sqrt{n}} = \frac{\sqrt{n+2} - \sqrt{n}}{(n+2) - n} = \frac{\sqrt{n+2} - \sqrt{n}}{2}

Eliminating radicals from the denominator reveals the underlying telescoping structure of the sequence.

2

Expand the summation

S = \sum_{n=1}^{98} a_n

S = \frac{1}{2} \left[ (\sqrt{3} - \sqrt{1}) + (\sqrt{4} - \sqrt{2}) + (\sqrt{5} - \sqrt{3}) + \dots + (\sqrt{99} - \sqrt{97}) + (\sqrt{100} - \sqrt{98}) \right]

Writing out initial and final terms demonstrates which terms cancel.

3

Simplify the telescoping sum

S = \frac{\sqrt{99} + \sqrt{100} - \sqrt{1} - \sqrt{2}}{2} = \frac{\sqrt{99} + 10 - 1 - \sqrt{2}}{2} = \frac{9 + \sqrt{99} - \sqrt{2}}{2}

All intermediate terms cancel out, leaving two positive boundary terms and two negative boundary terms.

4

Estimate square root values and perform rounding

Since

\sqrt{99} \approx 9.94987

and

\sqrt{2} \approx 1.41421

,

S \approx \frac{9 + 9.94987 - 1.41421}{2} = \frac{17.53566}{2} = 8.76783 \approx 8.8

Evaluating the radicals to two decimal places allows accurate rounding to the nearest tenth.

Anahtar Kavram

Telescoping Series Summation and Square Root Estimation

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram