SAT Preparation - Get Information, free practice and score high

Phase 1: Identify the contrast

The word "Despite" signals that successful historical reconstruction happened even with incomplete translations

Phase 2: Match inference to evidence

The passage shows historians achieved "detailed accounts" and understanding of a "sophisticated society" even though many texts remain undeciphered.

Eliminate A:

Contradicts the passage - historians gained substantial knowledge without complete translations.

Eliminate C:

The passage doesn't compare cuneiform's difficulty to other writing systems.

Eliminate D:

The passage mentions all document types equally; no preference for religious texts is stated.

Phase 1: Identify sentence structure

Both parts can stand alone: "His discovery showed..." (complete) and "the prevailing geocentric worldview faced..." (complete)

Phase 2: Apply punctuation rule

When "therefore" joins two independent clauses, use: [clause 1]; therefore, [clause 2] OR [clause 1], therefore [clause 2]. Since there's no semicolon before, we need a comma after.

Eliminate A:

Creates a run-on sentence - two independent clauses need punctuation.

Eliminate B:

A period would incorrectly create a sentence fragment starting with "the prevailing..."

Eliminate D:

A semicolon after "therefore" is incorrect punctuation.

Phase 1: Identify the antecedent

"The memorial" is the singular noun that possesses the walls.

Phase 2: Determine possession

We need to show that the walls belong to the memorial - this requires a possessive pronoun.

Eliminate B:

"It's" = "it is" (contraction), not possessive. Would create: "With it is two black granite walls..."

Eliminate C:

"Their" is plural possessive, but "memorial" is singular.

Eliminate D:

"They're" = "they are" (contraction), creates grammatical nonsense.

Phase 1: Identify the goal

Must emphasize "dual cultural identity" - this requires connecting the artwork to cultural meaning.

Phase 2: Evaluate synthesis

Choice A explicitly states "complex cultural identity" and links it to the two clothing styles representing different cultures.

Eliminate B:

Only provides dates; doesn't address cultural identity at all.

Eliminate C:

Mentions Mexican traditions but not the dual/bicultural aspect.

Eliminate D:

Too vague - doesn't specify the cultural significance of the different clothing.

Phase 1: Analyze relationship

Both examples illustrate the same phenomenon: simultaneous independent discoveries.

Phase 2: Select transition type

We need a transition that shows similarity or adds another supporting example.

Eliminate A:

"However" signals contrast, but both examples support the same point.

Eliminate B:

"Specifically" suggests the second example is a more detailed version of the first, which it isn't.

Eliminate D:

"Instead" implies replacement or alternative, inappropriate for parallel examples.

Phase 1: Context clues

"New species" + "never been observed before" = finding something for the first time.

Phase 2: Logical flow

The sequence is: find new species → document properties → suggest implications.

Eliminate A:

"Dismissed" means rejected/ignored - opposite of studying and documenting.

Eliminate C:

"Concealed" means hid - contradicts the documentation and findings mentioned.

Eliminate D:

"Distributed" means spread out - doesn't fit with finding a species in a specific location.

Phase 1: Express x in terms of y

Reason: The second equation can be easily solved for x, which allows substitution into the first equation.

From 4x = 5y, dividing both sides by 4 yields x = 5y/4

Phase 2: Substitute into first equation

Reason: Substituting eliminates one variable, creating an equation with only y.

Substituting x = 5y/4 into 2x + 3y = 22 yields:
2(5y/4) + 3y = 22
Simplifying: 10y/4 + 3y = 22
5y/2 + 3y = 22

Phase 3: Solve for y

Reason: Combining like terms allows us to isolate y.

Converting 3y to halves: 5y/2 + 6y/2 = 22
Combining: 11y/2 = 22
Multiplying both sides by 2: 11y = 44
Dividing by 11: y = 4

Phase 4: Solve for x

Reason: Now that we know y, we can find x using the second equation.

From 4x = 5y and y = 4:
4x = 5(4) = 20
x = 5

Therefore, the solution is (x, y) = (5, 4)

Verification:

Reason: Always verify the solution in both original equations.

First equation: 2(5) + 3(4) = 10 + 12 = 22 ✓
Second equation: 4(5) = 20 and 5(4) = 20 ✓

Eliminate B:

Choice B reverses the values. Checking (4, 5):
First equation: 2(4) + 3(5) = 8 + 15 = 23 ≠ 22 ✗

Eliminate C:

Checking (10, 8):
First equation: 2(10) + 3(8) = 20 + 24 = 44 ≠ 22 ✗
Second equation: 4(10) = 40 and 5(8) = 40, but the first equation fails.

Eliminate D:

Checking (8, 10):
First equation: 2(8) + 3(10) = 16 + 30 = 46 ≠ 22 ✗

Phase 1: Apply quotient rule to variable a

Reason: For positive values of a, a^m/aⁿ = a^m-n, where m and n are integers.

Since a > 0, this property can be applied: a⁸/a³ = a^8-3 = a⁵

Phase 2: Apply quotient rule to variable b

Reason: The same property applies to b since b > 0.

b⁵/b¹ = b^5-1 = b⁴

Phase 3: Combine results

Reason: The coefficient 3 remains in the denominator as it has no matching term in the numerator.

The complete simplified expression is: a⁵b⁴/3

Eliminate A:

Incorrect. This option has b in the denominator with a negative exponent. When we divide b⁵ by b¹, we get b⁴ in the numerator, not the denominator.

Eliminate C:

Incorrect. This option moves the 3 from the denominator to a coefficient in the numerator, which is mathematically incorrect. The 3 must remain in the denominator.

Eliminate D:

Incorrect. This option adds the exponents (8+3=11, 5+1=6) instead of subtracting them. Adding exponents is used for multiplication, not division. Also, the coefficient 3 is missing entirely.

Phase 1: Apply quotient rule to variable a

Reason: For positive values of a, a^m/aⁿ = a^m-n, where m and n are integers.

Since a > 0, this property can be applied: a⁸/a³ = a^8-3 = a⁵

Phase 2: Apply quotient rule to variable b

Reason: The same property applies to b since b > 0.

b⁵/b¹ = b^5-1 = b⁴

Phase 3: Combine results

Reason: The coefficient 3 remains in the denominator as it has no matching term in the numerator.

The complete simplified expression is: a⁵b⁴/3

Eliminate A:

Incorrect. This option has b in the denominator with a negative exponent. When we divide b⁵ by b¹, we get b⁴ in the numerator, not the denominator.

Eliminate C:

Incorrect. This option moves the 3 from the denominator to a coefficient in the numerator, which is mathematically incorrect. The 3 must remain in the denominator.

Eliminate D:

Incorrect. This option adds the exponents (8+3=11, 5+1=6) instead of subtracting them. Adding exponents is used for multiplication, not division. Also, the coefficient 3 is missing entirely.

Phase 1: Factor the quadratic

Reason: The left-hand side of the given equation can be factored to find the solutions more easily.

The equation 3x² + 11x - 20 = 0 can be factored as (3x - 4)(x + 5) = 0.
To factor: Find two numbers that multiply to (3)(-20) = -60 and add to 11. These are 15 and -4.
Rewrite: 3x² + 15x - 4x - 20 = 0
Factor by grouping: 3x(x + 5) - 4(x + 5) = 0
Factor out (x + 5): (3x - 4)(x + 5) = 0

Phase 2: Apply zero product property

Reason: When a product equals zero, at least one factor must equal zero.

Setting the first factor equal to zero: 3x - 4 = 0
Solving: 3x = 4, so x = 4/3

Phase 3: Find the second solution

Reason: A quadratic equation has two solutions; we need to identify which is positive.

Setting the second factor equal to zero: x + 5 = 0
Solving: x = -5

The two solutions are x = 4/3 and x = -5

Phase 4: Identify the positive solution

Reason: The question asks specifically for the positive solution.

Since 4/3 ≈ 1.33 is positive and -5 is negative, the positive solution is x = 4/3

Eliminate A:

Incorrect. This value doesn't satisfy the equation. Substituting x = 5/3:
3(⁵/₃)² + 11(⁵/₃) - 20 = 3(²⁵/₉) + 55/3 - 20 = 25/3 + 55/3 - 60/3 = 20/3 ≠ 0

Eliminate C:

Incorrect. This is a negative value. The question specifically asks for the positive solution, so any negative answer must be wrong.

Eliminate D:

Incorrect. This value doesn't satisfy the equation. Substituting x = 5:
3(5)² + 11(5) - 20 = 3(25) + 55 - 20 = 75 + 55 - 20 = 110 ≠ 0

Phase 1: Set up the equation

Reason: We need to translate the word problem into a mathematical equation.

Let x be the smaller integer. Then the larger integer is x + 7 (since it's 7 greater).
We know their product is 260: x(x + 7) = 260

Phase 2: Expand and rearrange

Reason: We need to convert this to standard quadratic form to solve it.

Expanding: x² + 7x = 260
Subtracting 260 from both sides: x² + 7x - 260 = 0

Phase 3: Factor the quadratic

Reason: Factoring allows us to find the solutions using the zero product property.

We need two numbers that multiply to -260 and add to 7.
Factor pairs of 260: (1, 260), (2, 130), (4, 65), (5, 52), (10, 26), (13, 20)
The pair 20 and -13 works: 20 × (-13) = -260 and 20 + (-13) = 7 ✓

Therefore: x² + 7x - 260 = (x + 20)(x - 13) = 0
Verification: (x + 20)(x - 13) = x² - 13x + 20x - 260 = x² + 7x - 260 ✓

Phase 4: Apply zero product property

Reason: When a product equals zero, at least one factor must equal zero.

From (x + 20)(x - 13) = 0:
Either x + 20 = 0, which gives x = -20
Or x - 13 = 0, which gives x = 13

Phase 5: Select the positive solution

Reason: The problem states we have two positive integers, so we reject negative solutions.

Since x must be positive (we're told both integers are positive), x = 13.
The two integers are 13 and 20 (since 13 + 7 = 20).
Verification: 13 × 20 = 260 ✓

Eliminate A:

If the smaller integer were 12, the larger would be 19.
Product: 12 × 19 = 228 ≠ 260 ✗

Eliminate C:

If the smaller integer were 19, the larger would be 26.
Product: 19 × 26 = 494 ≠ 260 ✗

Eliminate D:

If the smaller integer were 26, the larger would be 33.
Product: 26 × 33 = 858 ≠ 260 ✗