If x is an integer and 3x+2 is divisible by 5, which value could x be?

Write the equation clearly and identify the variable.

Look at the structure: If x is an integer and 3x+2 is divisible by 5, whi...

Keep both sides balanced while isolating the variable.

Identify the equation.
Move constants to one side.
Undo multiplication/division.
Solve for the variable.

Solve by isolating the variable step by step.

Forgetting to apply operations to both sides.


A price is increased by 20% and then decreased by 20%. The final price is what percent of the original?

Treat the original value as 100 unless a specific number is easier.

Focus on how the percentage is applied — is it increase, decrease, or part of a whole?

Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).

Apply each percentage step in order — don’t combine them directly.

Start with an easy base value (like 100).

Apply the second change to the new value.

Percent changes are multiplicative, not additive.

Adding/subtracting percentages directly instead of applying sequential changes.


If a and b are positive and a/b = 3/4, what is (a+b)/b?

Look at the structure: If a and b are positive and a/b = 3/4, what is (a+...


Look at the structure: If 5y - 3 = 22, what is y?...


A box contains 3 red and 5 blue balls. If one ball is chosen at random, what is the probability it is red?

Count total outcomes and favorable outcomes.

Count total outcomes.
Count favorable outcomes.
Divide favorable by total.

Probability is a ratio.
Clear counting is essential.


Look at the structure: If (x/3) = 5, what is 2x?...


The sum of two consecutive integers is 41. What is the larger integer?

Break the question into known and unknown parts.

Understand the problem.
Identify variables.
Set up relationships.
Solve step by step.

Translate words into math.
Solve systematically.


If a rectangle has perimeter 30 and length 9, what is its width?

Identify formula.
Substitute values.
Compute result.

Geometry relies on standard formulas.
Careful substitution avoids mistakes.


What is the smallest prime factor of 91?


The committee based its decision not only on cost but also ___ the long term impact.


Which sentence is grammatically correct?

Neither the managers nor the director were informed.

Neither the managers nor the director was informed.

Neither the manager nor the directors was informed.

Neither the managers or the director was informed.

Neither manager nor director were informed.


In the passage, the study is mentioned primarily to:

introduce a new topic unrelated to the argument

Write ratio as parts.
Sum the parts.
Divide total by parts.
Multiply by needed portion.

Ratios represent proportional relationships.

Breaking into equal units simplifies reasoning.

Using ratio numbers directly instead of total parts.


Choose the word closest in meaning to 'mitigate'.

Identify what measure is being asked (mean, median, etc.).

List values.
Apply formula (mean, median, etc.).
Compute carefully.

Different measures describe data differently.


Due to the fact that the roads were icy, the match was canceled.

Because the roads were icy, the match was canceled.

The match was canceled due to the icy roads that existed.

The match was canceled as a result of roads being icy.

Icy roads were the reason that the match was canceled.


Choose the correct verb form: Each of the reports ___ complete.


Choose the best transition: The hypothesis seemed plausible; ___, it lacked supporting data.


Which choice best fixes the modifier error? 'Walking to the station, the rain soaked Maria.'

Walking to the station, the rain soaked Maria.

Walking to the station, Maria was soaked by the rain.

Walking to the station, soaking Maria was the rain.

Walking to the station, the station soaked Maria with rain.

Walking to the station, Maria soaked the rain.


Revenue increased from 80000 to 92000. What was the percent increase?


Which dataset has the greatest variability?


If the median is greater than the mean, the distribution is most likely:


A table shows values 6, 9, 15, 20. What is the mean?


If 18 out of 60 customers choose Option A, what percent choose A?


Costs are 150 and revenue is 210. Profit is:


A pie chart shows 25% for Segment X. This equals:


Which measure represents the middle value of an ordered dataset?


If a value is far above most others, it is best described as a(n):


If sales are 30 on Monday and 45 on Tuesday, Tuesday sales are higher by:


If x and y are positive integers and x/y = 4/7 and x+y = 66, what is x?

Look at the structure: If x and y are positive integers and x/y = 4/7 and...


Pipe A fills a tank in 6 hours and Pipe B in 12 hours. After 2 hours together, what fraction remains unfilled?


Look at the structure: If 2a - 3b = 7 and a = 5, what is b?...


If n is an integer, which value of n makes (n^2 + 5n + 6) divisible by 6?

Look at the structure: If n is an integer, which value of n makes (n^2 + ...


A number is increased by 15% and then increased again by 20%. The final value is what percent of the original?


If the average of 5 numbers is 12 and four of the numbers are 9, 10, 11, and 14, what is the fifth number?


If a circle has circumference 18π, what is its area?


A store sells pens at 3 for 5. If you buy 12 pens, what is the total cost?


If x^2 - 9 = 0 and x is positive, what is x?


If the ratio of apples to oranges is 5:3 and there are 64 fruits total, how many apples are there?


The scientist’s theory, once dismissed as implausible, is now regarded as ___ recent evidence.


Which option best combines the sentences: 'The company expanded rapidly.' 'It underestimated logistical challenges.'

The company expanded rapidly but underestimated the logistical challenges.

The company expanded rapidly, it underestimated the logistical challenges.

Expanding rapidly, logistical challenges were underestimated.

The company expanded rapidly; underestimated logistical challenges.

Rapid expansion underestimated logistical challenges.


The author’s discussion of early failures primarily serves to:

illustrate the complexity of the process


Choose the best word: The report was praised for its ___ analysis.


Which sentence has correct subject verb agreement?


Choose the best revision: 'The policy is effective, it reduces costs.'

The policy is effective, and it reduces costs.

The policy is effective it reduces costs.

The policy is effective; reducing costs.

The policy is effective, reducing costs.

The policy is effective, which reducing costs.


Choose the word closest in meaning to 'equivocal'.


In the argument, the author assumes that:


Sales increase from 200 to 260. What is the percent increase?


What is the weighted average of 60 with weight 2 and 80 with weight 3?


If the mean of five numbers is 20, what is their sum?


Quarterly profits are 40, 60, 50, 70. Which statement is true?


If price rises 25% and demand falls 10%, revenue will most likely:


Which measure is least affected by outliers?


A dataset is skewed right if most values are:


If 3 out of 8 customers return a product, what percent is that?


If revenue is 500 and costs are 350, profit margin is:


Which display is best for checking correlation between two variables?


Look at the structure: If x + 1/x = 3, what is x^3 + 1/x^3?...


A positive integer n leaves remainder 1 when divided by 2 and remainder 2 when divided by 3. What could be the remainder when n is divided by 6?


In a geometric sequence, each term is (2/3) times the previous term. If the 4th term is 16, what is the 1st term?


If (x-2)(x-5)=0, and x is an integer greater than 3, what is x?

Look at the structure: If (x-2)(x-5)=0, and x is an integer greater than ...


Look at the structure: How many integers satisfy |x-5| ≤ 7?...


Look at the structure: If a^b = a^3 and a>0 and a≠1, what must be true?...


What is the remainder when 3^100 is divided by 4?


If a triangle has sides 7 and 10 and included angle 60 degrees, what is the length of the third side?


If f(x)=x^2-4x+k has exactly one real root, what is k?

Look at the structure: If f(x)=x^2-4x+k has exactly one real root, what i...


If the area of a circle is 49π, what is its circumference?


Although the proposal appears straightforward, it depends on assumptions that are far from ___.


Which sentence is grammatically correct and logically clear?

Having reviewed the data, the conclusions were revised by the analysts.

Having reviewed the data, the analysts revised the conclusions.

The analysts, having reviewed the data, the conclusions were revised.

The data having been reviewed, revising the conclusions was done by the analysts.

Reviewing the data, the conclusions revised the analysts.


The argument is most vulnerable because it:

uses a sample too small to justify any conclusion

assumes one factor cannot influence another

confuses a necessary condition with a sufficient one

draws a conclusion that contradicts its evidence


Choose the best word: The results were not definitive but merely ___.


Which option has correct parallel structure?

She values integrity, working hard, and to be punctual.

She values integrity, hard work, and punctuality.

She values to be honest, working hard, and punctual.

She values integrity, to work hard, and punctual.

She values being honest, to work hard, and being punctual.


present a single example without analysis


The author implies that a policy change would be effective only if it:


Choose the best completion: The theory was dismissed as ___ due to limited evidence.


Option A returns +10% then -10%. Option B returns -5% then +5%. Starting at 100, which ends higher?


Average weekly sales rise from 400 to 460 while stores rise from 8 to 10. Best supported conclusion?


A dataset has mean 50 and standard deviation 5 and is approximately normal. Which value is most likely?


Compound interest at 10% annually on 100 for 2 years yields:


A regression model has R^2 = 0.81. This means:


If revenue grows 20% and costs grow 30%, profit will most likely:


Which chart best displays the relationship between two quantitative variables?


If the median is greater than the mean, the distribution is:


Which metric best allows comparison across different scales?


A statistically significant result best supports which conclusion?

There is evidence against the null hypothesis