Luyện GMAT Định lượng & Ngôn ngữ

To isolate x, subtract 9 from both sides of the equation. This gives x = 17 - 9 = 8, which matches option c and can be checked by substituting 8 back: 8 + 9 = 17.

Convert 20 percent to its decimal form 0.20, then multiply by 150: 150 x 0.20 = 30. Option a, 20, is the result of using 20 instead of 20 percent, while option c is the correct 30.

Apply the distributive property: multiply 3 by each term inside the parentheses. This produces 3x + 15, so option b is correct; the x term must also be multiplied by 3.

In y = mx + b, m is the slope, so the slope is 5.

Area of a rectangle equals length times width. Substitute the given values: 8 x 3 = 24, so the correct option is c. Option a results from adding instead of multiplying.

Since x is positive, take the positive square root of both sides: the square root of 144 is 12. Options 10, 11, and 14 fail when squared because they do not equal 144.

A pentagon has 5 sides, so the sum is (5 - 2) x 180 = 540 degrees.

3^4 = 3 x 3 x 3 x 3 = 81.

Divide the numerator by the denominator: 5 divided by 8 equals 0.625. The other choices represent 0.58, 0.65, and 0.75, none of which equals 5/8.

Substitute x = 6 into the expression: y = 3(6) - 4 = 18 - 4 = 14. Option b is correct; option a, 12, would result if the subtraction was done before multiplying.

Perimeter is the sum of all four sides, so use 2(length + width) = 2(7 + 4) = 22. Option b is correct; option a, 11, is only the sum of one length and one width.

To find the mean, add the three numbers and divide by their count: (6 + 10 + 14) / 3 = 30 / 3 = 10. The middle option, 10, is correct.

Divide both sides of 4x = 32 by 4 to isolate x: x = 32 / 4 = 8. Substituting 8 back into the equation gives 4(8) = 32, confirming the answer.

Absolute value measures distance from zero on the number line, so it is never negative. The distance from -15 to 0 is 15, making option c correct.

Use the circle area formula A = πr^2 with r = 4: A = π(4^2) = 16π. Option c is correct; 8π would come from 2πr, which is circumference, not area.

Volume of a rectangular prism equals length x width x height: 3 x 4 x 5 = 60. Option c is correct; option d, 120, comes from multiplying by an extra factor of 2.

Multiplying both parts of 3:4 by 3 gives 9:12.

Convert 25 percent to 0.25 and multiply by 240: 240 x 0.25 = 60. Option c is correct; option d, 80, would be about one-third rather than one-quarter of 240.

Substitute q = 5 into p + q = 12, then subtract 5 from both sides: p = 12 - 5 = 7. The value can be checked because 7 + 5 = 12.

Because 3 x 3 x 3 = 27, the cube root of 27 is 3. Option b is correct; 6 and 9 produce much larger cubes such as 216 and 729.

Rate equals total units divided by total hours: 30 / 5 = 6, so the machine produces 6 units per hour. Option b is correct, and 10 units per hour would require 50 units in five hours.

Convert the fraction to a decimal by dividing: 5/8 = 0.625. Since both forms represent the same value, the quantities are equal, so option c is correct.

30 is divisible by 2, 3, and 5; the others are not.

1/5 = 2/10, and 7/10 + 2/10 = 9/10.

There are 3 favorable outcomes out of 8 total marbles, so the probability is 3/8.

Divide the part by the whole, then convert to a percent: 18 / 72 = 0.25 = 25 percent. Option b is correct; 20 percent of 72 is 14.4, not 18.

Subtract 4 from both sides to get 3x = 15, then divide by 3: x = 5. Substitute 5 back: 3(5) + 4 = 19, which matches the original equation.

Circumference equals 2πr, so with r = 7: 2π(7) = 14π. Option b is correct; 49π is the value from the area formula πr^2, not the circumference.

Average speed equals total distance divided by total time: 120 / 2 = 60 mph. Option b is correct; 240 mph would come from multiplying distance by time instead of dividing.

An even integer can be written as 2k. Adding 2 gives 2k + 2 = 2(k + 1), which is still even, so n + 2 must be even. Adding 1 or squaring and adding 1 makes the result odd.

Statement 1 gives x = 7 because 10 - 3 = 7, and Statement 2 gives x = 7 because 14 / 2 = 7. Since each statement alone is sufficient, option d is correct.

x > 3 guarantees x is positive. x^2 > 9 allows negative values, so statement 2 alone is not sufficient.

Area needs both length and width, so both statements together are sufficient.

y is found only by combining y = 2z with z = 5.

Any multiple of 8 is also a multiple of 4. Being even does not guarantee divisibility by 4.

The average is (a + b) / 2, so the sum alone is sufficient.

x - y > 0 is equivalent to x > y. The sum does not determine the comparison.

Either the side or the diagonal determines the square, so each statement alone is sufficient.

The sum requires both values, so both statements together are sufficient.

Having exactly two positive divisors is the definition of a prime number.

A close temporal link between the policy and the cost decline supports a causal connection.

If poor sleep leads people to drink more coffee, the direction of causation may be reversed.

The plan only works if lower prices actually increase demand.

The first premise states a rule about all managers, and the second premise identifies Maria as a manager. Applying the rule to Maria yields the valid conclusion that she attends training, so option a follows.

Generalizing from a sample requires that the sample represent the full customer population.

A prompt increase after the fare change supports the causal link.

If heavy homework leads to less sleep and worse grades, the argument is weakened.

The plan assumes that the new market has enough demand to justify the office.

A common seasonal factor can explain the association without direct causation.

Improved memory after the exercise program began supports the causal claim.

A team acting as a single unit takes a singular verb: The team is preparing.

The relative clause refers to employees, so the plural verb work is correct.

After a preposition such as between, use the object pronoun me.

In academic and GMAT usage, data is plural, so the verb is suggest.

With neither...nor, the verb agrees with the closer subject assistants, which is plural.

The introductory modifier must describe the team, which performed the action.

The comparison must be parallel: profits increased more than those of its rivals did.

Fewer is used with countable plural nouns such as mistakes, while less is used with uncountable quantities such as time. Because the report compares countable mistakes, option b is correct.

The noun phrase the reason should be followed by that plus a clause, not because. Therefore the correct idiomatic completion is that the server failed, making option b correct.

Each is a singular indefinite pronoun, so it takes a singular verb. Among the choices, has agrees with each, making option b correct; have would require a plural subject.

12, 20, and 32 are divisible by 4; 18 and 25 are not.

2, 11, 19, 23, and 29 all have exactly two positive divisors; each is prime.

6 x 4, 48 / 2, and 3 x 8 all equal 24.

Diligent describes someone who works carefully and steadily, so hardworking and industrious are close synonyms. Lazy, careless, and slow carry opposite or unrelated meanings, so options a and c are correct.

Obscure can mean not easily seen, not clearly expressed, or difficult to understand. Hidden, vague, and unclear capture those senses, while clear and obvious are antonyms, so options b, d, and e are correct.

Supporting evidence and expert testimony strengthen an argument; the others do not.

The first two pairs average 10, and (7 + 11 + 12) / 3 = 10.

Data is treated as plural and each takes a singular verb, so both are correct.

Subtract 6 from both sides to isolate the x term: 2x = 20 - 6 = 14. Then divide by 2 to get x = 7, and verify by substituting: 2(7) + 6 = 20.

Add the three numbers to get 4 + 9 + 11 = 24, then divide by the count of 3: 24 / 3 = 8. The mean is therefore 8, which can be verified by checking that 8 x 3 = 24.

Divide the numerator by the denominator: 3 divided by 8 equals 0.375. The decimal is exact because 8 x 0.375 = 3, confirming that 0.375 is the correct value.

Area of a triangle equals one-half times base times height: (1/2) x 10 x 6 = 30. This follows from the formula A = (1/2)bh; using 10 x 6 alone would give 60, twice the correct area.

Each term is multiplied by 3, so the next term is 135.

The slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. In y = 7x + 2, m = 7, so the slope is 7.

An integer has no fractional part, a prime has exactly two divisors, a composite has more, and a rational number is a ratio of integers.

A part is the portion compared, percent is per hundred, the base is the whole amount, and a ratio compares two quantities.

A premise supports, a conclusion is argued, an assumption is unstated, and a counterexample disproves.

The subject performs, the verb expresses action or state, a modifier describes, and a clause contains a subject and verb.

An average divides a sum by its count, a rate compares an amount to a unit, a proportion sets two ratios equal, and a variable changes.

Elimination removes wrong choices, estimation approximates, back-solving tests options, and pacing manages time.