Problem Solving

Problem Solving is the backbone of the GMAT Quant section: a question stem, five answer choices, and a two-minute budget. The questions here span arithmetic, algebra, geometry, number properties, inequalities, and word problems — the same mix you will see on test day. Work them untimed while you rebuild fundamentals, then switch to the timer and practice committing to an answer under the clock. Every question includes a full written explanation, so review the ones you miss and log them in your error log: on Quant, most score improvement comes from eliminating repeat mistakes, not from seeing more new questions.

Official GMAT Problem Solving questions with difficulty ratings and topic tags.·Show:20 30 50

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505-555 (Easy)

If S = 1 + 1 2 + 1 3 2 + 1 4 2 + 1 5 2 + 1 6 2 + 1 7 2 + 1 8 2 + 1 9 2 + 1 10 2 , which of the following is true?

505-555 (Easy)

A certain method for calculating pediatric drug dosages states that if

d

is the adult dosage, in milligrams, and

y

is the child’s age, in years, then the child’s dosage, in milligrams, is

d (\frac{y + 1}{24})

. If the adult dosage for a particular drug is 800 milligrams, what is an 8-year-old child’s dosage, in milligrams, according to this method?

705-805 (Hard)

At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?

605-655 (Medium)

The sides of each of two plastic cubes are numbered 1 through 6, and each number is equally likely to appear face up after either cube is rolled. What is the probability that after the two cubes are rolled, the sum of the two numbers appearing face up will be greater than 9?

605-655 (Medium)

If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?

605-655 (Medium)

On Saturday morning, Malachi will begin a camping vacation, and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?

705-805 (Hard)

In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?

605-655 (Medium)

According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skating. If the number of people who enjoy neither skiing nor skating is 2 times the number of people who enjoy both skiing and skating, how many people surveyed enjoy neither skiing nor skating?

555-605 (Medium)

To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x > y. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved?

605-655 (Medium)

If the relations shown hold for the operation

\oplus

and the numbers

m

n

p

q

, and

r

, then

[(m \oplus p) \oplus q] \oplus p =

m \oplus p = n

n \oplus r = m

n \oplus q = q

p \oplus q = p

q \oplus p = r

Sub 505 (Easy)

What is the value of √ 17 + √ 47 17 − √ + 47 − √ , to the nearest whole number?

605-655 (Medium)

To rent a tractor, it costs a total of

x

dollars for the first 24 hours, plus

y

dollars per hour for each hour in excess of 24 hours. Which of the following represents the cost, in dollars, to rent a tractor for 36 hours?

505-555 (Easy)

If a(a + 2) = 24 and b(b + 2) = 24, where a ≠ b, then a + b =

605-655 (Medium)

If the mass of 1 cubic centimeter of a certain substance is 7.3 grams, what is the mass, in kilograms, of 1 cubic meter of this substance? (1 cubic meter = 1,000,000 cubic centimeters; 1 kilogram = 1,000 grams)

505-555 (Easy)

Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

605-655 (Medium)

z \neq = 0

and

z + \frac{1 - 2 z ^{2}}{z} = \frac{w}{z}

, then

w =

555-605 (Medium)

Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?

605-655 (Medium)

For all real numbers

a, b, c, d, e,

and

f

, the operation

Θ

is defined by

(a, b, c) Θ (d, e, f) = a d + b e + c f

. What is the value of

(1, - 2, 3) Θ (1, \frac{1}{2}, \frac{1}{3})

705-805 (Hard)

A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?

605-655 (Medium)

The table above shows the distribution of the number of absences from a certain Math class during the spring semester. For those students who had at least 1 absence, what was the median number of absences?

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