GMAT Algebra is less about solving equations and more about choosing the fastest route: simplify first, substitute smart numbers, or backsolve from the answer choices. This set covers linear and quadratic equations, exponents and roots, functions, and algebraic translation from word problems. Watch for the classic GMAT moves — differences of squares in disguise, equations that share a common factor you should not cancel blindly, and expressions that beg to be factored rather than expanded.
Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w?
605-655 (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)
If 31 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in Bag Q?
605-655 (Medium)
If k and n are positive integers such that n>k, then k!+(n−k)⋅(k−1)! is equivalent to which of the following?
605-655 (Medium)
If xy+z=x(y+z), which of the following must be true?
605-655 (Medium)
The number of stamps that Kaye and Alberto had were in the ratio 5:3, respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of this event, Kaye had how many more stamps than Alberto?
605-655 (Medium)
The function f is defined by f(x)=−x1 for all nonzero numbers x. If f(a)=−21 and f(ab)=61, then b=
605-655 (Medium)
If 5x−5x−3=(124)(5y), what is y in terms of x?
605-655 (Medium)
If ∣y∣x=−1, which of the following must be true?
605-655 (Medium)
The table above is a 3 by 3 grid of 9 numbers, 5 of which are given. The 4 numbers that are not given are denoted by A, B, C, and D. The product of the numbers in each row and in each column is the same for all rows and columns. What is the value of the product ABCD?
655-705 (Hard)
The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of x, will it cost per person?
655-705 (Hard)
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?
655-705 (Hard)
If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake’s present weight, in pounds?
655-705 (Hard)
If x(2x+1)=0 and (x+21)(2x−3)=0, then x=
655-705 (Hard)
A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
655-705 (Hard)
The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?
655-705 (Hard)
Four extra-large sandwiches of exactly the same size were ordered for m students, where m>4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?
655-705 (Hard)
Which of the following equations has 1+2 as one of its roots?
655-705 (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?