GRE Test Prep Teach Yourself the GRE CAT in 24 Hours
    GRE Home  >  Test Yourself—Quantitative Ability  >  Algebra

 

T E S T    Y O U R S E L F 
Quantitative Ability Mini Test — Algebra
(10 questions, 17 minutes) 

This Mini-Test consists of 10 GRE-style Algebra questions, in both formats (Problem Solving and Quantitative Comparison). Select your responses by clicking on the buttons. Limit your time to 17 minutes. NOTE: This page contains everything you need for this Mini-Test (including explanations). So you can save the file if you wish, then test yourself offline.

Before attempting this Quantitative Ability Mini-Test, be sure you've read the following:

Directions for Problem Solving Questions
    Questions 1, 4, 6, 7, 8, and 10 are problem solving questions. Solve each one and select the best among the five answer choices provided.
    .
     All numbers used are real numbers.
Directions for Quantitative Comparison Questions
    Questions 2, 3, 5, and 9 each consists of two quantities, one in Column A and one in Column B. Compare the two quantities and indicate:
    .
     (A) if the quantity in Column A is greater
    (B) if the quantity in Column B is greater
    (C) if the quantities are equal
    (D) if the relationship cannot be determined from the information given
    .
     In some questions, additional information pertaining to one or both of the quantities to be compared is centered above the two columns.
    .
     Any symbol appearing in both columns represents the same thing in one column as in the other.
    .
     All numbers used are real numbers.

.GRE Algebra.Question 1 of 10

Answer

Next

 If .2t = 2.2 – .6s and .5s = .2t + 1.1, then s =

(A) 1
(B) 3
(C) 10
(D) 11
(E) 30

.GRE Algebra .Question 2 of 10

Answer

Previous

Next

 Five years ago, Beth's age was three times that of Amy. Ten
years ago, Beth's age was one half that of Chelsea. If C repre-
sents Chelsea's current age, which of the following represents
Amy's current age?

(A) ...... (B) 2C ...... (C)

(D) 3C – 5 ...... (E)

.GRE Algebra .Question 3 of 10

Answer

Previous

Next

a – b =
Column A

a2 – 2ab + b2

Column B

    (A) The quantity in Column A is greater.
    (B) The quantity in Column B is greater.
    (C) The quantities are equal.
    (D) The relationship cannot be determined from the
    ...........information given.

.GRE Algebra .Question 4 of 10

Answer

Previous

Next

 Diana's final grade for her sociology course was based entirely
on her scores of 90, 65, and 75 on her midterm exam, term
paper, and final exam, respectively. The three scores
accounted for 20%, 30%, and 50%, respectively, of Diana's
final grade.
Column A

Diana's final grade for
the course

Column B

Diana's final exam score

    (A) The quantity in Column A is greater.
    (B) The quantity in Column B is greater.
    (C) The quantities are equal.
    (D) The relationship cannot be determined from the
    ...........information given.

.GRE Algebra .Question 5 of 10

Answer

Previous

Next

 A portion of $7200 is invested at a 4% annual return, while
the remainder is invested at a 5% annual return. If the annual
income from both portions is the same, what is the total income
from the two investments?

(A) $160
(B) $320
(C) $400
(D) $720
(E) $1,600

.GRE Algebra .Question 6 of 10

Answer

Previous

Next

x + y = 3

y + x = 2

Column A

x

Column B

y

    (A) The quantity in Column A is greater.
    (B) The quantity in Column B is greater.
    (C) The quantities are equal.
    (D) The relationship cannot be determined from the
    ...........information given.

.GRE Algebra .Question 7 of 10

Answer

Previous

Next

 An empty swimming pool can be filled to capacity through an
inlet pipe in 3 hours, and it can be completely drained by a
drainpipe in 6 hours. If both pipes are fully open at the same
time, in how many hours will the empty pool be filled to
capacity?

(A) 4
(B) 4.5
(C) 5
(D) 5.5
(E) 6

.GRE Algebra .Question 8 of 10

Answer

Previous

Next

 If r = and s = p – q, for which of the following values
of p would r2 = s2?

(A) ...... (B) 10 – ...... (C) q – 1

(D) 3q ........ (E) – 9

.GRE Algebra .Question 9 of 10

Answer

Previous

Next

 At a garage sale, Jeff sold 80% of his books, which include both
hardbacks and paperbacks. He sold an equal number of each of
the two types of books, selling all paperbacks for $1 each and
all hardbacks for $3 each. Jeff's total revenue from the sale of
his books was $32.
Column A

The number of books Jeff
owned before the sale

Column B

18

    (A) The quantity in Column A is greater.
    (B) The quantity in Column B is greater.
    (C) The quantities are equal.
    (D) The relationship cannot be determined from the
    ...........information given.

.GRE Algebra .Question 10 of 10

Answer

Previous

 At 10 a.m. two trains started traveling toward each other from
stations 287 miles apart. They passed each other at 1:30 p.m.
the same day. If the average speed of the faster train exceeded
the average speed of the slower train by 6 miles per hour,
which of the following represents the speed of the faster train,
in miles per hour?

(A) 38
(B) 40
(C) 44
(D) 48
(E) 50

Question 1—Analysis
(Return to Question 1)
The correct response to Question 1 is (B). The amount of the decrease is $4. Because the t-terms are the same (.2t), the quickest way to solve for s here is with the addition-subtraction method. Manipulate both equations so that corresponding terms "line up," then add the two equations:

Question 2—Analysis
(Return to Question 2)
The correct response to Question 2 is (A). Express the first statement algebraically, in terms of B (Beth's age):

Express the second statement algebraically, also in terms of B (Beth's age):

Equate the two expressions that both equal B, then solve for A (Amy's age):

Question 3—Analysis
(Return to Question 3)
The correct response to Question 3 is (C).a2 – 2ab + b2 = (a – b) 2 = . Thus, the two quantities are equal.

Question 4—Analysis
(Return to Question 4)
The correct response to Question 4 is (C). Quantity B is given as 75. Quantity A is the "weighted average" of the three scores. You can determine her final grade by adding together three weight-adjusted scores:

(20%)(90) + (30%)(65) + (50%)(75)

= (.2)(90) + (.3)(65) + (.5)(75)

= 18 + 19.5 + 37.5

= 75

Question 5—Analysis
(Return to Question 5)
The correct response to Question 5 is (B). Letting x equal the amount invested at 4%, express the amount invested at 5% as 7200 – x. The return on these amounts is equal:

Multiply by 100 to eliminate decimals:

The income is .04(4,000) + .05(3,200) = $160 + $160 = $320.

Question 6—Analysis
(Return to Question 6)
The correct response to Question 6 is (D). The two equations given are actually the same equation. (One way to confirm this is to multiply each term in the second equation by .) Given one linear equation in two variables, it is impossible to determine the relative values of x and y.

Question 7—Analysis
(Return to Question 7)
The correct response to Question 7 is (E). You can answer this question with common sense, without resort to formal algebra. The drainpipe empties the pool at half the rate that the inlet pipe fills the pool. So it makes sense that if both pipes are fully open, after 3 hours the pool will only be half full. (The inlet pipe fills the pool, but at the same time the drainpipe empties half the pool.) It follows that it takes 6 hours to fill the pool to capacity with both pipes fully open.

You can also solve this problem formally, by applying the algebraic "work" formula.

Letting x equal the number of hours, subtract the drainpipe's rate from the inlet pipe's rate (subtract because the drainpipe works against the inlet pipe), using the "work" formula:

Multiply both sides by 6, then solve for x:

Question 8—Analysis
(Return to Question 8)
The correct response to Question 8 is (A). Assuming that r2 = s2 , . Square both quantities in this equation, isolate zero (0) on one side of the equation, then factor the quadratic expression into two binomials. Find the two roots of p by setting each binomial equal to 0:

One of these two roots, , is the same as , which is answer choice (A).

Question 9—Analysis
(Return to Question 9)
The correct response to Question 9 is (A). Given a total revenue of $32, you can find the number of each type of book sold by setting up and solving a simple algebraic equation. Letting x equal the number of each type of book sold: 3x + x = 32. Thus, x = 8, and Jeff must have sold exactly eight $3 books and eight $1 books, 16 books altogether. Given that Jeff sold 80% of his books at the sale, Jeff must have owned exactly 20 books before the sale (16 is 80% of 20).

Question 10—Analysis
(Return to Question 10)
The correct response to Question 10 is (C). The trains each traveled from 10 a.m. to 1:30 p.m., which is 3.5 hours. Let x equal the speed of the slower train, and let x + 6 equal the speed of the faster train:

Multiply by 10 to eliminate decimals, then solve for x:

The speed of the faster train was x + 6, or 44, m.p.h.