1951 AMC 12/AHSME

Part of AMC 12/AHSME

Subcontests

(50)

1

Tom, Dick, and Harry

Tom, Dick and Harry started out on a

100

-mile journey. Tom and Harry went by automobile at the rate of

25

mph, while Dick walked at the rate of

5

mph. After a certain distance, Harry got off and walked on at

5

mph, while Tom went back for Dick and got him to the destination at the same time that Harry arrived. The number of hours required for the trip was:

<span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 6 \qquad<span class='latex-bold'>(C)</span>\ 7 \qquad<span class='latex-bold'>(D)</span>\ 8 \qquad<span class='latex-bold'>(E)</span>\ \text{none of these answers}

1

Medians of Right Triangle

The medians of a right triangle which are drawn from the vertices of the acute angles are

5

\sqrt {40}

. The value of the hypotenuse is:

<span class='latex-bold'>(A)</span>\ 10 \qquad<span class='latex-bold'>(B)</span>\ 2\sqrt {40} \qquad<span class='latex-bold'>(C)</span>\ \sqrt {13} \qquad<span class='latex-bold'>(D)</span>\ 2\sqrt {13} \qquad<span class='latex-bold'>(E)</span>\ \text{none of these}

1

Squares Inscribed in Semicircle and Circle

The area of a square inscribed in a semicircle is to the area of the square inscribed in the entire circle as:

<span class='latex-bold'>(A)</span>\ 1: 2 \qquad<span class='latex-bold'>(B)</span>\ 2: 3 \qquad<span class='latex-bold'>(C)</span>\ 2: 5 \qquad<span class='latex-bold'>(D)</span>\ 3: 4 \qquad<span class='latex-bold'>(E)</span>\ 3: 5

1

Roots r,s of Quadratic

r

s

are the roots of the equation ax^2 \plus{} bx \plus{} c \equal{} 0, the value of \frac {1}{r^2} \plus{} \frac {1}{s^2} is: (A)\ b^2 \minus{} 4ac \qquad(B)\ \frac {b^2 \minus{} 4ac}{2a} \qquad(C)\ \frac {b^2 \minus{} 4ac}{c^2} \qquad(D)\ \frac {b^2 \minus{} 2ac}{c^2}

<span class='latex-bold'>(E)</span>\ \text{none of these}

1

Locus of Angle Bisector on a Semicircle

AB

is a fixed diameter of a circle whose center is

O

C

, any point on the circle, a chord

CD

is drawn perpendicular to

AB

C

moves over a semicircle, the bisector of angle

OCD

cuts the circle in a point that always:

<span class='latex-bold'>(A)</span>\ \text{bisects the arc } AB \qquad<span class='latex-bold'>(B)</span>\ \text{trisects the arc } AB \qquad<span class='latex-bold'>(C)</span>\ \text{varies}

<span class='latex-bold'>(D)</span>\ \text{is as far from }AB \text{ as from } D \qquad<span class='latex-bold'>(E)</span>\ \text{is equidistant from }B \text{ and } C

1

Calculating Logarithms

If you are given

\log 8 \approx .9031

\log 9 \approx .9542

, then the only logarithm that cannot be found without the use of tables is:

<span class='latex-bold'>(A)</span>\ \log 17 \qquad<span class='latex-bold'>(B)</span>\ \log \frac {5}{4} \qquad<span class='latex-bold'>(C)</span>\ \log 15 \qquad<span class='latex-bold'>(D)</span>\ \log 600 \qquad<span class='latex-bold'>(E)</span>\ \log .4

1

x In Terms of a,b,c

If \frac {xy}{x \plus{} y} \equal{} a, \frac {xz}{x \plus{} z} \equal{} b, \frac {yz}{y \plus{} z} \equal{} c, where

a,b,c

are other than zero, then

x

equals: (A)\ \frac {abc}{ab \plus{} ac \plus{} bc} \qquad(B)\ \frac {2abc}{ab \plus{} bc \plus{} ac} \qquad(C)\ \frac {2abc}{ab \plus{} ac \minus{} bc} (D)\ \frac {2abc}{ab \plus{} bc \minus{} ac} \qquad(E)\ \frac {2abc}{ac \plus{} bc \minus{} ab}

1

Five Statements

Of the following statements, the only one that is incorrect is:

<span class='latex-bold'>(A)</span>

An inequality will remain true after each side is increased, decreased, multiplied or divided (zero excluded) by the same positive quantity.

<span class='latex-bold'>(B)</span>

The arithmetic mean of two unequal positive quantities is greater than their geometric mean.

<span class='latex-bold'>(C)</span>

If the sum of two positive quantities is given, ther product is largest when they are equal.

<span class='latex-bold'>(D)</span>

a

b

are positive and unequal, \frac {1}{2}(a^2 \plus{} b^2) is greater than [\frac {1}{2}(a \plus{} b)]^2.

<span class='latex-bold'>(E)</span>

If the product of two positive quantities is given, their sum is greatest when they are equal.

1

Infinite Nested Radical

If x \equal{} \sqrt {1 \plus{} \sqrt {1 \plus{} \sqrt {1 \plus{} \sqrt {1 \plus{} \cdots}}}}, then: (A)\ x \equal{} 1 \qquad(B)\ 0 < x < 1 \qquad(C)\ 1 < x < 2 \qquad(D)\ x\text{ is infinite}

<span class='latex-bold'>(E)</span>\ x > 2 \text{ but finite}

1

Relationship Between x and y

The formula expressing the relationship between

x

y

in the table is: \begin{tabular}{|c|c|c|c|c|c|} \hline x & 2 & 3 & 4 & 5 & 6 \\ \hline y & 0 & 2 & 6 & 12 & 20 \\ \hline \end{tabular} (A)\ y \equal{} 2x \minus{} 4 \qquad(B)\ y \equal{} x^2 \minus{} 3x \plus{} 2 \qquad(C)\ y \equal{} x^3 \minus{} 3x^2 \plus{} 2x (D)\ y \equal{} x^2 \minus{} 4x \qquad(E)\ y \equal{} x^2 \minus{} 4

1

Large Expression

\left(\frac {(x \plus{} 1)^2(x^2 \minus{} x \plus{} 1)^2}{(x^3 \plus{} 1)^2}\right)^2 \cdot \left(\frac {(x \minus{} 1)^2(x^2 \plus{} x \plus{} 1)^2}{(x^3 \minus{} 1)^2}\right)^2 equals: (A)\ (x \plus{} 1)^4 \qquad(B)\ (x^3 \plus{} 1)^4 \qquad(C)\ 1 \qquad(D)\ [(x^3 \plus{} 1)(x^3 \minus{} 1)]^2 (E)\ [(x^3 \minus{} 1)^2]^2

1

Stone Dropped Into Well

A stone is dropped into a well and the report of the stone striking the bottom is heard

7.7

seconds after it is dropped. Assume that the stone falls

16t^2

t

seconds and that the velocity of sound is

1120

feet per second. The depth of the well is:

<span class='latex-bold'>(A)</span>\ 784 \text{ ft.} \qquad<span class='latex-bold'>(B)</span>\ 342 \text{ ft.} \qquad<span class='latex-bold'>(C)</span>\ 1568 \text{ ft.} \qquad<span class='latex-bold'>(D)</span>\ 156.8 \text{ ft.} \qquad<span class='latex-bold'>(E)</span>\ \text{none of these}

1

Railroad Line on a Mountain

600

feet is required to get a railroad line over a mountain. The grade can be kept down by lengthening the track and curving it around the mountain peak. The additional length of track required to reduce the grade from

3\%

2\%

is approximately:

<span class='latex-bold'>(A)</span>\ 10000 \text{ ft.} \qquad<span class='latex-bold'>(B)</span>\ 20000 \text{ ft.} \qquad<span class='latex-bold'>(C)</span>\ 30000 \text{ ft.} \qquad<span class='latex-bold'>(D)</span>\ 12000 \text{ ft.} \qquad<span class='latex-bold'>(E)</span>\ \text{none of these}

1

Number and Remainders

A number which when divided by

10

leaves a remainder of

9

, when divided by

9

leaves a remainder of

8

8

leaves a remainder of

7

, etc., down to where, when divided by

2

, it leaves a remainder of

1

<span class='latex-bold'>(A)</span>\ 59 \qquad<span class='latex-bold'>(B)</span>\ 419 \qquad<span class='latex-bold'>(C)</span>\ 1259 \qquad<span class='latex-bold'>(D)</span>\ 2519 \qquad<span class='latex-bold'>(E)</span>\ \text{none of these answers}

1

Proving a Locus

Which of the following methods of proving a geometric figure a locus is not correct?

<span class='latex-bold'>(A)</span>\ \text{Every point of the locus satisfies the conditions and every point not on the locus does not satisfy the conditions.}

<span class='latex-bold'>(B)</span>\ \text{Every point not satisfying the conditions is not on the locus and every point on the locus does satisfy the conditions.}

<span class='latex-bold'>(C)</span>\ \text{Every point satisfying the conditions is on the locus and every point on the locus satisfies the conditions.}

<span class='latex-bold'>(D)</span>\ \text{Every point not on the locus does not satisfy the conditions and every point not satisfying} \\ \text{the conditions is not on the locus.}

<span class='latex-bold'>(E)</span>\ \text{Every point satisfying the conditions is on the locus and every point not satisfying the conditions is not on the locus.}

1

Equations of Exponents

If a^x \equal{} c^q \equal{} b and c^y \equal{} a^z \equal{} d, then (A)\ xy \equal{} qz \qquad(B)\ \frac {x}{y} \equal{} \frac {q}{z} \qquad(C)\ x \plus{} y \equal{} q \plus{} z \qquad(D)\ x \minus{} y \equal{} q \minus{} z (E)\ x^y \equal{} q^z

1

Exponent of a Log

10^{\log_{10}7}

<span class='latex-bold'>(A)</span>\ 7 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 10 \qquad<span class='latex-bold'>(D)</span>\ \log_{10} 7 \qquad<span class='latex-bold'>(E)</span>\ \log_7 10

1

Graphically Obtaining Roots

The roots of the equation x^2 \minus{} 2x \equal{} 0 can be obtained graphically by finding the abscissas of the points of intersection of each of the following pairs of equations except the pair: (A)\ y \equal{} x^2, y \equal{} 2x \qquad(B)\ y \equal{} x^2 \minus{} 2x, y \equal{} 0 \qquad(C)\ y \equal{} x, y \equal{} x \minus{} 2 (D)\ y \equal{} x^2 \minus{} 2x \plus{} 1, y \equal{} 1 \qquad(E)\ y \equal{} x^2 \minus{} 1, y \equal{} 2x \minus{} 1 [Note: Abscissas means x-coordinate.]

1

Triangle Incribed in Semicircle

\triangle ABC

is inscribed in a semicircle whose diameter is

AB

, then AC \plus{} BC must be

<span class='latex-bold'>(A)</span>\ \text{equal to }AB \qquad<span class='latex-bold'>(B)</span>\ \text{equal to }AB\sqrt {2} \qquad<span class='latex-bold'>(C)</span>\ \geq AB\sqrt {2}

<span class='latex-bold'>(D)</span>\ \leq AB\sqrt {2} \qquad<span class='latex-bold'>(E)</span>\ AB^2

1

28 Handshakes

28

handshakes was exchanged at the conclusion of a party. Assuming that each participant was equally polite toward all the others, the number of people present was:

<span class='latex-bold'>(A)</span>\ 14 \qquad<span class='latex-bold'>(B)</span>\ 28 \qquad<span class='latex-bold'>(C)</span>\ 56 \qquad<span class='latex-bold'>(D)</span>\ 8 \qquad<span class='latex-bold'>(E)</span>\ 7

1

Two Poles

20''

80''

100''

apart, then the height of the intersection of the lines joining the top of each pole to the foot of the opposite pole is:

<span class='latex-bold'>(A)</span>\ 50'' \qquad<span class='latex-bold'>(B)</span>\ 40'' \qquad<span class='latex-bold'>(C)</span>\ 16'' \qquad<span class='latex-bold'>(D)</span>\ 60'' \qquad<span class='latex-bold'>(E)</span>\ \text{none of these}

1

Determining the Shape of a Triangle

Of the following sets of data the only one that does not determine the shape of a triangle is:

<span class='latex-bold'>(A)</span>\ \text{the ratio of two sides and the included angle} \\ \qquad<span class='latex-bold'>(B)</span>\ \text{the ratios of the three altitudes} \\ \qquad<span class='latex-bold'>(C)</span>\ \text{the ratios of the three medians} \\ \qquad<span class='latex-bold'>(D)</span>\ \text{the ratio of the altitude to the corresponding base} \\ \qquad<span class='latex-bold'>(E)</span>\ \text{two angles}

1

Wind on a Sail

(P)

of wind on a sail varies jointly as the area

(A)

of the sail and the square of the velocity

(V)

of the wind. The pressure on a square foot is

1

pound when the velocity is

16

miles per hour. The velocity of the wind when the pressure on a square yard is

36

<span class='latex-bold'>(A)</span>\ 10\frac {2}{3} \text{ mph} \qquad<span class='latex-bold'>(B)</span>\ 96 \text{ mph} \qquad<span class='latex-bold'>(C)</span>\ 32\text{ mph} \qquad<span class='latex-bold'>(D)</span>\ 1\frac {2}{3} \text{ mph} \qquad<span class='latex-bold'>(E)</span>\ 16 \text{ mph}

1

Six Triangular Sections

Through a point inside a triangle, three lines are drawn from the vertices to the opposite sides forming six triangular sections. Then:

<span class='latex-bold'>(A)</span>\ \text{the triangles are similar in opposite pairs}

<span class='latex-bold'>(B)</span>\ \text{the triangles are congruent in opposite pairs}

<span class='latex-bold'>(C)</span>\ \text{the triangles are equal in area in opposite pairs}

<span class='latex-bold'>(D)</span>\ \text{three similar quadrilaterals are formed}

<span class='latex-bold'>(E)</span>\ \text{none of the above relations are true}

1

Equal Roots of an Equation

In the equation \frac {x(x \minus{} 1) \minus{} (m \plus{} 1)}{(x \minus{} 1)(m \minus{} 1)} \equal{} \frac {x}{m} the roots are equal when (A)\ m \equal{} 1 \qquad(B)\ m \equal{} \frac {1}{2} \qquad(C)\ m \equal{} 0 \qquad(D)\ m \equal{} \minus{} 1 \qquad(E)\ m \equal{} \minus{} \frac {1}{2}

1

Apothem of a Square

The apothem of a square having its area numerically equal to its perimeter is compared with the apothem of an equilateral triangle having its area numerically equal to its perimeter. The first apothem will be:

<span class='latex-bold'>(A)</span>\ \text{equal to the second} \qquad<span class='latex-bold'>(B)</span>\ \frac {4}{3} \text{ times the second} \qquad<span class='latex-bold'>(C)</span>\ \frac {2}{\sqrt {3}} \text{ times the second} \\ <span class='latex-bold'>(D)</span>\ \frac {\sqrt {2}}{\sqrt {3}} \text{ times the second} \qquad<span class='latex-bold'>(E)</span>\ \text{indeterminately related to the second}

[Note: The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides.]

1

Simplifying a Fraction

\frac {2^{n \plus{} 4} \minus{} 2(2^n)}{2(2^{n \plus{} 3})} when simplified is: (A)\ 2^{n \plus{} 1} \minus{} \frac {1}{8} \qquad(B)\ \minus{} 2^{n \plus{} 1} \qquad(C)\ 1 \minus{} 2^n \qquad(D)\ \frac {7}{8} \qquad(E)\ \frac {7}{4}

1

Augmenting a Cylindrical Box

The radius of a cylindrical box is

8

inches and the height is

3

inches. The number of inches that may be added to either the radius or the height to give the same nonzero increase in volume is: (A)\ 1 \qquad(B)\ 5\frac {1}{3} \qquad(C)\ \text{any number} \qquad(D)\ \text{non \minus{} existent} \qquad(E)\ \text{none of these}

1

Equation with a

a

in the equation: \log_{10}(a^2 \minus{} 15a) \equal{} 2 are: (A)\ \frac {15\pm\sqrt {233}}{2} \qquad(B)\ 20, \minus{} 5 \qquad(C)\ \frac {15 \pm \sqrt {305}}{2}

<span class='latex-bold'>(D)</span>\ \pm20 \qquad<span class='latex-bold'>(E)</span>\ \text{none of these}

1

Inequalities

x > 0, y > 0, x > y

and z\not \equal{} 0. The inequality which is not always correct is: (A)\ x \plus{} z > y \plus{} z \qquad(B)\ x \minus{} z > y \minus{} z \qquad(C)\ xz > yz

<span class='latex-bold'>(D)</span>\ \frac {x}{z^2} > \frac {y}{z^2} \qquad<span class='latex-bold'>(E)</span>\ xz^2 > yz^2

1

Expressing in Negative Exponents

When simplified and expressed with negative exponents, the expression (x \plus{} y)^{ \minus{} 1}(x^{ \minus{} 1} \plus{} y^{ \minus{} 1}) is equal to: (A)\ x^{ \minus{} 2} \plus{} 2x^{ \minus{} 1}y^{ \minus{} 1} \plus{} y^{ \minus{} 2} \qquad(B)\ x^{ \minus{} 2} \plus{} 2^{ \minus{} 1}x^{ \minus{} 1}y^{ \minus{} 1} \plus{} y^{ \minus{} 2} \qquad(C)\ x^{ \minus{} 1}y^{ \minus{} 1} (D)\ x^{ \minus{} 2} \plus{} y^{ \minus{} 2} \qquad(E)\ \frac {1}{x^{ \minus{} 1}y^{ \minus{} 1}}

1

Three and Six Place Numbers

A six place number is formed by repeating a three place number; for example,

256256

678678

, etc. Any number of this form is always exactly divisible by:

<span class='latex-bold'>(A)</span>\ 7 \text{ only} \qquad<span class='latex-bold'>(B)</span>\ 11 \text{ only} \qquad<span class='latex-bold'>(C)</span>\ 13 \text{ only} \qquad<span class='latex-bold'>(D)</span>\ 101 \qquad<span class='latex-bold'>(E)</span>\ 1001

1

Factoring a Trinomial

The expression 21x^2 \plus{} ax \plus{} 21 is to be factored into two linear prime binomial factors with integer coefficients. This can be one if

a

<span class='latex-bold'>(A)</span>\ \text{any odd number} \qquad<span class='latex-bold'>(B)</span>\ \text{some odd number} \qquad<span class='latex-bold'>(C)</span>\ \text{any even number}

<span class='latex-bold'>(D)</span>\ \text{some even number} \qquad<span class='latex-bold'>(E)</span>\ \text{zero}

1

Directly and Inversly Proportional

Indicate in which one of the following equations

y

is neither directly nor inversely proportional to

x

: (A)\ x \plus{} y \equal{} 0 \qquad(B)\ 3xy \equal{} 10 \qquad(C)\ x \equal{} 5y \qquad(D)\ 3x \plus{} y \equal{} 10 (E)\ \frac {x}{y} \equal{} \sqrt {3}

1

Applying the Quadratic Formula

If in applying the quadratic formula to a quadratic equation f(x)\equiv ax^2 \plus{} bx \plus{} c \equal{} 0, it happens that c \equal{} \frac {b^2}{4a}, then the graph of y \equal{} f(x) will certainly: (A)\ \text{have a maximum} \qquad(B)\ \text{have a minimum} \qquad(C)\ \text{be tangent to the x \minus{} axis} \\ \qquad(D)\ \text{be tangent to the y \minus{} axis} \qquad(E)\ \text{lie in one quadrant only}

1

Divisibility of n^3-n

The largest number by which the expression n^3 \minus{} n is divisible for all possible integral values of

n

<span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ 5 \qquad<span class='latex-bold'>(E)</span>\ 6

1

Statements About Geometry Proofs

In connection with proof in geometry, indicate which one of the following statements is incorrect:

<span class='latex-bold'>(A)</span>\ \text{Some statements are accepted without being proved.}

<span class='latex-bold'>(B)</span>\ \text{In some instances there is more than one correct order in proving certain propositions.}

<span class='latex-bold'>(C)</span>\ \text{Every term used in a proof must have been defined previously.}

<span class='latex-bold'>(D)</span>\ \text{It is not possible to arrive by correct reasoning at a true conclusion if, in the given, there is an untrue proposition.}

<span class='latex-bold'>(E)</span>\ \text{Indirect proof can be used whenever there are two or more contrary propositions.}

1

Two Workers

A

can do a piece of work in

9

B

50\%

more efficient than

A

. The number of days it takes

B

to do the same piece of work is:

<span class='latex-bold'>(A)</span>\ 13\frac {1}{2} \qquad<span class='latex-bold'>(B)</span>\ 4\frac {1}{2} \qquad<span class='latex-bold'>(C)</span>\ 6 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ \text{none of these answers}

1

Hands of a Clock at 2:15

2: 15

o'clock, the hour and minute hands of a clock form an angle of:

<span class='latex-bold'>(A)</span>\ 30^{\circ} \qquad<span class='latex-bold'>(B)</span>\ 5^{\circ} \qquad<span class='latex-bold'>(C)</span>\ 22\frac {1}{2}^{\circ} \qquad<span class='latex-bold'>(D)</span>\ 7\frac {1}{2} ^{\circ} \qquad<span class='latex-bold'>(E)</span>\ 28^{\circ}

1

Geometric Progression of Squares

The limit of the sum of an infinite number of terms in a geometric progression is \frac {a}{1 \minus{} r} where

a

denotes the first term and \minus{} 1 < r < 1 denotes the common ratio. The limit of the sum of their squares is: (A)\ \frac {a^2}{(1 \minus{} r)^2} \qquad(B)\ \frac {a^2}{1 \plus{} r^2} \qquad(C)\ \frac {a^2}{1 \minus{} r^2} \qquad(D)\ \frac {4a^2}{1 \plus{} r^2} \qquad(E)\ \text{none of these}

1

Statements About Doubling

Of the following statements, the one that is incorrect is:

<span class='latex-bold'>(A)</span>\ \text{Doubling the base of a given rectangle doubles the area.}

<span class='latex-bold'>(B)</span>\ \text{Doubling the altitude of a triangle doubles the area.}

<span class='latex-bold'>(C)</span>\ \text{Doubling the radius of a given circle doubles the area.}

<span class='latex-bold'>(D)</span>\ \text{Doubling the divisor of a fraction and dividing its numerator by 2 changes the quotient.}

<span class='latex-bold'>(E)</span>\ \text{Doubling a given quantity may make it less than it originally was.}

1

Infinite Equilateral Triangles

An equilateral triangle is drawn with a side of length

a

. A new equilateral triangle is formed by joining the midpoints of the sides of the first one. Then a third equilateral triangle is formed by joining the midpoints of the sides of the second; and so on forever. The limit of the sum of the perimeters of all the triangles thus drawn is:

<span class='latex-bold'>(A)</span>\ \text{Infinite} \qquad<span class='latex-bold'>(B)</span>\ 5\frac {1}{4}a \qquad<span class='latex-bold'>(C)</span>\ 2a \qquad<span class='latex-bold'>(D)</span>\ 6a \qquad<span class='latex-bold'>(E)</span>\ 4\frac {1}{2}a

1

Price of an Article

The price of an article is cut

10\%

. To restore it to its former value, the new price must be increased by:

<span class='latex-bold'>(A)</span>\ 10\% \qquad<span class='latex-bold'>(B)</span>\ 9\% \qquad<span class='latex-bold'>(C)</span>\ 11\frac {1}{9}\% \qquad<span class='latex-bold'>(D)</span>\ 11\% \qquad<span class='latex-bold'>(E)</span>\ \text{none of these answers}

1

Relative Errors

.02''

is made in the measurement of a line

10''

long, while an error of only

.2''

is made in a measurement of a line

100''

long. In comparison with the relative error of the first measurement, the relative error of the second measurement is:

<span class='latex-bold'>(A)</span>\ \text{greater by }.18 \qquad<span class='latex-bold'>(B)</span>\ \text{the same} \qquad<span class='latex-bold'>(C)</span>\ \text{less}

<span class='latex-bold'>(D)</span>\ 10 \text{ times as great} \qquad<span class='latex-bold'>(E)</span>\ \text{correctly described by both (A) and (D)}

1

Rectangular Box

The bottom, side, and front areas of a rectangular box are known. The product of these areas is equal to:

<span class='latex-bold'>(A)</span>\ \text{the volume of the box} \qquad<span class='latex-bold'>(B)</span>\ \text{the square root of the volume} \qquad<span class='latex-bold'>(C)</span>\ \text{twice the volume}

<span class='latex-bold'>(D)</span>\ \text{the square of the volume} \qquad<span class='latex-bold'>(E)</span>\ \text{the cube of the volume}

1

Selling and Reselling a House

Mr. A owns a home worth

\$ 10000

. He sells it to Mr. B at a

10\%

profit based on the worth of the house. Mr. B sells the house back to Mr. A at a

10\%

<span class='latex-bold'>(A)</span>\ \text{A comes out even} \qquad<span class='latex-bold'>(B)</span>\ \text{A makes }\$ 1100\text{ on the deal}\qquad <span class='latex-bold'>(C)</span>\ \text{A makes }\$ 1000\text{ on the deal}

<span class='latex-bold'>(D)</span>\ \text{A loses }\$ 900\text{ on the deal} \qquad<span class='latex-bold'>(E)</span>\ \text{A loses }\$ 1000\text{ on the deal}

1

Painting a Barn

A barn with a flat roof is rectangular in shape,

10

13

yd. long and 5 yd. high. It is to be painted inside and outside, and on the ceiling, but not on the roof or floor. The total number of sq. yd. to be painted is:

<span class='latex-bold'>(A)</span>\ 360 \qquad<span class='latex-bold'>(B)</span>\ 460 \qquad<span class='latex-bold'>(C)</span>\ 490 \qquad<span class='latex-bold'>(D)</span>\ 590 \qquad<span class='latex-bold'>(E)</span>\ 720

1

Square's Diagonal

If the length of a diagonal of a square is a \plus{} b, then the area of the square is: (A)\ (a \plus{} b)^2 \qquad(B)\ \frac {1}{2}(a \plus{} b)^2 \qquad(C)\ a^2 \plus{} b^2 (D)\ \frac {1}{2}(a^2 \plus{} b^2) \qquad(E)\ \text{none of these}

1

Rectangular Field

A rectangular field is half as wide as it is long and is completely enclosed by

x

yards of fencing. The area in terms of

x

<span class='latex-bold'>(A)</span>\ \frac {x^2}{2} \qquad<span class='latex-bold'>(B)</span>\ 2x^2 \qquad<span class='latex-bold'>(C)</span>\ \frac {2x^2}{9} \qquad<span class='latex-bold'>(D)</span>\ \frac {x^2}{18} \qquad<span class='latex-bold'>(E)</span>\ \frac {x^2}{72}

1

Percent Difference

The percent that

M

is greater than

N

is: (A)\ \frac {100(M \minus{} N)}{M} \qquad(B)\ \frac {100(M \minus{} N)}{N} \qquad(C)\ \frac {M \minus{} N}{N} \qquad(D)\ \frac {M \minus{} N}{M} (E)\ \frac {100(M \plus{} N)}{N}