# FREE EA Quantitative Problems Question and Answers

#### Verbal – Sentence Correction

This is an age where ephemeral work will likely even endure far longer than was once possible, at least in some form.

B. Yes. The modifier “even” properly modifies the noun “ephemeral work” and the pronoun phrase “in which” can describe “an age”.

#### Division & Factoring

If 72x−x=y and x is a positive integer less than 10, how many positive integer values are possible for y?

The correct answer is: C)

To satisfy the conditions of the problem, x must be a factor of 72 less than 10, which are 1, 2, 3, 4, 6, 8, and 9.

1:721−12:722−23:723−34:724−46:726−68:728−89:729−9=71=34=21=14=6=1=−1

Therefore, 6 integer values less than 10 for x produce positive integer values for y.

#### Percentages (Data Sufficiency)

If x is 75 percent of y, what is the value of x ?

(1) y>300

(2) y–x=45

The correct answer is: B)

(1) To find the value of x requires a single value for x or y. This statement only provides a minimum value, and so the question cannot be answered; NOT SUFFICIENT.

(2) Substitute the given value of y in terms of x, which is y=43x, to produce the equation 43x–x=45 which can be solved for the single variable of x as equal to 105; SUFFICIENT.

The correct answer is B; statement 2 alone is sufficient.

#### Geometry (Data Sufficiency)

Three-quarters of a cylindrical tank is filled with water.

What is the area of the tank’s surface that is in contact with the water?

(1) The diameter of the tank is a third of the height of the tank.

(2) The ratio of the base area to that of the curved surface is 1 to 12.

The correct answer is: E)

Area of the curved surface = 2πrh where r and h are the radius of the base and the height of the cylinder respectively and the area of the base touching water is πr2.

(1) 13h=d=2r hence r=16h or h=6r, but no values are provided for either variable; NOT sufficient.

(2) The ratio = πr22πrh=r2h=112, and r in terms of h is r=h6; NOT SUFFICIENT.

(Together) Both statements produce the same equation r=h6 for two unknowns; NOT sufficient.

The correct answer is E; both statements together are still not sufficient.

#### Fractions and Decimals

A pastry shop began yesterday with 200 dozen cookies available for sale. Three-quarters of the cookies were sold by 3 in the afternoon, and 20 percent of the remaining cookies were sold between then and closing time.

How many dozen cookies had not been sold when the pastry shop closed yesterday?

The correct answer is: C)

Three-quarters or 75% of 200 dozen is 150 dozen cookies that were sold by 3 in the afternoon, leaving 50 dozen unsold.

10 percent of 50 dozen is 5 dozen, so 10 dozen were sold between 3 in the afternoon and closing time, leaving 200 – 150 – 10 = 40 dozen unsold at closing time.

#### For all integers n , the function f is defined by f(n)=(a)6n, where a is a constant. What is the value of f(1)
?

(1) f(2)=64

(2) f(3)=16

Let's see the correct solution:

We are given that f(n)=(a)6n

, where a

is a constant.

We have to find out the value of f(1)

Statement 1:

Given that f(2)=64

Thus, f(2)=(a)62=a3=64

⇒a=(64)13=4

Thus, f(1)=(a)61=a6=46

. - Sufficient

Statement 2:

Given that f(3)=16

Thus, f(3)=(a)63=a2=16

⇒a=(16)12=±4

Thus, f(1)=(a)61=a6=(±4)6=46

. - Sufficient

#### Question 1: Which of the following best describes the trajectory of the passage?

C. Yes. This choice clearly summarizes the flow of the passage. Attention is called to the lack of African-American representation in the AIDS Memorial Quilt; Call My Name is a response to this oversight.

#### Exponents & Radicals (Data Sufficiency)

Is –4≤x≤4 ?

(1) x2+y2=16

(2) x2+y≤16

The correct answer is: A)

(1) That x2+y2=16 indicates that both x and y must be between – 4 and 4 inclusive as all squares must be positive values; SUFFICIENT.

(2) Subtract y from each side of the inequality to produce x2≤16–y. Because there is no limit on the value of y, there is no limit on the value of x, and so the answer cannot be answered definitively; NOT SUFFICIENT.

The correct answer is A; statement 1 alone is sufficient.

#### Verbal – Sentence Correction

Bees play important roles in the environment, including germinating agricultural crops, such as apples, melons, and cranberries; supporting food supplies of wild animals by pollinating berry-, seed-, and nut-bearing plants; and produce honey, a nutritious food for animals, insects, and humans alike.

C. Correct. The sentence communicates a list of roles bees play in the environment and maintains the parallel structure for all items in the list.

#### If neither x nor y is equal to 0, is 3x−2y=0?

(1) 27x3−8y3=0

(2) 9x2−4y2=0

Let's see the detailed solution:

We have to find out whether 3x−2y=0

Alternatively, we can write 3x−2y=0

as x=23y

Thus, we have to determine whether x=23y

..

.

Statement 1:

We are given that 27x3−8y3=0

⇒27x3=8y3

⇒x3=827y3

⇒x=23y

; taking the cube root of both the sides. (Remember that the real number x3
has only one real cube root.)

The answer is Yes. - Sufficient!

Statement 2:

We are given that 9x2−4y2=0

⇒9x2=4y2

⇒x2=49y2

⇒x=±23y

; taking the square root of both the sides. (Remember that the positive number x2
has two square roots, one positive and the other negative.)

If x=23y

, the answer is Yes; however, if x=−23y

, the answer is No.

No unique value of x. - Insufficient!

#### Inequalities

How many integers n are there such that 1<4n+4<24?

Solve the inequality for n by isolating n. −3<4n<20, so −34<n<5. There are 5 integers that fulfill n (0, 1, 2, 3, 4).