Free EA Quantitative Problems Question and Answers — Questions and Answers
Question 1: Division & Factoring <br> If 72x−x=y and x is a positive integer less than 10, how many positive integer values are possible for y?
- A )9
- 7
- 6 (Correct answer)
- 2
- 1
Correct answer: 6
The correct answer is: C)<br> 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.<br> 1:721−12:722−23:723−34:724−46:726−68:728−89:729−9=71=34=21=14=6=1=−1<br> Therefore, 6 integer values less than 10 for x produce positive integer values for y.
Question 2: Fractions and Decimals<br> 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. <br> How many dozen cookies had not been sold when the pastry shop closed yesterday?
- 10
- 20
- 40 (Correct answer)
- 50
- 600
Correct answer: 40
The correct answer is: C)<br> Three-quarters or 75% of 200 dozen is 150 dozen cookies that were sold by 3 in the afternoon, leaving 50 dozen unsold.<br> 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.
Question 3: Percentages (Data Sufficiency) <br> If x is 75 percent of y, what is the value of x ?<br> (1) y>300<br> (2) y–x=45
- Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
- Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient. (Correct answer)
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are not sufficient.
Correct answer: Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
The correct answer is: B) <br> (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.<br> (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.<br> The correct answer is B; statement 2 alone is sufficient.
Question 4: Exponents & Radicals (Data Sufficiency)<br> Is –4≤x≤4 ?<br> (1) x2+y2=16<br> (2) x2+y≤16
- Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient. (Correct answer)
- Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are not sufficient.
Correct answer: Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
The correct answer is: A)<br> (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.<br> (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.<br> The correct answer is A; statement 1 alone is sufficient.
Question 5: Geometry (Data Sufficiency)<br> Three-quarters of a cylindrical tank is filled with water. <br>What is the area of the tank’s surface that is in contact with the water?<br> (1) The diameter of the tank is a third of the height of the tank.<br> (2) The ratio of the base area to that of the curved surface is 1 to 12.
- Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
- Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are not sufficient. (Correct answer)
Correct answer: Statements (1) and (2) TOGETHER are not sufficient.
The correct answer is: E)<br> 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.<br> (1) 13h=d=2r hence r=16h or h=6r, but no values are provided for either variable; NOT sufficient.<br> (2) The ratio = πr22πrh=r2h=112, and r in terms of h is r=h6; NOT SUFFICIENT.<br> (Together) Both statements produce the same equation r=h6 for two unknowns; NOT sufficient.<br> The correct answer is E; both statements together are still not sufficient.
Question 6: Inequalities<br> How many integers n are there such that 1<4n+4<24?
- 1
- 2
- 3
- 4
- 5 (Correct answer)
Correct answer: 5
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).
Question 7: Verbal – Sentence Correction <br> 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.
- supporting food supplies of wild animals by pollinating berry-, seed-, and nut-bearing plants; and produce
- supporting food supplies of wild animals by pollinating berry-, seed-, and nut-bearing plants; and they produced
- supporting food supplies of wild animals by pollinating berry-, seed-, and nut-bearing plants; and producing (Correct answer)
- they support food supplies of wild animals by pollinating berry-, seed-, and nut-bearing plants; yet producing
- they support food supplies of wild animals by pollinating berry-, seed-, and nut-bearing plants; producing
Correct answer: supporting food supplies of wild animals by pollinating berry-, seed-, and nut-bearing plants; and producing
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.
Question 8: Verbal – Sentence Correction<br> This is an age where ephemeral work will likely even endure far longer than was once possible, at least in some form.
- where ephemeral work will likely even endure far longer
- in which even ephemeral work will likely endure far longer (Correct answer)
- where even ephemeral work will likely endure more
- in which ephemeral work will likely even endure more
- where ephemeral work likely will endure far more
Correct answer: in which even ephemeral work will likely endure far longer
B. Yes. The modifier “even” properly modifies the noun “ephemeral work” and the pronoun phrase “in which” can describe “an age”.
Question 9: Question 1: Which of the following best describes the trajectory of the passage?
- A series of proposals are put forward concerning the best way to address a crisis; one such proposal is approved and acted upon.
- An oversight is detected and quickly addressed; the way in which the oversight is resolved is questioned.
- Attention is called to a disconnect between the way in which a crisis has been memorialized and the reality of that crisis; steps are taken to resolve that disconnect. (Correct answer)
- Several possible responses to a crisis are evaluated; no solution is immediately reached.
- Conventional wisdom about a national tragedy is discussed; new research confirms that perspective.
Correct answer: Attention is called to a disconnect between the way in which a crisis has been memorialized and the reality of that crisis; steps are taken to resolve that disconnect.
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.
Question 10: If neither x nor y is equal to 0, is 3x−2y=0? <br> (1) 27x3−8y3=0 <br> (2) 9x2−4y2=0
- Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient to answer the question asked. (Correct answer)
- Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer: Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient to answer the question asked.
Let's see the detailed solution:<br> We have to find out whether 3x−2y=0<br> <br><br> Alternatively, we can write 3x−2y=0<br> as x=23y<br> <br><br> Thus, we have to determine whether x=23y<br> ..<br>.<br> Statement 1:<br> <br><br> We are given that 27x3−8y3=0<br> <br><br> ⇒27x3=8y3<br> ⇒x3=827y3<br> ⇒x=23y<br> ; taking the cube root of both the sides. (Remember that the real number x3 has only one real cube root.)<br> <br><br> The answer is Yes. - Sufficient!<br> <br><br> Statement 2:<br> <br><br> We are given that 9x2−4y2=0<br> ⇒9x2=4y2<br> ⇒x2=49y2<br> ⇒x=±23y<br> ; taking the square root of both the sides. (Remember that the positive number x2 has two square roots, one positive and the other negative.)<br> <br><br> If x=23y<br> , the answer is Yes; however, if x=−23y<br> , the answer is No.<br> <br><br> No unique value of x. - Insufficient!
Question 11: 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) ?<br> (1) f(2)=64<br> (2) f(3)=16
- Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient to answer the question asked.
- Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked. (Correct answer)
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer: EACH statement ALONE is sufficient to answer the question asked.
Let's see the correct solution:<br> <br><br> We are given that f(n)=(a)6n<br> , where a <br> is a constant. <br> <br><br> We have to find out the value of f(1)<br> Statement 1:<br> <br><br> Given that f(2)=64<br> Thus, f(2)=(a)62=a3=64<br> ⇒a=(64)13=4<br> Thus, f(1)=(a)61=a6=46<br> . - Sufficient<br> <br><br> Statement 2:<br> <br><br> Given that f(3)=16<br> Thus, f(3)=(a)63=a2=16<br> ⇒a=(16)12=±4<br> Thus, f(1)=(a)61=a6=(±4)6=46<br> . - Sufficient
Free EA Quantitative Problems Question and Answers
Division & Factoring
If 72x−x=y and x is a positive integer less than 10, how many positive integer values are possible for y?