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