SAT Mathematics Practice Test 4

1) Which of the following numbers is between 3 and 4?

A. 12/15

B. 15/4

C. 17/4

D. 13/6

E. 11/6

Option A is not correct as 12/5 = 2.4
Option B is correct as 15/4 = 3.75 and 3.75 lies between 3 and 4.
Option C is not correct as 17/4 = 4.25
Option D is not correct as 13/6 = 2.1666...
Option E is not correct as 11/6 = 1.83...

Explanation

Option A is not correct as 12/5 = 2.4
Option B is correct as 15/4 = 3.75 and 3.75 lies between 3 and 4.
Option C is not correct as 17/4 = 4.25
Option D is not correct as 13/6 = 2.1666...
Option E is not correct as 11/6 = 1.83...

2) A team of 24 men can complete a job in 18 days working 9 hours per day. How many hours a day would 27 men have to work in order to finish it in 12 days?

A. 12

B. 24

C. 27

D. 36

E. 18

As other options are not equal to the calculated answers, only option A is correct.
Men Days Hours
24 18 9
27 12 ?
The number of men and the number of days vary inversely with the number of hours.

No. of hours = 24*18*9 / 27*12 = 12 hours

Explanation

As other options are not equal to the calculated answers, only option A is correct.
Men Days Hours
24 18 9
27 12 ?
The number of men and the number of days vary inversely with the number of hours.

No. of hours = 24*18*9 / 27*12 = 12 hours

3) The table given below shows the number of credit points scored by five students in a five week course. Which student has earned total maximum credit points in the course?

A. Jane

B. Mike

C. Mathew

D. Peter

E. Stephen

Option A is correct. Jane´s total credit points = 9 + 7 + 20 + 21 + 7 = 64
Option B is not correct. Mike´s total credit points = 10 + 6 + 16 + 22 + 8 = 62
Option C is not correct. Mathew's total credit points = 15+ 8 +22 + 5 + 11 = 61
Option D is not correct. Peter´s total credit points = 20 + 6 + 14 + 5 + 12 = 57
Option E is not correct. Stephen´s total credit points = 8 + 20 + 16 + 7 + 5 = 56

Explanation

Option A is correct. Jane´s total credit points = 9 + 7 + 20 + 21 + 7 = 64
Option B is not correct. Mike´s total credit points = 10 + 6 + 16 + 22 + 8 = 62
Option C is not correct. Mathew's total credit points = 15+ 8 +22 + 5 + 11 = 61
Option D is not correct. Peter´s total credit points = 20 + 6 + 14 + 5 + 12 = 57
Option E is not correct. Stephen´s total credit points = 8 + 20 + 16 + 7 + 5 = 56

4) If y = 3/4 xz, what is the value of z when x = 2 and y = 27

A. 2

B. 6

C. 18

D. 27

E. 9

Option A is not correct. If z =2, 3/4 xz = 3/4 * 2 * 2 = 3 ≠ 27
Option B is not correct. If z = 6, 3/4 xz = 3/4 * 2 * 6 = 9 ≠ 27
Option C is correct. If z = 18, 3/4 xz = 3/4 * 2 * 18 = 27 = y
Option E is not correct. If z = 27, 3/4 xz = 3/4 *2 * 27 = 81/2 ≠ 27
Option E is not correct. If z = 9, 3/4 xz = 3/4 * 2 * 9 = 27/2 ≠ 27

Explanation

Option A is not correct. If z =2, 3/4 xz = 3/4 * 2 * 2 = 3 ≠ 27
Option B is not correct. If z = 6, 3/4 xz = 3/4 * 2 * 6 = 9 ≠ 27
Option C is correct. If z = 18, 3/4 xz = 3/4 * 2 * 18 = 27 = y
Option E is not correct. If z = 27, 3/4 xz = 3/4 *2 * 27 = 81/2 ≠ 27
Option E is not correct. If z = 9, 3/4 xz = 3/4 * 2 * 9 = 27/2 ≠ 27

5) In a group of 15 persons 10 are mathematicians and 8 are statisticians. How many people are both mathematicians and statisticians?

A. 15

B. 10

C. 3

D. 8

E. 25

As the calculated answer is not equal to the other options given, only option C is correct.

Total number of persons in the group = n(M∪S) = 15
Number of mathematicians = n(M) = 10
Number of statisticians = n(S) = 8
Number of persons who know both subjects = n(M∩S)
n(M∪S) =n(M) + n(S) - n(M∩S) or n(M∩S) = 10 + 8 + 15 + 18 - 15 = 3

Explanation

As the calculated answer is not equal to the other options given, only option C is correct.

Total number of persons in the group = n(M∪S) = 15
Number of mathematicians = n(M) = 10
Number of statisticians = n(S) = 8
Number of persons who know both subjects = n(M∩S)
n(M∪S) =n(M) + n(S) - n(M∩S) or n(M∩S) = 10 + 8 + 15 + 18 - 15 = 3

6) If x is a positive integer, which of the following is(are) true.

If x is odd, then (x+1)²is even.
If x is even, then (x-1)²is odd.
If x is even, then is irrational.

A. I and II

B. I and III

C. II and III

D. Only I

E. Only I

Option A is correct.
Let us take x as 5 which is odd, then (x + 1)^2 is (5 + 1)^2 which is equal to 36, which is even. Hence I is true. Let us take x as 8 which is even, then (x - 1)^2 is (8 - 1)^2 which is equal to 49, which is odd. Hence II is also true. As I and II are true option A is correct.
Option B is not correct.
I is true as seen above. If x is 8 which is even, then √(8-1) = √7
is irrational, but If x is 10 which is even, then √(10-1) = √9 = 3 is rational, hence III is not true.
Option C is not correct.
II is true as seen above but III is not true as seen above.
Option D is not correct.
Only I is false, as both I and II are true.
Option E is not correct.
Only II is false, as both I and II are true.

Explanation

Option A is correct.
Let us take x as 5 which is odd, then (x + 1)^2 is (5 + 1)^2 which is equal to 36, which is even. Hence I is true. Let us take x as 8 which is even, then (x - 1)^2 is (8 - 1)^2 which is equal to 49, which is odd. Hence II is also true. As I and II are true option A is correct.
Option B is not correct.
I is true as seen above. If x is 8 which is even, then √(8-1) = √7
is irrational, but If x is 10 which is even, then √(10-1) = √9 = 3 is rational, hence III is not true.
Option C is not correct.
II is true as seen above but III is not true as seen above.
Option D is not correct.
Only I is false, as both I and II are true.
Option E is not correct.
Only II is false, as both I and II are true.

7) Which of the following is the correct factorization of the quadratic expression 6z² - 11z + 4?

A. (3z - 4)(2z - 1)

B. (3z + 4)(2z - 1)

C. (3z - 4)(2z + 1)

D. (3z + 4)(2z + 1)

E. (2z - 4)(3z - 1)

Option A is correct: 6z^2 - 11z + 4 = 6z^2 - 8z - 3z + 4
= 2z(3z - 4) - 1(3z -4)
= (3z-4) (2z - 1)
Option B is not correct as 6z^2 - 11z + 4 ≠ (3z + 4) ( 2z -1)
Option C is not correct as 6z^2 - 11z + 4 ≠ (3z -4) (2z +1)
Option D is not correct as 6z^2 - 11z + 4 ≠ (3z + 4) (2z +1)
Option E is not correct as 6z^2 - 11z + 4 ≠ (2z -4) (3z -1)

Explanation

Option A is correct: 6z^2 - 11z + 4 = 6z^2 - 8z - 3z + 4
= 2z(3z - 4) - 1(3z -4)
= (3z-4) (2z - 1)
Option B is not correct as 6z^2 - 11z + 4 ≠ (3z + 4) ( 2z -1)
Option C is not correct as 6z^2 - 11z + 4 ≠ (3z -4) (2z +1)
Option D is not correct as 6z^2 - 11z + 4 ≠ (3z + 4) (2z +1)
Option E is not correct as 6z^2 - 11z + 4 ≠ (2z -4) (3z -1)

8) A club has 108 members. Two-thirds of them are men and the rest are women. All members are married except for 9 women members. How many married women are there in the club?

A. 20

B. 24

C. 27

D. 30

E. 9

As the calculated answer is not equal to the other options, only option C is correct.
Total number of members in the club = 108
Number of male members = 2/3 * 108 = 72
Number of women members = 108 - 72 = 36
Number of women who are not married = 9
Number of married women in the club = 36 - 9 = 27

Explanation

As the calculated answer is not equal to the other options, only option C is correct.
Total number of members in the club = 108
Number of male members = 2/3 * 108 = 72
Number of women members = 108 - 72 = 36
Number of women who are not married = 9
Number of married women in the club = 36 - 9 = 27

9) Johnson has to cover a distance of 240 miles, of which

A. 240

B. 30

C. 40

D. 50

E. 120

As the calculated answer is not equal to the other options, only option C is correct.
Total distance traveled = 240 miles.
Distance traveled at a speed of 30 miles/hr =1/4 * 240 miles = 60 miles.
Time taken to travel 60 miles = 60/30 hrs = 2 hrs (Time = distance/speed)
Distance traveled at a speed of 40 miles/hr = 1/3 * 240 miles = 80 miles.
Time taken to travel 80 miles = 80/40 hrs = 2 hrs.
Distance traveled at a speed of 50 miles/hr = {240 - (60 + 80)}miles
= 100 miles.
Time taken to travel 100 miles = 100/50 hrs = 2 hrs.
Total time taken to travel 240 miles = 2hrs + 2hrs + 2hrs = 6hrs
Average speed of Johnson = total distance traveled/total time taken
= 240 miles/6hrs
= 40 miles/hr.

Explanation

As the calculated answer is not equal to the other options, only option C is correct.
Total distance traveled = 240 miles.
Distance traveled at a speed of 30 miles/hr =1/4 * 240 miles = 60 miles.
Time taken to travel 60 miles = 60/30 hrs = 2 hrs (Time = distance/speed)
Distance traveled at a speed of 40 miles/hr = 1/3 * 240 miles = 80 miles.
Time taken to travel 80 miles = 80/40 hrs = 2 hrs.
Distance traveled at a speed of 50 miles/hr = {240 - (60 + 80)}miles
= 100 miles.
Time taken to travel 100 miles = 100/50 hrs = 2 hrs.
Total time taken to travel 240 miles = 2hrs + 2hrs + 2hrs = 6hrs
Average speed of Johnson = total distance traveled/total time taken
= 240 miles/6hrs
= 40 miles/hr.

10) Which of the following has the greatest perimeter?

A. A square with an area of 36 square units.

B. An equilateral triangle with a side of 9 units.

C. A rectangle with 10 units length and 40 square units area.

D. A right triangle whose one side is 4 units and hypotenuse 5 units.

E. All the given figures have the same perimeter.

Option A is not correct.
Area of the square = 36 square units = s2 or s = 6 units.
Perimeter of the square= 4s = 4 * 6 units = 24 units.
Option B is not correct.
Side of the equilateral triangle = a = 9 units.
Perimeter of an equilateral triangle = 3a = 3 * 9 units = 27 units.
Option C is correct.
Length of the rectangle = 10 units.
Area of the rectangle = 40 square units.
Width of the rectangle = 40/10 units = 4 units.
Perimeter of the rectangle = 2(l + w)
= 2(10 + 4) units
= 2 * 14 = 28 units.
Option D is not correct.
In a right triangle c2= a2 + b2 or 52 = 42 + b2 or b2 = 25 - 16 or b2 = 9
Or b = 3. Perimeter of the triangle = (3 + 4 + 5) units = 12 units.
Option E is not correct as is observed no two of the given figures have the same perimeter.

Explanation

Option A is not correct.
Area of the square = 36 square units = s2 or s = 6 units.
Perimeter of the square= 4s = 4 * 6 units = 24 units.
Option B is not correct.
Side of the equilateral triangle = a = 9 units.
Perimeter of an equilateral triangle = 3a = 3 * 9 units = 27 units.
Option C is correct.
Length of the rectangle = 10 units.
Area of the rectangle = 40 square units.
Width of the rectangle = 40/10 units = 4 units.
Perimeter of the rectangle = 2(l + w)
= 2(10 + 4) units
= 2 * 14 = 28 units.
Option D is not correct.
In a right triangle c2= a2 + b2 or 52 = 42 + b2 or b2 = 25 - 16 or b2 = 9
Or b = 3. Perimeter of the triangle = (3 + 4 + 5) units = 12 units.
Option E is not correct as is observed no two of the given figures have the same perimeter.

11) The average sale of soaps of 24 salesmen excluding Michael´s is 46 pieces per day, whereas Michael alone sells 96 pieces per day. What will be the average sale of soaps if Michael´s sale is also included in it?

A. 36

B. 38

C. 48

D. 42

E. 140

Option A is not correct as average sale of 24 salesmen itself is greater than 36.
Option B is not correct as average sale of 24 salesmen itself is greater than 38.
Option C is correct.
Average sale = total sale / number of salesmen or
Total sale = Average sale * number of salesmen
= 46 * 24 = 1104
Michael´s sale per day = 96
Total sale including Michael´s sale = 1104 + 96 = 1200
Total number of salesmen including Michael =24 + 1 = 25
Average sale of soaps including Michael´s sale = 1200/25 = 48
Option D is not correct as average sale of 24 salesmen itself is greater than 46.
Option E is not correct as average sale figure of 140 is too high, compared to the average sale of 24 salesmen.

Explanation

Option A is not correct as average sale of 24 salesmen itself is greater than 36.
Option B is not correct as average sale of 24 salesmen itself is greater than 38.
Option C is correct.
Average sale = total sale / number of salesmen or
Total sale = Average sale * number of salesmen
= 46 * 24 = 1104
Michael´s sale per day = 96
Total sale including Michael´s sale = 1104 + 96 = 1200
Total number of salesmen including Michael =24 + 1 = 25
Average sale of soaps including Michael´s sale = 1200/25 = 48
Option D is not correct as average sale of 24 salesmen itself is greater than 46.
Option E is not correct as average sale figure of 140 is too high, compared to the average sale of 24 salesmen.

12) In the given figure, O is the centre of the circle.

Note: Figure not drawn to scale.

A. 30 degrees

B. 20 degrees

C. 50 degrees

D. 100 degrees

E. 90 degrees

As the calculated answer is not equal to the other options, only option D is correct.

Join PO. ∠OQP = ∠OPQ = 30 degrees (Isosceles triangle property)
∠ORP = ∠OPR = 20 degrees (Isosceles triangle property)
∠QPR = ∠OPQ + ∠OPR = 30 degrees + 20 degrees = 50 degrees
∠QOR = 2 * ∠QPR = 2 * 50 degrees = 100 degrees (angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any other point on the remaining circle)

Explanation

As the calculated answer is not equal to the other options, only option D is correct.

Join PO. ∠OQP = ∠OPQ = 30 degrees (Isosceles triangle property)
∠ORP = ∠OPR = 20 degrees (Isosceles triangle property)
∠QPR = ∠OPQ + ∠OPR = 30 degrees + 20 degrees = 50 degrees
∠QOR = 2 * ∠QPR = 2 * 50 degrees = 100 degrees (angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any other point on the remaining circle)

13) Mrs. Alice is four times as old as her son. After 4 years the sum of their ages would be 63 years. Find her son´s present age.

A. 12

B. 11

C. 4

D. 2

E. 15

Option A is not correct. If son is 12 years, then mother would be 48 years old, after 4 years sum of their ages = 12 + 4 + 48 + 4 = 68 63.
Option B is correct.
Let´s son´s present age be x years.
Mrs. Alice´s age = 4x years
Son's age's age after 4 years = (x + 4) years
Mrs. Alice's age after 4 years = (4x + 4) years
Given, x + 4 + 4x + 4 = 63
Or 5x + 8 = 63 or 5x = 63 - 8 = 55 or 5x = 55 or x = 11
Hence son's present age = 11 years.
Option C is not correct. If son is 4 years, then mother would be 16 years old,after 4 years sum of their ages = 4 + 4 +16 + 4 = 28 63
Option D is not correct. If son is 2 years, then mother would be 8 years old, which is absurd.
Option E is not correct. If son is 15 years, then mother would be 60 years old,after 4 years sum of their ages = 15 + 4 + 60 + 4 = 83 63

Explanation

Option A is not correct. If son is 12 years, then mother would be 48 years old, after 4 years sum of their ages = 12 + 4 + 48 + 4 = 68 63.
Option B is correct.
Let´s son´s present age be x years.
Mrs. Alice´s age = 4x years
Son's age's age after 4 years = (x + 4) years
Mrs. Alice's age after 4 years = (4x + 4) years
Given, x + 4 + 4x + 4 = 63
Or 5x + 8 = 63 or 5x = 63 - 8 = 55 or 5x = 55 or x = 11
Hence son's present age = 11 years.
Option C is not correct. If son is 4 years, then mother would be 16 years old,after 4 years sum of their ages = 4 + 4 +16 + 4 = 28 63
Option D is not correct. If son is 2 years, then mother would be 8 years old, which is absurd.
Option E is not correct. If son is 15 years, then mother would be 60 years old,after 4 years sum of their ages = 15 + 4 + 60 + 4 = 83 63

14) 4 pens cost as much as 6 pencils; 2 pencils cost as much as 4 erasers; If the cost of 1 eraser is $1, what is the cost of four pens?

A. $6

B. $3

C. $1

D. $12

E. $18

As other options are not equal to the calculated answer, only option D is correct.
Cost of 4 pens = cost of 6 pencils or
Cost of 1 pen = 6/4 cost of 1 pencil = 3/2 cost of 1 pencil
Cost of 2 pencils = cost of 4 erasers or
Cost of 1 pencil = 4/2 cost of 1 eraser = 2 cost of 1 eraser
Cost of 1 eraser = $1
Cost of 1 pencil = 2 * cost of 1 eraser = 2 * 1 = $2
Cost of 1 pen = 3/2 cost of 1 pencil
= 3/2 * 2 = $3
Cost of 4 pens = 4 * 3 = $12

Explanation

As other options are not equal to the calculated answer, only option D is correct.
Cost of 4 pens = cost of 6 pencils or
Cost of 1 pen = 6/4 cost of 1 pencil = 3/2 cost of 1 pencil
Cost of 2 pencils = cost of 4 erasers or
Cost of 1 pencil = 4/2 cost of 1 eraser = 2 cost of 1 eraser
Cost of 1 eraser = $1
Cost of 1 pencil = 2 * cost of 1 eraser = 2 * 1 = $2
Cost of 1 pen = 3/2 cost of 1 pencil
= 3/2 * 2 = $3
Cost of 4 pens = 4 * 3 = $12

15) If x > 2y and

, then which of the following is true?

A. x > 6z

B. x < 6z

C. y < 6/x

D. z > 6/x

E. x = 6z

Only option A is correct as other options do not satisfy the given inequalities.

x > 2y and z 2y and 3z 3z or x > 2* 3z or x > 6z

Explanation

Only option A is correct as other options do not satisfy the given inequalities.

x > 2y and z 2y and 3z 3z or x > 2* 3z or x > 6z

16) If p#q@r = (p + q + r)(p² + q² + r²), then find the value of 8#5@2.

A. 15

B. 80

C. 120

D. 135

E. 1395

Option A is not correct. 8#5@2 ≠ 15
Option B is not correct. 8#5@2 ≠ 80
Option C is not correct. 8#5@2 ≠ 120
Option D is not correct. 8#5@2 ≠ 135
Option E is correct. According to the give rule,
Here p = 8, q = 5, and r = 2,
hence, 8#5@2 = (8 + 5 + 2 )(8^2 + 5^2 + 2^2)
= 15 * (64 + 25 + 4)
= 15 * 93
= 1395

Explanation

Option A is not correct. 8#5@2 ≠ 15
Option B is not correct. 8#5@2 ≠ 80
Option C is not correct. 8#5@2 ≠ 120
Option D is not correct. 8#5@2 ≠ 135
Option E is correct. According to the give rule,
Here p = 8, q = 5, and r = 2,
hence, 8#5@2 = (8 + 5 + 2 )(8^2 + 5^2 + 2^2)
= 15 * (64 + 25 + 4)
= 15 * 93
= 1395

17) The percent increase from 8 to 14 is equal to the percent increase from 12 to what number.

A. 21

B. 28

C. 14

D. 16

E. 24

As the calculated answer is not equal to the other options only option A is correct.This problem can be solved either using percentages or ratios.
Using ratios makes it simpler.
(14 - 8)/8 = (x - 12)/1 2
Or 6/8 = (x - 12)/12
Or (x - 12) * 8 = 6 * 12
Or x - 12 = 72/8 or x - 12 = 9 or x = 9 + 12 or x = 21
Therefore, the required number is 21.

Explanation

As the calculated answer is not equal to the other options only option A is correct.This problem can be solved either using percentages or ratios.
Using ratios makes it simpler.
(14 - 8)/8 = (x - 12)/1 2
Or 6/8 = (x - 12)/12
Or (x - 12) * 8 = 6 * 12
Or x - 12 = 72/8 or x - 12 = 9 or x = 9 + 12 or x = 21
Therefore, the required number is 21.

18) If x and y are multiples of 3, which of the following cannot also be a multiple of 3?

A. x + y

B. xy

C. xy + 3

D. x - y

E. x + y + 1

Option A is not correct. x + y is a multiple of 3. For example 6 and 15 are multiples of 3, 6 + 15 = 21 is also a multiple of 3.
Option B is not correct. xy is a multiple of 3. For example 6 and 9 are multiples of 3 their product 6 * 9 = 54 is also a multiple of 3.
Option C is not correct. xy + 3 is a multiple of 3. For example 3 and 6 are multiples of 3. 3 * 6 + 3 = 21 is also a multiple of 3.
Option D is not correct. For example 12 and 9 are multiples of 3, 12 - 9 = 3 is also a multiple of 3.
Option E is correct. For example 6 and 21 are multiples of 3, 6 + 21 + 1 = 28 is not a multiple of 3.

Explanation

Option A is not correct. x + y is a multiple of 3. For example 6 and 15 are multiples of 3, 6 + 15 = 21 is also a multiple of 3.
Option B is not correct. xy is a multiple of 3. For example 6 and 9 are multiples of 3 their product 6 * 9 = 54 is also a multiple of 3.
Option C is not correct. xy + 3 is a multiple of 3. For example 3 and 6 are multiples of 3. 3 * 6 + 3 = 21 is also a multiple of 3.
Option D is not correct. For example 12 and 9 are multiples of 3, 12 - 9 = 3 is also a multiple of 3.
Option E is correct. For example 6 and 21 are multiples of 3, 6 + 21 + 1 = 28 is not a multiple of 3.

19) If a and b are the lengths of the legs of a right triangle whose hypotenuse is 10 units and whose area is 20 square units, what is the value of (a + b)²?

A. 120

B. 10

C. 20

D. 100

E. 180

As other options are not equal to the calculated answer, only option E is correct. Let the sides of the right triangle be a, b and c in increasing order. Hence, c is its hypotenuse. According to Pythagora's theorem,
a^2 + b^2 = c^2, or a^2 + b^2 = 102 or a^2 + b^2 = 100
Area of a right triangle = 1/2 ab or 1/2 ab = 20 or ab = 40
(a+b)^2 = a^2 + b^2 + 2ab = 100 + 2 * 40 = 180

Explanation

As other options are not equal to the calculated answer, only option E is correct. Let the sides of the right triangle be a, b and c in increasing order. Hence, c is its hypotenuse. According to Pythagora's theorem,
a^2 + b^2 = c^2, or a^2 + b^2 = 102 or a^2 + b^2 = 100
Area of a right triangle = 1/2 ab or 1/2 ab = 20 or ab = 40
(a+b)^2 = a^2 + b^2 + 2ab = 100 + 2 * 40 = 180

20) If a - 5/6 = 1/243, then what does a equal?

A. 3

B. 81

C. 243

D. 729

E. 27

Option A is not correct. 1/243 = 3^-5, If a = 3, then 3^-5/6 6z^2 - 11z + 4 ≠ 3^-5
Option B is not correct. 1/243 = 3^-5. If a = 81, then (81)^-5/6 = (3^4)^-5/6 ≠ 3^-5
Option C is not correct. 1/243 = 3^-5. If a = 243, then (243)^-5/6 = (3^5)^-5/6 ≠ 3^-5
Option D is not correct 1/243 = 3^-5. If a = 729, then (729)^-5/6 = (^6)^-5/6 ≠ 3^-5
Option E is not correct 1/243 = 3^-5. If a = 3, then (27)^-5/6 = (^3)^-5/6 ≠ 3^-5

Explanation

Option A is not correct. 1/243 = 3^-5, If a = 3, then 3^-5/6 6z^2 - 11z + 4 ≠ 3^-5
Option B is not correct. 1/243 = 3^-5. If a = 81, then (81)^-5/6 = (3^4)^-5/6 ≠ 3^-5
Option C is not correct. 1/243 = 3^-5. If a = 243, then (243)^-5/6 = (3^5)^-5/6 ≠ 3^-5
Option D is not correct 1/243 = 3^-5. If a = 729, then (729)^-5/6 = (^6)^-5/6 ≠ 3^-5
Option E is not correct 1/243 = 3^-5. If a = 3, then (27)^-5/6 = (^3)^-5/6 ≠ 3^-5