HARDEST SAT MATH QUESTIONS (Part - 8)

Question 1 :

If a = 5√2 and 2a = √(2x), what is the value of x?

Answer : 

2a = √(2x)

Substitute a = 5√2.

2(5√2)  =  √(2x)

10√2  =  √(2x)

Square both sides. 

(10√2)²  =  [√(2x)]²

10²(√2)²  =  2x

100(2)  =  2x

200  =  2x

Divide each side by 2. 

100  =  x

Question 2 :

Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?

Answer : 

Wyatt can husk at least 12 dozen ears of corn per hour. 

Maximum time required to husk 72 dozen of ears : 

=  72/12

=  6 hours

He can husk at most 18 dozen ears of corn per hour.

Minimum time required to husk 72 dozen of ears : 

=  72/18

=  4 hours

Therefore, the possible times it could take Wyatt to husk 72 dozen ears of corn are 4 hours to 6 hours, inclusive.

Question 3 :

A landscaping company estimates the price of a job, in dollars, using the expression 60 + 12nh, where n is the number of landscapers who will be working and h is the total number of hours the job will take using n landscapers. Which of the following is the best interpretation of the number 12 in the expression?

A) The company charges $12 per hour for each  landscaper.

B)  A minimum of 12 landscapers will work on each job.

C)  The price of every job increases by $12 every hour.

D)  Each landscaper works 12 hours a day.

Answer :

The price of the job, in dollars, is calculated using the expression 60 + 12nh, where 60 is a fixed price and 12nh  is a variable price which depends on the number of landscapers and number of hours each landscaper works. 

nh ----> number of  landscaper times number of hours each landscaper 

nh ----> total number of hours works done by n landscapers. 

Because 'nh' is multiplied by 12 in the given expression, 12 is the money paid for each hour of work done. 

The correct option is (A).

Question 4 :

9a⁴ + 12a²b² + 4b⁴

Which of the following is equivalent to the expression shown above?

A)  (3a² + 2b²)²

B)  (3a + 2b)⁴

C)  (9a² + 4b²)²

D)  (9a + 4b)⁴

Answer :

9a⁴ + 12a²b² + 4b⁴ :

=  3²(a²)² + 12a²b² + 2²(b²)²

=  (3a²)² + 2(3a²)(2b²) + (2b²)²

Let x = 3a², y = 2b².

=  x² + 2xy + y²

Use algebraic identity (a + b)² = a² + 2ab + b².

=  (x + y)²

Substitute 3a² for x and 2b²for y. 

=  (3a² + 2b²)²

The correct option is (A).

Question 5 :

nA = 360

The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 50°, what is the greatest number of sides it can have?

A)  5

B)  6

C)  7

D)  8

Answer :

nA  =  360

Divide each side by n. 

A  =  360/n

It is given that the measure of A is greater than 50°.

A > 50

Substitute 360/n for a. 

360/n > 50

Multiply each side by n.

360 > 50n

50n < 360

Divide each side by 50.

n < 72

n has to be less than 7.2 and also n is an integer. 

n  =  7

The correct option is (C). 

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