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

=

number of  landscaper

x

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)  (9a+ 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 3afor 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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