# HARDEST SAT MATH QUESTIONS (Part - 8)

Question 1 :

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

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?

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.

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

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

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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