10 Tricky SAT Math Questions with Answers

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Question 1 :

If r = 0.345, s = (0.345)² and t = √0.345, which of the following is the correct ordering of r, s and t?

A) r < s < t

B) r < t < s

C) s < t < r

D) s < r < t

Answer :

Given r = 0.345, s = (0.345)² and t = √0.345.

s = r²

t = √r

Since the value of r (= 0.345) is less than 1, it can be written as an inequality.

r < 1

Multiply both sides by r.

r ⋅ r < r ⋅ 1

r² < r

Plug in s for r².

s < r ----(1)

Take square root on both sides.

√r = √1

√r = 1

Multiply both sides by √r.

√r ⋅ √r < √r ⋅ 1

r < √r

Plug in t for √r.

r < t ----(2)

Combining (1) and (2),

s < r < t

The correct answer choice is (D).

Question 2 :

A) 3/2

B) 2/3

C) 15/7

D) 7/15

Answer :

Question 3 :

Volume of a cylinder is 6000π cm³. The radius is increased by 10% and the height is decresed by 20%. Which of the following is the volume of new cylinder?

A) 5808π cm³

B) 5832π cm³

C) 5280π cm³

D) 6480π cm³

Answer :

Let r, h and V be the radius, height and volume of the original cylinder respectively.

V = πr²h = 6000π cm³

Given : The radius is increased by 10% and the height is decresed by 20%.

New Radius :

= (100 + 10)% ⋅ r

= 110% ⋅ r

= 1.1r

New Height :

= (100 - 20)% ⋅ h

= 80% ⋅ h

= 0.8h

Volume of New Cylinder :

= π(1.1r)²(0.8h)

= π(1.1)²r²(0.8h)

= π(1.21)r²(0.8h)

= 0.968πr²h

Plug in πr²h = 6000π cm³.

= 0.968 ⋅ 6000π cm³

= 5808π cm³

The correct answer choice is (A).

Question 4 :

If the function f is defined by f[(x – 1)/3] = x² + 1, which of the following equations gives the function f(x)?

A) f(x) = 3x² + 2x + 1

B) f(x) = 3x² + 2x + 2

C) f(x) = 9x² + 6x + 1

D) f(x) = 9x² + 6x + 2

Answer :

f[(x – 1)/3] = x² + 1 ----(1)

Let z = (x - 1)/3 and solve for z in terms of x.

z = (x - 1)/3

Multiply both sides by 3.

3z = x - 1

Add 1 to both sides.

3z + 1 = x

Plug in z = (x - 1)/3 on the left side and x = 3z + 1 on the right side in (1).

f(z) = (3z + 1)² + 1

f(z) = (3z + 1)(3z + 1) + 1

f(z) = 9z² + 3z + 3z + 1 + 1

f(z) = 9z² + 6z + 2

Replace z by x.

f(x) = 9x² + 6x + 2

The correct answer choice is (D).

Question 5 :

A parabola with vertex (2, –3) has two x-intercepts. Which of the following points must lie on the parabola?

A) (0, –4)

B) (3, –3)

C) (7, –5)

D) (–1, 15)

Answer :

Question 6 :

To prepare for class, Mr. Tom has to print a number of booklets with p pages per booklet. If every 5 pages cost c cents to print and he spent a total of d dollars, how many booklets did Mr. Tom print in terms of p, c and d?

A) cp/500d

B) 100d/cp

C) 500d/cp

D) 5d/cp

Answer :

From the given information, we have

c cents ----> 5 pages

To convert cents to dollars, divide the cents by 100.

c/100 dollars ----> 5 pages

Multiply both the quantities by 100.

c dollars ----> 500 pages ----(1)

Given : Mr. Tom spent a total of d dollars.

Find : Number of booklets printed by Mr.Tom in terms of p, c and d.

Multiply both the quantities of (1) by d/c.

(d/c) ⋅ c dollars ----> (d/c) ⋅ 500 pages

d dollars ----> 500d/c pages ----(2)

Given : There are p pages per booklet.

To convert 500d/c pages to booklets, divide 500d/c by p.

500d/c ÷ p = 500d/c ⋅ 1/p = 500d/cp booklets

(2)----> d dollars ----> 500d/pc booklets

The correct answer choice is (C).

Question 7 :

In triangle ABC, the measure of angle C is 90° and the length of AB is 30. If cos(A) = 5/6. What is the length of AC?

Answer :

Question 8 :

When the price of a product was decreased in the ratio 6 : 5, the sale of number of units increased in the ratio 3 : 4. If the revenue before the above changes was $3600, determine the revenue after changes.

Answer :

Question 9 :

In ΔABC, ∠C is right angle and m∠A = 30°. If the area of ΔABC is 84.5 √3 square units, what is the length of hypotenuse?

Answer :

Question 10 :

The average salary of a group of unskilled workers is $10,000 and that of a group of skilled workers is $15,000. If the two groups are combined, the average salary is $12,000. What is the percentage of skilled workers?

A) 30%

B) 40%

C) 50%

D) 60%

Answer :