Digital SAT Math Questions and Answers (Part - 2)

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Question 1 :

A bakery gave out coupons to celebrate its grand opening. Each coupon was worth either $1, $3 or $5. Twice as many $1 coupons were given out as $3 coupons and 3 times as many $3 coupons were given out as $5 coupons. The total value of all the coupons given out was $360. How many $3 coupons were given out?

A) 40

B) 45

C) 48

D) 54

Answer :

Question 2 :

3x + b = 5x - 7

3y + c = 5y - 7

In the equations above, b and c are constants. If b is c minus ½, which of the following is true?

A) x is y minus ¼

B) x is y minus ½

C) x is y minus 1

D) x is y plus ½

Answer :

Question 3 :

(4x + 4)(ax – 1) – x² + 4

In the expression above, a is a constant. If the expression is equivalent to bx, where b is a constant, what is the value of b?

A) -5

B) -3

C) 0

D) 12

Answer :

Question 4 :

If (x, y) is the solution to the system of equations above, what is the value of y?

Answer :

Question 5 :

mx – 6y = 10

2x – ny = 5

In the system of equations above, m and n are constants. If the system has infinitely many solutions, what is the value of m/n?

Answer :

Question 6 :

The equation 10z² + 3z + c = 0 has a solution of

What is the value of c?

Answer :

Question 7 :

y = -1.5

y = x² + 8x + a

In the given system of equations, a is a positive constant. The system has exactly one distinct real solution. What is the value of a?

Answer :

Question 8 :

In the xy-plane above, the graphs of y = x² – 4x + 5 and y = x + 1 intersect at points B and C. What is the area of the quadrilateral ABCD?

Answer :

Question 9 :

In the circle shown above, AB is a diameter. AB and CE are perpendicular to each other. If AD is 2 units long and DB is 8 units long, what is DE/DB?

Answer :

Question 10 :

A) -1/27

B) 1/3

C) -1/9

D) 9

Answer :

Question 11 :

In the given figure, four circles, each with radius 4, are tangent to each other. What is the area of the shaded region?

A) 16 - 4π

B) 64 - 4π

C) 64 - 8π

D) 64 - 16π

Answer :

Question 12 :

A right triangle has legs with lengths of 24 centimeters and 21 centimeters. If the length of this triangle’s hypotenuse, in centimeters, can be written in the form 3√d , where d is an integer, what is the value of d?

Answer :

Question 13 :

Two data sets of 23 integers each are summarized in the histograms shown. For each of the histograms, the first interval represents the frequency of integers greater than or equal to 10, but less than 20. The second interval represents the frequency of integers greater than or equal to 20, but less than 30, and so on. What is the smallest possible difference between the mean of data set A and the mean of data set B?

A) 0

B) 1

C) 10

D) 23

Answer :

Question 14 :

A cube is inscribed in a sphere where all the vertices intersect the sphere. The sphere has a radius 6√2. The volume of cube is k√6. What is the value of k?

Answer :

Question 15 :

What is the area in square units, of the triangle formed by connecting the three points shown?

Answer :

Question 16 :

The table above shows some values for the function f. If f is a linear function, what is the value of a + b?

A) 24

B) 36

C) 48

D) 60

Answer :

Question 17 :

A candle is made of 17 ounces of wax. When the candle is burning, the amount of wax in the candle decreases by 1 ounce every 4 hours. If 6 ounces of wax remain in this candle, for how many hours has it been burning?

A) 3

B) 6

C) 24

D) 44

Answer :

Question 18 :

Triangle FGH is similar to triangle JKL, where angle F corresponds to angle J and angles G and K are right angles. If sin(F) = ³⁰⁸⁄₃₁₈, what is the value of sin(J) ?

A) 75/317

B) 308/317

C) 317/308

D) 317/75

Answer :

Question 19 :

The product of two positive integers is 546. If the first integer is 11 greater than twice the second integer, what is the smaller of the two integers?

A) 7

B) 14

C) 39

D) 78

Answer :