October 2014 - week 1

Vocabulary

100

promontory

What is high point of land which juts into the water on the coastline

200

scrimmage

What is a minor competition between two teams; a confused fight

300

Accelerograph

What is instrument for measuring and recording motion of the ground during an earthquake

400

Currant

What is small raisin having no seeds

500

Sorority

What is a club consisting of women in college

Number Theory

100

Each of A, B, C, D, E are distinct numbers from the set {2,15,25,31,34} such that A is prime, B is even, C and D are multiples of 5, and A

What is 31 ************* Since A is prime, it is either 2 or 31. Since B is even and greater than A it must be 34. Since C and D are multiples of 5 they must be 15 and 25 (not necessarily in that order). So E must be 31.

200

Bill has cows, pigs and chickens on his farm. The number of chickens he has is three times the number of pigs, and the number of pigs he has is 2 more than the number of cows. Which of the following could be the total number of these animals? (A) 14 (B) 15 (C) 16 (D) 17 (E) 18

What is (E) 18 **************** If we let x represent the number of cows, then the number of pigs is x + 2, and the number of chickens is 3(x + 2). Thus, the total number of animals is x + (x + 2) + 3(x + 2) = x + x + 2 + 3x + 6 = 5x + 8. So some possible totals are 13, 18, 23, … which we get by substituting 1, 2, 3, … for x. Substituting 2 in for x gives 18 which is answer choice (E).

300

If p is the greatest prime factor of 34 and q is the smallest prime factor of 77, what is the value of pq?

What is 119 ****************** The prime factorization of 34 is 2·17. So p = 17. The prime factorization of 77 is 7·11. So q = 7. Therefore pq = 17·7= 119.

400

How much less than Z + 4 is Z - 3 ?

What is 7 *****************

500

If k is divided by 9, the remainder is 7. What is the remainder if 4k is divided by 6?

What is 4? ******** Let’s choose a positive integer whose remainder is 7 when it is divided by 9. A simple way to find such a k is to add 9 and 7. So let k = 16. Then we have 4k = 4·16 = 64. 6 goes into 64 ten times with a remainder of 4.

Algebra

100

If 3^x = 11, then 3^2x = (A) 5.5 (B) 22 (C) 33 (D) 121 (E) 1331

What is (D) 121 ******************* 32x = (3x)2 = 112 = 121. Thus, the answer is choice (D).

200

Which of the following expressions is equivalent to 15 less than the product of x and y ? (A) x + y - 15 (B) xy - 15 (C) 15xy (D) 15(x - y) (E) (x-15)y

What is (B) xy 15 ****************** The product of x and y is xy, and so 15 less than the product of x and y is xy – 15, choice (B).

300

Dawn is selling 5d CDs at a price of p dollars each. If x is the number of CDs she did not sell, which of the following represents the total dollar amount she received in sales from the CDs? (A) px - 5d (B) 5d - px (C) 5pd - x (D) p(x - 5d) (E) p(5d - x)

What is (E) p(5d - x)? ********************* Dawn sold (5d – x) CDs (5d is the total and x is the number she did not sell). Thus the total dollar amount Dawn received in sales is p(5d – x) (here p is the price per CD and (5d – x) is the number of CDs that Dawn sold). Thus, the answer is choice (E).

400

If y/z = -3, then y + 3z = , then (A) -1 (B) 0 (C) 1 (D) y (E) z

What is (B) 0 ********************** Multiplying each side of the equation by z gives us y = -3z. We now add 3z to each side to get y + 3z = 0, choice (B)

500

If x is 3/5 of y, and y is 5/7 of z, what is the value of z/x? (A) 1/4 (B) 3/7 (C) 5/4 (D) 10/7 (E) 7/3

What is (E) 7/3 ? ************************* x = 3y/5 and y = 5z/7. Solving the last equation for z gives us z= 7y/5. Then z/x = 7y/5 / 3y/5 = (7y/5) * (5/3y) = 7/3 Thus, the answer is choice (E).

Geometry

100

C:\home\SAT\Oct2014\fig1.jpg

What is (C) y = 1(1/2)x + 2 ***************** (0, 2) is the y-intercept of the point. Thus, b = 2. The slope of the given line is m = -2/4 = -1/2 Thus, the equation of the line is y = –(1/2)x + 2, choice (C).

200

C:\home\SAT\Oct2014\fig2.jpg

What is 28 Since there are 180 degrees in a triangle, the other interior angle is 180 – 32 – 61 = 87 degrees. Furthermore, the measure of an exterior angle to a triangle is the sum of the measures of the two opposite interior angles of the triangle. So we have x = 87 + 32 = 119 y = 32 + 61 = 93 z = 87 + 61 = 148 So, x + y + z = 119 + 93 + 148 = 360.

300

C:\home\SAT\Oct2014\fig2.jpg

What is 2? ******************** Slope formula (2b - 0) / (0 - (-b)) = 2b / b = 2

400

Which of the following is an equation of the line in the -plane that passes through the point (0,-3) and is perpendicular to the line y = (1/4)x + 7? (A) y = -4x - 6 (B) y = -4x - 3 (C) y = -4x + 3 (D) y = (1/4)x + 3 (E) y = (1/4)x + 6

What is 8 ? ***************** y = mx + b (0,-3) is the y-intercept of the point. Thus, b = -3. The slope of the given line is 1/4. Since the new line is perpendicular to this line, its slope is -4, and the equation of the new line is y = -4x – 3, choice (B).

500

C:\home\SAT\Oct2014\fig4.jpg

What is 0

Statistics

100

There are exactly 13 coins in a bag. There are 4 pennies, 2 nickels, 3 dimes, and the rest are quarters. If one coin is selected at random from the bag, what is the probability that the coin is a quarter?

What is 4/13 *************** The number of quarters in the bag is 13 – 4 – 2 – 3 = 4. Therefore the probability of selecting a quarter from the bag is 4/13.

200

In a jar there are exactly 75 marbles, each of which is yellow, purple, or blue. The probability of randomly selecting a yellow marble from the jar is 2/5, and the probability of randomly selecting a purple marble from the jar is 1/5. How many marbles in the jar are blue?

What is 30 ********************** The probability of selecting a blue marble from the jar is 1 – 2/5 - 1/5 = 2/5. Therefore the number of blue marbles in the jar is(2/5)(75) = 30.

300

A number is to be selected at random from the list 3, 5, 6, 15, 27, 35, 45, 75. What is the probability that the number selected will be a multiple of both 3 and 5?

What is 3/8 ? ******************** The total number of outcomes is 8. The number of “successes” is 3. Therefore the probability is 3/8 or .375.

400

There are y tiles in a row. If one tile is to be selected at random, the probability that it will not be cracked is 6/7. In terms of y, how many of the tiles are cracked?

What is y/7 ? ******************* Let x be the number of cracked tiles. It follows that x/y = 1/7. Now cross multiply and divide to solve for x. 7x = y, and therefore x = y/7.

500

If the letters from the list Y, A, R, Z, C are to be randomly ordered, what is the probability that the letters will appear in the order C, R, A, Z, Y?

What is 1/120 *********************** The total number of arrangements of the five letters given is (5)(4)(3)(2)(1) = 120. Only one of these results in C, R, A, Z, Y. Therefore the probability is 1/120 which is approximately 008333333. So we grid in .008