Algebra
What is 44 · 47?
A) 411 B) 428 C) 1611 D) 1628 E) 811
A) 411
How many different goody bag combinations can you make from a choice of a red or blue pen, three different flavors of juice box, and seven different kinds of chips (each goody bag must have a pen, a juice box, and a bag of chips)?
A) 14 B) 21 C) 28 D) 42 E) 56
D) 42
Rayna has a standard deck of 52 cards. What is the probability that she draws 2 consecutive hearts without replacement?
A) 1/16 B) 1/17 C) 3/52 D) 1/169 E) 3/169
B) 1/17
What is the Greatest Common Factor of 132 and 204?
A) 4 B) 17 C) 6 D) 11 E) 12
E) 12
The diameters of two circles are 8 inches and 12 inches respectively. The ratio of the area of the smaller to the area of the larger circle is:
A) 2/3 B) 4/9 C) 9/4 D) 1/2 E) None of these
B) 4/9
If the graphs of 2y + x + 3 = 0 and 3y + ax + 2 = 0 are perpendicular, the value of a is:
A) 2/3 B) -2/3 C) -3/2 D) 6 E) -6
E) -6
An ant stands on the bottom-left corner of a 5x5 grid. How many paths are there to get to the top-right corner considering the ant only moves up and right?
A) 192 B) 216 C) 252 D) 264 E) 288
C) 252
What is the probability that Andrew rolls a sum of 8 with a pair of dice?
A) 1/9 B) 5/36 C) 1/6 D) 7/36 E) 5/6
B) 5/36
Which of the following represents 45 in base-6?
A) 416 B) 456 C) 736 D) 1136 E) 1256
D) 1136
When the base of a triangle is increased 10% and the altitude to this base is decreased 10%, the change in area is:
A) 1% increase B) 0.5% increase C) 0% D) 0.5% decrease E) 1% decrease
E) 1% decrease
Ethan can mow a lawn in 8 hours and Floppa can mow the same lawn in 6 hours. How many hours will it take to mow 35 lawns if they work together?
A) 80 B) 96 C) 120 D) 140 E) 144
C) 120
A number is considered to be "swag" if it is divisible by neither 5 nor 7. How many positive integers less than 1000 are swag?
A) 688 B) 686 C) 684 D) 658 E) 630
B) 686
Jason has 4 red balls and 4 blue balls lined up in a row. What is the probability that, after Jason swaps the positions of two balls, there is no net change in the order of the balls?
A) 1/4 B) 3/7 C) 1/2 D) 4/7 E) None of these
B) 3/7
Let A be a digit in 318A543. What value of A makes the number divisible by both 3 and 11?
A) 0 B) 3 C) 5 D) 6 E) 9
B) 3
A pentagon is formed by cutting a triangular corner from a rectangular piece of paper. The five sides of the pentagon have lengths 13, 19, 20, 25 and 31, although this is not necessarily their order around the pentagon. The area of the pentagon is:
A) 459 B) 600 C) 680 D) 720 E) 745
E) 745
For a given arithmetic series the sum of the first 50 terms is 200, and the sum of the next 50 terms is 2700. The first term in the series is:
A) -1221 B) -21.5 C) -20.5 D) 3 E) 3.5
C) -20.5
Six straight lines are drawn in a plane with no two parallel and no three concurrent. The number of regions into which they divide the plane is:
A) 16 B) 20 C) 22 D) 24 E) 26
C) 22
Four distinct points, A, B, C, and D, are to be selected from 2023 points evenly spaced around a circle. All quadruples are equally likely to be chosen. What is the probability that the chord AB intersects the chord CD?
A) 1/4 B) 1/3 C) 1/2 D) 2/3 E) 3/4
B) 1/3
Find the last non-zero digit of 11!.
A) 1 B) 2 C) 4 D) 6 E) 8
E) 8
The length of rectangle ABCD is 5 inches and its width is 3 inches. Diagonal AC is divided into three equal segments by points E and F. The area of triangle BEF, expressed in square inches, is:
A) 3/2 B) 5/3 C) 5/2 D) 15/2 E) 15/34
C) 5/2
Let the roots of ax2 + bx + c = 0 be r and s. The equation with roots ar + b and as + b is:
A) x2 - bx - ac = 0 B) x2 - bx + ac = 0 C) x2 + 3bx + ca + 2b2 = 0 D) x2 + 3bx - ca + 2b2 = 0 E) x2 + bx(2 - a) + a2c + b2(a + 1) = 0
B) x2 - bx + ac = 0
Nine chairs in a row are to be occupied by six students and Presidents Obama, Trump, and Biden. These three presidents arrive before the six students and decide to choose their chairs so that each president will be between two students. In how many ways can Presidents Obama, Trump, and Biden choose their chairs?
A) 12 B) 36 C) 60 D) 84 E) 630
C) 60
A box contains 3 red balls and 4 blue balls. One by one, balls are drawn at random from the box and not replaced. If the probability is a/b that it will take more than four draws until the third red ball appears and a/b is in lowest terms, then a + b =
A) 11 B) 20 C) 35 D) 58 E) 66
E) 66
Find the remainder when 2! + 4! + 6! + 8! + 10! + … + 4046! is divided by 35.
A) 11 B) 19 C) 24 D) 27 E) None of these
A) 11
A girls' camp is located 300 feet from a straight road. On this road, a boys' camp is located 500 feet from the girls' camp. It is desired to build a canteen on the road which will be exactly the same distance from each camp. The distance of the canteen from each of the camps in feet is:
A) 400 B) 250 C) 87.5 D) 200 E) None of these
E) None of these