logic
Sat math
Harder SAT math
100
There are two ducks in front of a duck, two ducks behind a duck and a duck in the middle. How many ducks are there?
Three. Two ducks are in front of the last duck; the first duck has two ducks behind; one duck is between the other two.
100
The ratio of a certain parallelogram’s height to its base is 40 to 75. If the parallelogram’s base is decreased by 9 inches, how must the height change to maintain the same ratio?
It must decrease by 4.8 inches
100
In △𝑋𝑌𝑍, cos(𝑍)=12/37 and ∠X is a right angle. What is the value of cos(𝑌)?
35/37
200
Bob is looking at Anne. Anne is looking at George. Bob is married, George is not, and we don't know if Anne is married. Is a married person looking at an unmarried person?
Yes. If Anne is married, then she is married and looking at George, who is unmarried. If Anne is unmarried, then Bob, who is married, is looking at her. Either way, the statement is correct.
200
In triangle ABC, angle B is a right angle. If sin(A) = 
, what is the value of sin(C)?
9/41
200
In the system of equations, y=−2 and y=x2+6x+b, where b is a positive constant, and there is precisely one unique real solution for the system. What is the value of 5b?
35
300
ou're at a fork in the road in which one direction leads to the City of Lies (where everyone always lies) and the other to the City of Truth (where everyone always tells the truth). There's a person at the fork who lives in one of the cities, but you're not sure which one. What question could you ask the person to find out which road leads to the City of Truth?
“Which direction do you live?” Someone from the City of Lies will lie and point to the City of Truth; someone from the City of Truth would tell the truth and also point to the City of Truth.
300
Out of a school of 300 students, 50 were chosen at random and asked to sample a new flavor of an energy drink and provide their opinions in a survey. Based on the results of the survey, it is estimated that 66% of students in the school dislike the flavor, with an associated margin of error of 9%. Based on these results, which of the following is a reasonable value for the total number of students in the school who dislike the new flavor?
1) 17
2) 33
3) 114
4) 188
4) 188
300
The function f(x)=(x−4)(x−1)(x+5) is given. In the xy-plane, the graph of y=g(x) is obtained by translating the graph of y=f(x) up 6 units. What is the value of g(2)?
-8
400
farmer wants to cross a river and take with him a wolf, a goat and a cabbage. He has a boat, but it can only fit himself, plus either the wolf, the goat or the cabbage. If the wolf and the goat are alone on one shore, the wolf will eat the goat. If the goat and the cabbage are alone on the shore, the goat will eat the cabbage. How can the farmer bring the wolf, the goat and the cabbage across the river without anything being eaten?
First, the farmer takes the goat across. The farmer returns alone and then takes the wolf across but returns with the goat. Then, the farmer takes the cabbage across, leaving it with the wolf and returning alone to get the goat.
400
In the xy-plane, a parabola has the equation y = –3x2 + 5x. If a line with the equation 3y = k intersects the parabola at exactly one point, and k is a constant, what is the value of k?
6.25
400
In the given equation, b is a positive integer. The equation has no real solution. What is the greatest possible value of b?
(-2x^2)+bx-800 = 0
A(78) B(79) C(80) D(81)
B(79)
Use the discriminant equation (b^2) - 4ac
(b^2)-4ac < 0 means no solution
500
. Four people are crossing a bridge at night, so they all need a torch—but they just have one that only lasts 15 minutes. Alice can cross in one minute, Ben in two minutes, Cindy in five minutes and Don in eight minutes. No more than two people can cross at a time; and when two cross, they have to go at the slower person's pace. How do they get across in 15 minutes?
Alice and Ben cross first in two minutes, and Alice crosses back alone with the torch in one minute. Then, the two slowest people, Cindy and Don, cross in eight minutes. Ben returns in two minutes, and Alice and Ben return in two minutes. They just made it in 15 minutes exactly.
500
There are exactly 8 positive integers greater than 10 in data set D. The list shown gives 7 of the integers from data set D.
18, 25, 17, 19, 27, 26, 29
The mean of these 7 integers is 23. If the mean of data set D is an integer that is less than 23, what is the value of the smallest integer from data set D?
15
500
A local council is assembling a task force to review the development of a community park. Of those asked to serve on the task force, 20% are community leaders, 35% are representatives from local businesses, 30% are city council members, and the remaining 9 individuals are volunteers. How many more representatives from local businesses were asked to serve on the task force than city council members?
3