GRE Math Exam 146 Questions with Verified Answers
The sum of the angles in a quadrilateral is - CORRECT ANSWER 360°
Any n-sided polygon can be
... [Show More] divided into how many triangles? (by drawing diagonals from one vertical) - CORRECT ANSWER n-2
The sum of the measures of the n angles in a polygon with n sides - CORRECT ANSWER (n-2) x 180
In any polygon, all external angles equal up to - CORRECT ANSWER 360°
If you measure all exterior angles in a polygon, they all equal - CORRECT ANSWER 360°
In any Regular Polygon, the measure of each interior angle - CORRECT ANSWER (n-2)x180/n
In a Regular Polygon, the measure of each exterior angle - CORRECT ANSWER 360/n
The consecutive angles in a parallelogram equal - CORRECT ANSWER 180°
A quadrilateral where two diagonals bisect each other - CORRECT ANSWER Parallelogram
In a rectangle, all angles are - CORRECT ANSWER Right
In a Rectangle, each angles measures - CORRECT ANSWER 90°
Each diagonal divides a square into 2 - CORRECT ANSWER 45 45 90 Right triangles (x, x, x*square root of 2)
What kind of trapezoid has equal parallel sides? - CORRECT ANSWER Isosceles Trapezoid
The Perimeter of a rectangle - CORRECT ANSWER P=2(l+w)
The Perimeter of a Square - CORRECT ANSWER P=4s (s=side)
Area of a Parallelogram: - CORRECT ANSWER A=(base)(height)
Area of a Rectangle: - CORRECT ANSWER A=(side)² or A=½(diagonal)²
Area of a Trapezoid: - CORRECT ANSWER A=½(base₁+base₂)(height)
For any given perimeter, the rectangle with the largest AREA is a - CORRECT ANSWER Square (versus a rectangle)
For any given Area, the rectangle with the smallest perimeter is a - CORRECT ANSWER Square (versus a rectangle)
(x-y)(x+y) - CORRECT ANSWER x²-y²
(x-y)² - CORRECT ANSWER x²-2xy+y²
(x+y)² - CORRECT ANSWER x²+2xy+y²
An Angle that's 180° - CORRECT ANSWER Straight Angle
The sum of all angles around a point - CORRECT ANSWER 360°
If one of the angles formed by an intersection is right, they're all right - CORRECT ANSWER True
If a pair of parallel lines is cut by a transversal that's not perpendicular, the sum of any acute angle and any obtuse angle is - CORRECT ANSWER 180
Distance - CORRECT ANSWER (rate)(time) d=rt
Rate - CORRECT ANSWER d/t (distance)/(time)
Time - CORRECT ANSWER (distance)/(rate) d/r
Average - CORRECT ANSWER Sum/n
Sum of numbers in an average - CORRECT ANSWER n/Average
The total deviation below the average is equal to - CORRECT ANSWER The total deviation above the average (80, 90, 90, 90, 100)
Assume that the average of a set of numbers is A. If a number x is added to the set and a new average is calculated, then the new average will be less than, equal to, or greater than A, depending on whether x is less than, equal to , or greater than A, respectfully. - CORRECT ANSWER 1+2+3/3=2 1+2+3+4/4=10/4=2.5
If "n" is even, the average of the numbers is the average of what? - CORRECT ANSWER The middle two terms (10, 20, 30, 40, 50, 60) 30+40/2=35
To calculate the weighted average: Multiply each number in the set by the number of times it appears, add all the products, and divide by the total number of numbers in the set. - CORRECT ANSWER ...
In a set of n numbers that are arranged in increasing order, it is the middle number, if n is odd or the average of the middle two if it is even. - CORRECT ANSWER Median
It is the number in the set that occurs most often - CORRECT ANSWER Mode
Ratios: If a set of objects is divided into 2 groups in the ratio of a:b, then the first group contains - CORRECT ANSWER a/a+b and the second group contains b/a+b of the objects. 4:6 becomes 4/4+6=4/10=2/5 6/4+6=6/10=3/5
If two numbers are in the ratio of a:b (2:4), then for some number x (3), the first number is ax (2x3) and the second number is bx (4x3). If the ratio is in the lowest terms, and if the quantities must be integers, then x(3) is also an integer. - CORRECT ANSWER 2(3)+4(3)=6(3)
If a set of objects is divided into 3 groups in the radio a:b:c, then the first group contains a/a+b+c, second group contains b/a+b+c, etc. - CORRECT ANSWER 2:3:4
An equation that states that two ratios are equivalent i.e. 4/6=10/15=2/3 - CORRECT ANSWER Proportion
How do you solve proportions? - CORRECT ANSWER Cross multiplication a/b=c/d ad=cb 4/6=10/15
4(15)=6(10) 60=60
A fraction that compares two quantities measures in different units - CORRECT ANSWER Rate. "Miles per hour" "Dollars per week" "cents per ounce" "students per classroom"
½% of 100 is - CORRECT ANSWER ½
a% of b - CORRECT ANSWER b% of a
The percent increase of a quantity - CORRECT ANSWER (Actual increase/original amount)100%
If a lamp increases from $80 to $100, what is the percent increase? - CORRECT ANSWER 25%. (actual increase/original amount)100%
20/80x100%=1/4x100%=25%
The percent decrease of a quantity - CORRECT ANSWER (actual decrease/Original amount)100%
If a lamp decreases to $80, from $100, what is the decrease in price? - CORRECT ANSWER (actual decrease/Original amount)100%
20/100x100% is 20%
If aalways results in a larger increase than a single increase of (a+b)% - CORRECT ANSWER True
An increase (or decrease) of a% (50%) followed by another increase (or decrease) of a% (50%) is NEVER the same as a single increase/decrease of 2a% (100%) - CORRECT ANSWER True
If a number is the result of increasing another number by k%, to find the original number - CORRECT ANSWER divide by 1+k%
125=100+25%
125÷1.25=100
If a number is the result of decreasing another number by k%, to find the original number - CORRECT ANSWER divide it by 1-k%
75=100-25%
75÷(1-25)=75÷.75=100
THE DENOMINATOR CAN NEVER - CORRECT ANSWER BE ZERO! 1/∅=null
If a>b then - CORRECT ANSWER -a<-b
The reciprocal of any non-zero number - CORRECT ANSWER 1/x
To divide any number by a fraction, multiply number by the reciprocal of the fraction - CORRECT ANSWER 20÷2/3=20/1x3/2=30
To simplify a complex fraction, multiply every term in the numerator and denominator by the least common multiple of all the denominators that appear in the fraction. - CORRECT ANSWER Simplify numerators and denominators and divide
Probability of an Event - CORRECT ANSWER P(E)=number of favorable outcomes/total number of possible outcomes
If Event is impossible - CORRECT ANSWER P(E)=ø
If E is certain - CORRECT ANSWER P(E)=1/1=1
Probability of Event all cases - CORRECT ANSWER ∅≤P(E)≤1
Probability of E not occurring: - CORRECT ANSWER 1-P(E)
If an experiment is done 2 or more times, the probability that first one event (heads) will occur and then a second event (heads) will occur is a product of the probabilities. - CORRECT ANSWER Heads 1/2x1/2x1/2=1/8
Formula if two jobs need to be completed and there are m ways to do the first job and n ways to do the second job. - CORRECT ANSWER mxn
Pi - CORRECT ANSWER Circumference/diameter c/d
Circumference of a circle - CORRECT ANSWER pi(diameter)
Circumference of a circle - CORRECT ANSWER 2(pi)r
Area of a circle - CORRECT ANSWER (pi)r²
If an arc measures x, the length of the arc is - CORRECT ANSWER x/360 x 2(pi)r or x/360 x C
The area of a sector formed by an arc and 2 radii - CORRECT ANSWER x/360 x (pi)r² or x/360 x A
Volume of a Cylinder - CORRECT ANSWER (pi)r²h
Surface area of a cylinder - CORRECT ANSWER 2(pi)rh
The surface area of a cynlinder plus top and bottom - CORRECT ANSWER 2(pi)rh+2(pi)r²
Volume of a rectangular solid - CORRECT ANSWER (length)(width)(height)
Volume of a cube - CORRECT ANSWER edge³
Surface area of a rectangular solid - CORRECT ANSWER 2(lw+lh+wh)
Formula for the surface area of a cube - CORRECT ANSWER 6e²
Formula for a diagonal - CORRECT ANSWER l²+w²+h²=d²
Volume of a Sphere - CORRECT ANSWER 4/3(pi)r³
Vertical lines - CORRECT ANSWER Do not have slopes!
Any Horizontal line slope - CORRECT ANSWER zero
Slope of any line that goes up from left to right - CORRECT ANSWER Positive
Slope of any line that goes down as you move from left to right is - CORRECT ANSWER Negative
Slope - CORRECT ANSWER y₂-y₁/x₂-x₁
Distance Formula - CORRECT ANSWER d=Square root of (x₂-x₁)²+(y₂-y₁)²
For any number x - CORRECT ANSWER Can be negative, zero, or positive
X is the opposite of - CORRECT ANSWER -X
3 is the opposite of - CORRECT ANSWER -3
The only number that is equal to its opposite - CORRECT ANSWER ∅ ∅=∅
Product of any number and ∅ is - CORRECT ANSWER ∅
If a product of two numbers is ∅, one number must be - CORRECT ANSWER ∅
7 divided by ∅ - CORRECT ANSWER Null
∅ divided by 7 - CORRECT ANSWER ∅
The product of odd number of negative numbers - CORRECT ANSWER Negative
The reciprocal of any non-zero #x is - CORRECT ANSWER 1/x
The product of any number x and its reciprocal - CORRECT ANSWER 1
Dividing by a number is the same as multiplying it by its - CORRECT ANSWER Reciprocal
∅ Is neither - CORRECT ANSWER Positive or Negative
Consecutive integers - CORRECT ANSWER x, x+1, x+2
One is - CORRECT ANSWER NOT A PRIME
Positive integers that have exactly 2 positive divisors are - CORRECT ANSWER Prime numbers (2, 3, 5, 7, 11, 13, 17, 19, 23)
∅ Is - CORRECT ANSWER EVEN
∅ is a multiple of - CORRECT ANSWER Two (∅×2=∅)
∅ is a multiple of - CORRECT ANSWER Every number
2 is the only - CORRECT ANSWER Even prime number
b¹ - CORRECT ANSWER 1
bⁿ - CORRECT ANSWER b∧b∧b (where b is used as a factor n times)
2⁵+2³ - CORRECT ANSWER 2⁸
2⁵/2³ - CORRECT ANSWER 2²
(2²)³ - CORRECT ANSWER 2⁶
2³×7³ - CORRECT ANSWER (2x7)³
∅² - CORRECT ANSWER ∅
If a is positive, aⁿ is - CORRECT ANSWER Positive
If a is negative and n is even - CORRECT ANSWER aⁿ is positive
-3² - CORRECT ANSWER 9
-3³ - CORRECT ANSWER -27
a(b+c) - CORRECT ANSWER ab+ac
a(b-c) - CORRECT ANSWER ab-ac
b+c/a - CORRECT ANSWER b/a+c/a
b-c/a - CORRECT ANSWER b/a-c/a
a>b - CORRECT ANSWER a-b is positive
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