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154 terms

GMAT QUANT 5

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(1/2)(b)(h)
Area of a triangle
A triangle with two equal sides and two equal angles is...
An isosceles triangle
(b)(h)
(f) Area of a parallelogram
(π)(r2)
(f) Area of a circle
(2)(π)(r)
(f) Circumference of a circle
(l)(w)(h)
(f) Volume of a rectangular solid
(f) Volume of a cube
(π)(r2)(h)
(f) Volume of a cylinder
180(n-2) n=number of sides
(f) Sum of interior angles of a polygon
Even exponents always result in...
A positive integer
An exponential expression with a base of 1 =
1
An exponential expression with a base of -1 =
-1 if the exponent is odd, 1 if the exponent is even
When the base of an exponential expression is a positive proper fraction, the value of the expression __________ as the exponent increases
decreases
When the base of an exponential expression is a positive decimal between 0 and 1, the value of the expression _________ as the exponent increases
decreases
(ab)ⁿ
aⁿbⁿ
(a+b)ⁿ ≠
aⁿ + bⁿ
aⁿ + bⁿ ≠
(a+b)ⁿ
nᵃnᵇ =
nᵃᶧᵇ
nᵃᶧᵇ =
nᵃnᵇ
When multiplying two exponential terms with the same base...
Combine exponents by adding
When can you combine exponents via addition?
When you are multiplying exponential terms with the same base
nᵃ/nᵇ =
nᵃ⁻ᵇ
nᵃ⁻ᵇ =
nᵃ/nᵇ
When dividing two exponential terms with the same base...
Combine exponents by subtracting
When can you combine exponents via subtraction?
When you are dividing exponential terms with the same base
(nᵃ)ᵇ =
nᵃᵇ
When raising a power to a power...
Combine exponents by multiplying
When can you combine exponents via multiplication?
When you are raising one power by another power
nˉᵃ =
1/nᵃ
1/nᵃ =
nˉᵃ
(n/m)ˉᵃ =
(m/n)ᵃ = mᵃ/nᵃ
(m/n)ᵃ = mᵃ/nᵃ =
(n/m)ˉᵃ
A negative exponent implies...
The reciprocal of the base
Any base raised to the first power is...
The base
n¹ =
n
-n¹ =
-n
What exponent is always implied on a number?
1
Any nonzero base raised to the power of 0 is...
1
n⁰ =
1
-n⁰ =
1
0⁰ =
Indeterminate
0⁰ ≠
1
For fractional exponents, the base number is raised to the _______ and taken to the root of the ________.
raise: numerator, root: denominator
nᵃʹᵇ =
ᵇ√(nᵃ) = (ᵇ√n)ᵃ
ᵇ√(nᵃ) =
(ᵇ√n)ᵃ = nᵃ/ᵇ
(ᵇ√n)ᵃ =
nᵃʹᵇ = ᵇ√(nᵃ)
(xᵃ)(xᵇ) =
xᵃ+ᵇ
xᵃ+ᵇ =
(xᵃ)(xᵇ)
(c⁴)(c⁵) =
c⁹
(3⁴)(3⁵) =
3⁹
5(5ⁿ) =
5ⁿ+¹
(aⁿ)(bⁿ) =
(ab)ⁿ
(ab)ⁿ =
(aⁿ)(bⁿ)
(2⁴)(3⁴) = (simplify)
6⁴
12⁵ = (simplify)
(4⁵)(3⁵) = (2¹⁰)(3⁵)
2⁵/2¹¹ = (simplify)
1/2ˉ⁶ = 2⁶
x¹⁰/x⁶ =
x⁴
(a/b)ⁿ =
aⁿ/bⁿ
aⁿ/bⁿ =
(a/b)ⁿ
(10/2)⁶ = (simplify)
10⁶/2⁶ = 5⁶
3⁵/9⁵ = (simplify)
(3/9)⁵ = (1/3)⁵ = 3ˉ⁵
aᵐⁿ =
(aᵐ)ⁿ = (aⁿ)ᵐ
(3⁴)⁵ =
(3⁵)⁴ = 3²⁰
xˉᵃ =
1/xᵃ
1/xᵃ =
xˉᵃ
(3/2)ˉ² =
(2/3)² = 4/9
2xˉ⁴ =
2/x⁴
27⁴ʹ³ =
³√(27⁴) = (³√27)⁴ = 3⁴ = 81
³√x¹⁵ =
x¹⁵ʹ³ = x⁵
aⁿ + aⁿ + aⁿ =
3aⁿ
3⁴ + 3⁴ + 3⁴ = (simplify)
3(3⁴) = 3⁵
3ⁿ + 3ⁿ + 3ⁿ =
3(3ⁿ) = 3ⁿ⁺¹
You can simplify exponential expressions that are linked by...
multiplication or division
You can not simplify exponential expressions that are linked by...
addition or subtraction
You can simplify exponential expressions linked by multiplication/division if...
they have an exponent or base in common
(x+y)² =
x² + 2xy + y²
(x-y)² =
x² - 2xy + y²
(d) Root
Radical, Opposite of an exponent
When taking the even root of a number, only use the...
nonnegative root
Odd roots have the _____ of the base
sign
Describe the numerator and denominator of a fractional exponent
numerator = power raised, denominator = root taken
You can find the root of a number by...
Breaking the number down into prime factors
You can simplity roots by combining/separating in...
multiplication or division
(d) Imperfect square
Square root of the the number is not an integer
How do you estimate the roots of imperfect squares?
Find the two closest perfect squares. If there is a coefficient, transfer it to under the root before searching for the two closest perfect squares
(ⁿ√x) / (ⁿ√y) =
ⁿ√(x/y)
(√10) / (√5) =
√2
(³√16) / ³(√2) =
³√8 = 2
(ⁿ√x)(ⁿ√y) =
ⁿ√(xy)
(√10)(√5) =
√50
(³√24)(³√9) =
³√216 = 6
ᵇ√xᵃ =
(ᵇ√x)ᵃ = ᵇ(√xᵃ) = xᵃʹᵇ
25³ʹ² = (solve)
(√25)³ = 5³ = 125
49ˉ¹ʹ² = (solve)
1/√49 = 1/7
⁵√x¹⁵ =
x¹⁵ʹ⁵ = x³
√(x+y) =
Cannot be simplified
√x + √y =
Cannot be simplified
√(x-y) =
Cannot be simplified
√x - √y =
Cannot be simplified
1² = (solve)
1
1.4² ≈ (solve)
2
1.7²≈ (solve)
3
2.25²≈ (solve)
5
2² = (solve)
4
3² = (solve)
9
4² = (solve)
16
5² = (solve)
25
6² = (solve)
36
7² = (solve)
49
8² = (solve)
64
9² = (solve)
81
10² = (solve)
100
11² = (solve)
121
12² = (solve)
144
13² = (solve)
169
14² = (solve)
196
15² = (solve)
225
16² = (solve)
256
20² = (solve)
400
25² = (solve)
625
30² = (solve)
900
√1 = (solve)
1
√2 ≈ (solve)
1.4
√3 ≈ (solve)
1.7
√5 ≈ (solve)
2.25
√4 = (solve)
2
√9 = (solve)
3
√16 = (solve)
4
√25 = (solve)
5
√36 = (solve)
6
√49 = (solve)
7
√64 = (solve)
8
√81 = (solve)
9
√100 = (solve)
10
√121 = (solve)
11
√144 = (solve)
12
√169 = (solve)
13
√225 = (solve)
15
√256 = (solve)
16
√400 = (solve)
20
√625 = (solve)
25
√900 = (solve)
30
1³ = (solve)
1
2³ = (solve)
8
3³ = (solve)
27
4³ = (solve)
64
5³ = (solve)
125
³√1 = (solve)
1
³√8 = (solve)
2
³√27 = (solve)
3
³√64 = (solve)
4
³√125 = (solve)
5
PEMDAS
Order of Operations: Parentheses, Exponents, Multiplication/Division (Left to Right), Addition/Subtraction (Left to Right)
Within PEMDAS, absolute values signs are equitable to...
Parentheses