135 terms

GMAT: MANHATTAN 4ED, NUMBER PROPERTIES 4TH EDITION PT 1/2

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What integers are a factor of 48?
1 2 3 4 6 8
What integers are a factor of 8748?
1 2 3 4 6 9
How many factor pairs are there for 72? How many factors?
6 (1 2 3 4 6 8, 9 is a pair with 8 so isnt counted twice) 7 (1 2 3 4 6 8, 9)
How many factor pairs for 48? How many factors?
6 (1 2 3 4 6 8) 6 (1 2 3 4 6 8)
How many factor pairs for 21? How many factors?
3 (1 3 7) 3 (1 3 7)
What are the 1st 15 prime numbers?
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
What are all the prime numbers between 50 and 100?
53 59 61 67 71 73 79 83 89 97
Is one a prime number? (Y/N/CBD)
N
What are 72's prime factors?
2 2 2 3 3
What are 48's prime factors
2 2 2 2 3
What is the GCF between 30 (235) & 24 (2223) ? LCM?
6 120
x has a prime box with the following numbers (5 5 5) what is x?
125
x has a prime box with the following numbers (5 2 3) what is x?
30
What is the LCD & GCF between 12 & 24?
12 24
What is the LCD & GCF between 30 & 3?
3 30
What is the LCD & GCF between 72 & 7?
1 504
What common factors would go in the common area for a venn diagram of 12 & 16?
2 2
If 2 numbers have no primes in common then their GCF is? There LCM is?
1 & their product
If z is divided by 7 or by 18, an integer results. Is z/42 an integer? ("whole number") (Y/N/CBD)
Y
If 80 (22225) is a factor of r, is 15 (35) a factor of r? (Y/N/CBD)
CBD
If j is divisible by 12 (223) and 10 (25) is j divisible by 24 (2223)? (Y/N/CBD)
N (one of the 2's is shared)
Given that 6 is a divisor of r and r is a factor of s, is 6 a factor of s? (Y/N/CBD)
Y
If 24 (2223) is a factor of h and 28 (227) is a factor of k, must 21 (37) be a factor of hk? (Y/N/CBD)
Y
If k is divisible by 6 (k=23) and 3k is not divisible by 5, is k divisible by 10? (3=3, k=23) (Y/N/CBD)
N (there is no 5 in venn diagram)
If 60 (2233) is a factor of u, is 18 (233)a factor of u? (Y/N/CBD)
CBD
If s is a product of 12 and t is a multiple of 12, is 7x + 5t a multiple of 12? (Y/N/CBD)
Y
With a total point count of 21 how many times did Timmy win? 1st=7 pts, 2nd=3pts 3rd=1pt
2 (1st once & 2nd once)
When mulptilpying integers if you have even one even number the product will be even? (Y/N/CBD) If 3 even the product will be divisible by 8? (Y/N/CBD)
Y Y
The only way to have an odd answer when adding, subtracting or multiplying is if you add or subtract and odd & an even?
N (OxO=O)
Division has one simple rule of divisibility for odds and evens? (Y/N/CBD)
CBD
odd+even+odd=odd (Y/N/CBD)
N
If t is odd then t² is odd? (t-1)² ? (t-1/100)² ? (Y/N/CBD)
Y N CBD
Because OxO=O then the opposite O/O=O? (Y/N/CBD)
CBD (There are no rules to division)
If a+b is even, ab is even? (Y/N/CBD)
CBD
If h is even, j is odd and k is odd then k(h+j)=even? (Y/N/CBD)
N
If xy is even and z is even, then x + z is even? (Y/N/CBD)
CBD
│-5│ , │5│, both are the same thing? (Y/N/CBD)
Y
If Signs are the Same the answers poSitive, if Not the answer is Negative? (Y/N/CBD) If both intergers are Even the answEr is Even if nOt then Odd? (Y/N/CBD)
Y CBD
56 / (-7) = NEG#? (Y/N/CBD)
Y
(-7) x 7 x (-6) x (-2) / -5 = NEG#? (Y/N/CBD)
N
5 negative values plus unknown number of positive values will always equal negative value? (Y/N/CBD)
CBD (rules do not apply to addition. ex )
Count the number of negatives in a DIV or MULT problem, if there is an even number the problem is positive if an odd number then negative? (Y/N/CBD)
Y
If │z-4│ = 4-z then we know z is a number between n-n?
0-4
│z│× y², given that zy ╪ 0? (P/N/CBD)
P
│ab│/b, given that b<a<0? (P/N/CBD)
N (P/N=N)
h²×²k³m², given that k<0 and hm╪0? (P/N/CBD)
N (odd # of odds = N)
What is the sum of all integers from 20 to 100, inclusive?
4860 (60×81)
If there are a set of 3 consecutive integers the product will always be divisible by what numbers?
1 2 3 6
If there are a set of k consecutive integers the product will always be divisible by what?
k!
If z² = 16, is z equal to 4? (Y/N/CBD)
CBD (pg64)
Is -4² equal the same as 4²? (Y/N/CBD)
Y (16)
An even exponent changes the sign of its base? Is -4² = a positive integer? Is 4² = a positive integer (Y/N/CBD)
CBD Y Y
-65³ = ? -1³ ? -0³ ? (N/P/0)
N N 0 (this is the only way exponent can change base)
5493³ = ? 1³ ? 0³ ? (N/P/0)
P P 0
-738² = ? -1² ? -0² ? (N/P/0)
P P 0
94787² = ? 1² ? 0² ? (N/P/0)
P P 0
A negeative base with an odd exponent is the only way the product will result in a negative? -3³ = -9? (Y/N/CBD)
Y Y
z¹ = z¹×² = z¹×³ if z = ?
0 1
z²×² = z¹×² = z² if z = ?
0 1 -1
¾² =
9/16
¾³ =
27/64
Is this a true statement: 0.6² > 0.6³ (Y/N/CBD) 0.6² > 0.5² ? 0.6³ > 0.5²
Y Y N
0.5³ = 0.125 = ? / ?
1/8
0.6³ = 0.216 ≈ ? / ?
1/5 (roughly)
8 × 125 = 2³ × 5³ = (? × ?)³
2 5 (2×2×2=8 & 5×5×5=125)
2³+5³=?, (2+5)³=?, 2³×5³=?, (2×5)³ =?
133 343 1000 1000 (+ is different then ×when compounding bases w/ exponents)
3² × 3² = 3×3×3×3 = 3²×² (Y/N/CBD)
Y
3² + 3² = 3×3×3×3 = 3²×² (Y/N/CBD)
N (3² +3²=18)
3² + 3² = 3×3 + 3×3 (Y/N/CBD)
Y
3^7/3^7=?
1
3×3²= ?
27
3^0 =
1
3^6/3^2 =
3^4
(3/4)^-3 =
64/27
1/4-² =
16
(-2)-³ = 1/(-2)³
-1/8
25²/³ =
125
2^4 × 3^4 =
6^4
Simplify: 5³ × 2² =
10³
Simplify: yⁿ× zⁿ
(yz)ⁿ
Simplify: z^a × z^b
z^a+b
Simplify: z^a / z^b
Z^(a-b)
Simplify: (a/b)ⁿ
aⁿ/bⁿ
Simplify: (aª)º or (aº)ª
aºª
Simplify: z-ⁿ
1/zⁿ
Simplify: º√xª = (º√x)ª
xª/º
Simplify: aⁿ + aⁿ + aⁿ =
3aⁿ
You can/cannot simplify exponential expressions when they are linked by multoplication and division?
can
Simplify: 12^7/3^7 = (3x2x2)^7/3
4^7
3º4³
3ⁿ-ⁿ(2x2)³
Factor: 3³+12³
3³(1+4³)
Factor: 7²² + 7³³*²
7^4(7²+1) or 7^4(50)
You can/cannot factor exponential expressions when they are linked by addition and subtraction?
can
Factor: 6^5-6³
6³(6²-1)
Factor: 4^20 + 4^21 +4^22
4^20(21) or 4^20(3x7)
If r³ + │r│ =0, what are the possible values of r?
0 -1
Simplify: y² × y^5/(y²)^4
1/y
If b>a?0, and c╪0, is a²b³c^4 positive?
yes
if y^5>0, is y<0?
no
if x^4 =16, what is │x│?
2
x³ < x². Describes the possible values of x.
Any non-zero less then 1
Does a² + a^4 = a^6 for all the values of a? (Y/N/CBD)
N
2^-5
1/32
8^5/3
32
9^-1/2
1/3
(4/9)^-3/2
27/8
7^6 / 7^4
49
8^4(5^4)
2560000
2^4 × 2^5 / 2^7 -2^4
-12
9^4 / 3^4 + (4²)³
4177
Root is the opposite of ?
exponent
³√64
4
√1
1
√2
1.4
√3
1.7
√4
2
√ 5
2.25
√9
3
√16
4
√25
5
√36
6
√49
7
√64
8
√81
9
√100
10
√121
11
√144
12
√169
13
√196
14
√225
15
√256
16
√400
20
√625
25
√900
30
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