Number Properties Flashcards

1
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2
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3
Q

Is 0 odd or even?

Is 0 positive or negative?

A

0 is even.

0 is neither positive or negative. Problems often use the phrase “positive integers”– read carefully and realize they are talking about 1, 2, 3…. etc

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4
Q

What are the first 10 prime numbers?

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

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5
Q

Data Sufficiency:

Is x prime?

(1) x > 2
(2) x is even

A

Answer is C– Together they are sufficient.

The only even prime is 2. So if x >2 and x is even, the answer to the question is “NO”. Alone each statement is insufficient.

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6
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7
Q

Do the following have the same meaning? Or are any of them different?

a. 3 is a factor of 12
b. 3 is a divisor of 12
c. 12 is a multiple of 3
d. 12 is divisible by 3
e. 12/3 is an integer
f. 12 is equal to 3n, where n is an integer
g. 12/3 yields a remainder of 0
h. 12 items can be shared among 3 people so that each person has the same number of items

A

Yes, they all have the same meaning!

The GMAT often writes questions in different ways to confuse you.

It’s important to be able to translate the language into something you understand.

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8
Q

What is the Least Common Multiple of 18 and 24?

A

We factor each number and then find the “unique factors” – we find the highest power of each different prime factor and then multiply them.

18 = 3<strong>2</strong> * 2

24 = 2<strong>2</strong> * 3

The Least Common Multiple is 32 * 22 = 72

We can confirm this by writing out the multiples:

18: 18, 36, 54, 72
24: 24, 48, 72

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9
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10
Q

Data Sufficiency:

A
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11
Q

1) If the units digit of N is 0, what do we know about the factors of N?

A

1) The factors include 2 and 5, because N must be a multiple of 10.

(For any number we want to factor that ends in one or more 0’s, it is easiest to factor the 10’s out first)

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12
Q

What is the prime factorization of 360?

(Draw a factor tree and then write the exponents)

Example:

A
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13
Q

If the integer N ends with “5000”, what do we know about the factors of N?

A

From the 3 zeros at the end, the factors include 3 pairs of 2’s and 5’s, because N is a multiple of 1000.

Once we factor out 1000, we know that there is another 5 as a factor, since N/1000 would end with a 5.

Factors include 23 * 54

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14
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15
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16
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17
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18
Q

What are Permutations?

A

Permutations are the number of ways to choose, when order matters.

Ex: How many different license plates can be made, using 3 DISTINCT letters, choosing from the letters A, B, C, D, E, F, G

Write out 3 “Slots”, one for each letter.

___ ___ ___

There are 7 possibilites for the first slot, then 6 possibilites for the 2nd slot, then 5 for the 3rd slot (because the letters must be distinct). We multiply them to find the total number of ways.

_7_ * _6_ *_5_ = 210

19
Q

How many different ways are there to create a code, using 3 DISTINCT digits, using only integers greater than 2 and less than 8?

A

This is a Permutations problem

How many integers are greater than 2 and less than 8?

3, 4, 5, 6, 7 —> 5 digits

Slots method —> 3 slots —> _5_ * _4\_ *_3\_ = 60

20
Q

The diagram shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

A

Permutations (we multiply the number of options for each slot/choice/fork)

There are 3 forks along the path: 2 choices for the first one, 2 for the second and 3 for the third.

Total # of ways is 2*2*3 = 12

21
Q

If 4 people each shake everyone else’s hand one time, how many total handshakes are made?

A

Small numbers, so we could list them. (With larger numbers we would want the formula)

Name them: A, B, C, D. List the pairs:

AB, AC, AD

BC, BD

CD

Total = 6

General formula: 4 people * 3 handshakes made by each person / 2 (because we double counted each handshake–> each handshake is shared by 2 people. AB is the same as BA)

22
Q

If xy < 0 , what can we conclude about x and y?

A

x and y have opposite signs:

one is positive, one is negative

23
Q

If xyz > 0 , what can we conclude about x, y and z?

A

All 3 can be positive, OR there are 2 negatives and 1 positive