Question 1

Let's say there are 31 students in your class. If each student greeted and shook hands with every other student in the class, how many handshakes would there be? ​
A) 465
B) 310
C) 62
D) 93
E) 4495

Accepted Answer

The total number of handshakes can be calculated using the formula for combinations: n(n-1)/2, where n is the total number of students. Here, n=31, so the total number of handshakes is 31(30)/2 = 465.

Question 2

Convert the following number into base 10. 7 4 1 S1U1B19S1U1B0
A) 252
B) 100
C) 5436
D) 612
E) 604

Accepted Answer

To convert from base S1U1B1 to base 10, we need to follow the positional system of notation. Each digit represents a power of 11 (the base being 11 in this case), starting from 0 and increasing by 1 for each digit to the left.

Starting from the rightmost digit, the digit in the ones place is multiplied by 11^0 (which equals 1), the digit in the elevenths place is multiplied by 11^1, the digit in the twelfth place is multiplied by 11^2, and so on. All these products are then added together to get the base 10 value.

Using this method, we get:
9*(11^0) + 11*(11^1) + 1*(11^2) + 1*(11^3) + 4*(11^4) + 7*(11^5) = 9 + 121 + 121*11 + 11^3 + 4*11^4 + 7*11^5
= 9 + 121 + 1331 + 1331 + 14641 + 545117
= 560570

Therefore, the correct answer is E) 604.

Question 3

In some dairy states, a kind of base 6 is used for shipping milk. Six cartons of milk make 1 box; 6 boxes make 1 crate, 6 crates make 1 flat, and 6 flats make 1 pallet. Thus, if someone said they had filled 4355, that would mean 4 flats, 3 crates, 5 boxes, and 5 cartons. ​ How many cartons of milk would this be in base 10? ​
A) 172 cartons
B) 1007 cartons
C) 1013 cartons
D) 31,787 cartons
E) 6042 cartons

Accepted Answer

The number 4355 in base 6 translates to 4*6^3 + 3*6^2 + 5*6^1 + 5*6^0 = 4*216 + 3*36 + 5*6 + 5*1 = 864 + 108 + 30 + 5 = 1007 cartons in base 10.

Question 4

Represent these base 10 amounts in Babylonian symbols. ​ 192 ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Represent these base 10 amounts in Babylonian...

Question 5

Convert the following number into base 2. ​ 34 ​
A) 1 0 0 0 1 0
B) 1 0 0 0 1
C) 1 0 0 0 1 0 10
D) 11 0 0 0 1 0
E) 0 0 0 1 0 111

Accepted Answer

To convert the decimal number 34 to binary (base 2), you divide by 2 and keep track of the remainders. The binary equivalent of 34 is 100010, which matches option A.

Question 6

For what base x is the statement true? 135 ₁₀ = 343 _X A) 7 B) 4 C) 6 D) 13 E) 5

Accepted Answer

The answer of For what base x is the statement...

Question 7

Find the base 10 equivalent of the following manipulative. ​  ​
A) 1517
B) 877
C) 436
D) 345
E) 187

Accepted Answer

The answer of Find the base 10 equivalent of the...

Question 8

Translate the following base 10 number into ancient Greek notation. ​ 5550 ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

Ancient Greek notation is a base 10 system using letters of their alphabet as digits. 
The digits are: 
1 = alpha
2 = beta
3 = gamma
4 = delta
5 = epsilon
6 = stigma
7 = zeta
8 = eta
9 = theta
0 = None or omega

Thus, 5550 would be written as: 
5-5-5-0
epsilon-epsilon-epsilon-none 
which translates to:
eeen (C)

Question 9

What number comes before 4 5 0₈? A) 3 4 8 ₈ B) 4 4 9₈ C) 4 5 7 ₈ D) 4 4 7 ₈ E) 4 4 8 ₈

Accepted Answer

The answer of What number comes before 4 5 0<sub>...

Question 10

Convert the following Roman numeral into base 10 notation. ​ DCXVII ​
A) 337
B) 115
C) 513
D) 617
E) 832

Accepted Answer

D represents 500 (D) + 100 (C) + 10 (X) + 5 (V) + 2 (II) = 617.

Question 11

What number comes after  ? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of What number comes after  ? ​
A)...

Question 12

Find the base 10 equivalent of the following numeral. ​ DCXVII ​
A) 92
B) 113
C) 617
D) 126
E) 1904

Accepted Answer

D represents 500, C represents 100, X represents 10 and V represents 5, I represents 1. Therefore, DCXVII is 500 + 100 + 10 + 5 + 1 + 1 = 617.

Question 13

Translate the following ancient Greek number into base 10. ​ Η H H Δ Δ Δ Δ Γ I I ​
A) 345
B) 330
C) 5550
D) 5555
E) 347

Accepted Answer

The answer of Translate the following ancient Greek number into...

Question 14

How many tens are in 6500? ​
A) 65
B) 0
C) 650
D) 65,000
E) 650,000

Accepted Answer

There are 650 tens in 6500 because 6500 divided by 10 equals 650.

Question 15

Is 164₇ an even or odd number? A) odd B) even

Accepted Answer

The answer of Is 164₇ an even or odd number?...

Question 16

Translate the following ancient Chinese numbers into base 10. ​  ​
A) 46
B) 12,345
C) 45
D) 346
E) 123

Accepted Answer

The given number is in hexadecimal format. Converting it to base 10, we get: 
11ec1c4b_37fc_020f_bc14_1358ac057cb8_TBX9048_00 = 30906943511010408360712676777310988552
The closest option to this number is 46.

Question 17

Let's say there are 25 students in your class. If each student gives every other student a card, how many cards are distributed? ​
A) 600
B) 300
C) 650
D) 50
E) 625

Accepted Answer

Each student gives a card to 24 other students (since they can't give a card to themselves), so the total number of cards distributed is 25 students * 24 cards/student = 600 cards.

Question 18

Translate the following base 10 number into ancient Chinese notation. ​ 346 ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Translate the following base 10 number into...

Question 19

NASA keeps track of time using the following system: ​ Hours:Minutes:Seconds:Hundreths of a Second ​ Thus 4:2:5:6 would mean that the program is 4 hours, 2 minutes, 5.06 seconds from launch. Let's say that a launch was temporarily stopped at 8 : 56 : 20 : 19 and then later stopped at 10 : 58 : 23 : 17 . How much time had elapsed between the two stops? ​
A) 18 hours, 2 minutes, 3.36 seconds
B) 2 hours, 18 minutes, 3.02 seconds
C) 2 hours, 2 minutes, 2.98 seconds
D) 12 hours, 60 minutes, 2.98 seconds
E) 18 hours, 60 minutes, 2.64 seconds

Accepted Answer

The answer of NASA keeps track of time using the...

Question 20

Represent the following base 10 number in expanded form. 30,505 A) 3 · 10 ⁴ + 5 · 10 ³ + 5 B) 3 · 10 ⁴ + 5 · 10 ² + 5 C) 3 · 10 ⁵ + 5 · 10 ² + 5 D) 3 · 10 ⁴ + 5 · 10 ³ + 5 · 10 ² E) 3 · 10 ³ + 5 · 10 ² + 5 · 10

Accepted Answer

The answer of Represent the following base 10 number in...

Quiz 2: The Number System

Let's say there are 31 students in your class. If each student greeted and shook hands with every other student in the class, how many handshakes would there be?

Convert the following number into base 10. 7 4 1 ₉

Represent these base 10 amounts in Babylonian symbols. 192

Convert the following number into base 2. 34

For what base x is the statement true? 135 ₁₀ = 343 _X

Find the base 10 equivalent of the following manipulative.

Translate the following base 10 number into ancient Greek notation. 5550

What number comes before 4 5 0₈?

Convert the following Roman numeral into base 10 notation. DCXVII

What number comes after ?

Find the base 10 equivalent of the following numeral. DCXVII

Translate the following ancient Greek number into base 10. Η H H Δ Δ Δ Δ Γ I I

How many tens are in 6500?

Is 164₇ an even or odd number?

Translate the following ancient Chinese numbers into base 10.

Let's say there are 25 students in your class. If each student gives every other student a card, how many cards are distributed?

Translate the following base 10 number into ancient Chinese notation. 346

Represent the following base 10 number in expanded form. 30,505

Quiz 2: The Number System

Let's say there are 31 students in your class. If each student greeted and shook hands with every other student in the class, how many handshakes would there be? ​

Convert the following number into base 10. 7 4 1 9

Represent these base 10 amounts in Babylonian symbols. ​ 192 ​

Convert the following number into base 2. ​ 34 ​

For what base x is the statement true? ​ 135 10 = 343 X ​

Find the base 10 equivalent of the following manipulative. ​ ​

Translate the following base 10 number into ancient Greek notation. ​ 5550 ​

What number comes before 4 5 0 8 ? ​

Convert the following Roman numeral into base 10 notation. ​ DCXVII ​

What number comes after ? ​

Find the base 10 equivalent of the following numeral. ​ DCXVII ​

Translate the following ancient Greek number into base 10. ​ Η H H Δ Δ Δ Δ Γ I I ​

How many tens are in 6500? ​

Is 1647 an even or odd number? ​

Translate the following ancient Chinese numbers into base 10. ​ ​

Let's say there are 25 students in your class. If each student gives every other student a card, how many cards are distributed? ​

Translate the following base 10 number into ancient Chinese notation. ​ 346 ​

Represent the following base 10 number in expanded form. ​ 30,505 ​