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Quiz about Sorry Wrong Number
Quiz about Sorry Wrong Number

Sorry, Wrong Number Trivia Quiz


Ten mathematical problems asking for ten different numbers but you got them all wrong on your first attempts. Do you know the correct answers to these ten questions? Let's see.

A multiple-choice quiz by Matthew_07. Estimated time: 4 mins.
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Author
Matthew_07
Time
4 mins
Type
Multiple Choice
Quiz #
359,988
Updated
Dec 03 21
# Qns
10
Difficulty
Easy
Avg Score
8 / 10
Plays
546
Awards
Top 35% Quiz
Last 3 plays: federererer (8/10), Guest 76 (7/10), wellenbrecher (10/10).
1. "Which number is the first prime number?" "Oh, that's an easy one, it's number one!" "Sorry, wrong number." "Huh? I have always thought that 1 is the first prime number..."

Which number is actually the first prime number?
Hint

3
2
4
5

2. "I am thinking of a number. Could you guess what number is it?" "Okay, give me a hint." "Well, it's an even number that is neither positive nor negative." "An even number, aha, the answer is 2. Am I right?" "Sorry, wrong number."

Which even number is neither positive nor negative?
Hint

-2
4
-4
0

3. "The two values on the opposite sides of a die always add up to this prime number. Do you know what number is it?" "A die? Hm, I know that the six values that appear on a die are 1, 2, 3, 4, 5 and 6. I am not sure about the arrangement though. But since you mentioned that the sum is a prime number, I would guess it's 5?" "Sorry, wrong number."

If you add up the two values of any opposite sides of a die, what value would you get?
Hint

7
3
2
1

4. "The numbers 142857 is a very special number." "Oh yeah? Convince me." "You see, 1 x 142857 = 142857, 2 x 142857 = 285714, 3 x 142857 = 428571, 4 x 142857 = 571428, 5 x 142857 = 714285, and 6 x 142857 = 857142. Do you notice that after multiplication, all the digits remain the same just that they appear in different order?" "Oh yeah, that's true!" "Now, do you know what's the answer for 7 x 142857? I will give you a hint. It's a 6-digit number where all the digits are identical." "Is it 888888?" "Sorry, wrong number."

What is 7 x 142857?
Hint

999999
555555
777777
333333

5. "Any number greater than 10 that ends in the digit x is definitely not a prime number because the number itself is divisible by x. There are two values that fit the description of x. One of them is 2. Could you guess the other one?" "Hm, tough question again involving prime numbers. Is the answer 1? "Sorry, wrong number." "Why?" "Here are some counter examples to prove that your answer is wrong. 11 and 31 are both prime numbers."

Apart from 2, which number fits the description of x?
Hint

5
7
3
9

6. "How many weeks are there in 10! seconds?" "10! what?" "10 factorial, which means 10 x 9 x ... x 2 x 1." "That's a very large number, I would take a wild guess and say it's 100 weeks. Is the number 100?" "Sorry, wrong number."

10! seconds is equivalent to how many weeks? (Hint: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
Hint

9
7
6
8

7. "Evaluate the square of the sum of the given two numbers, 11 and 19." "Oh, I can apply the formula that I have learned in my algebra class here. (a + b)^2 = a^2 + b^2. Here, a is 11 and b is 19. Is the answer 11^2 + 19^2 = 121 + 361 = 482?" "Sorry, wrong number." "But why?" "The formula that you used is incorrect."

Using the correct formula, what is the square of the sum of 11 and 19?
Hint

300
121
900
361

8. "Find the least common multiple of the two given numbers 6 and 8". "Okay, I will just multiply the two numbers together. Easy peasy. Is 6 x 8 = 48 the correct answer?" "Sorry, wrong number."

What number is actually the least common multiple of 6 and 8?
Hint

72
120
96
24

9. "Find the greatest 3-digit number that ends in the digit 8 such that the number is divisible by 3." "That's an easy one. Is the number 998?" "Sorry, wrong number." "Why?" "998 is not divisible by 3. A simple way to determine if a number is divisible by 3 is to find the sum of the individual digits. The number is divisible by 3 if the sum is divisible by 3. 9 + 9 + 8 = 26. 26 is not divisible by 3." "Ah, I see."

What is the greatest 3-digit number that ends in the digit 8 and is divisible by 3?
Hint

988
978
968
958

10. "Given the four values 1, 2, 3, and 4, form two 2-digit numbers such that the product of the two numbers is as big as possible." "Hm, let's see. I will tackle the problem by forming two numbers. Let's try with 42 x 31 = 1302. Is the greatest possible product 1302?" "Sorry, wrong number." "Wrong number? I am pretty sure 1302 is the greatest number that I can form..."

Which multiplication operation actually gives the greatest value?
Hint

42 x 13
43 x 12
41 x 32
43 x 21


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Quiz Answer Key and Fun Facts
1. "Which number is the first prime number?" "Oh, that's an easy one, it's number one!" "Sorry, wrong number." "Huh? I have always thought that 1 is the first prime number..." Which number is actually the first prime number?

Answer: 2

In the fields of real analysis and discrete mathematics, a prime number is defined as a number that is greater than 1 and has no positive divisors other than 1 and the number itself. So, by this definition, 1 is not a prime number. The divisors of 2 are 1 and 2. So 2 fits the description of a prime number.

The next number, 3, also fits the criteria and hence, is also a prime number. The divisors of the next number, 4, are 1, 2, and 4. Using the definition given, 4 is not a prime number. It is a composite number from the fact that 4 = 2 x 2.
2. "I am thinking of a number. Could you guess what number is it?" "Okay, give me a hint." "Well, it's an even number that is neither positive nor negative." "An even number, aha, the answer is 2. Am I right?" "Sorry, wrong number." Which even number is neither positive nor negative?

Answer: 0

Zero is neither positive nor negative. Zero is actually an even number. In mathematics, an even number is defined as a number that can be written in the form of 2k, where k is an integer. Notice that 0 = 2 x 0. The number zero itself is also an integer.

The numbers 2 and 4 are positive even numbers. On the other hand, -2 and -4 are negative even numbers.
3. "The two values on the opposite sides of a die always add up to this prime number. Do you know what number is it?" "A die? Hm, I know that the six values that appear on a die are 1, 2, 3, 4, 5 and 6. I am not sure about the arrangement though. But since you mentioned that the sum is a prime number, I would guess it's 5?" "Sorry, wrong number." If you add up the two values of any opposite sides of a die, what value would you get?

Answer: 7

Notice that 1 + 2 + 3 + 4 + 5 + 6 = 21. 21/3 = 7. So even if you have no idea on the arrangement of the pips or values on a die, a clever and educated guess is 7.
4. "The numbers 142857 is a very special number." "Oh yeah? Convince me." "You see, 1 x 142857 = 142857, 2 x 142857 = 285714, 3 x 142857 = 428571, 4 x 142857 = 571428, 5 x 142857 = 714285, and 6 x 142857 = 857142. Do you notice that after multiplication, all the digits remain the same just that they appear in different order?" "Oh yeah, that's true!" "Now, do you know what's the answer for 7 x 142857? I will give you a hint. It's a 6-digit number where all the digits are identical." "Is it 888888?" "Sorry, wrong number." What is 7 x 142857?

Answer: 999999

A few more interesting properties of the number 142857:

142 + 857 = 999
14 + 28 + 57 = 99

142857 x 142857 = 20408122449
20408 + 122449 = 142857
5. "Any number greater than 10 that ends in the digit x is definitely not a prime number because the number itself is divisible by x. There are two values that fit the description of x. One of them is 2. Could you guess the other one?" "Hm, tough question again involving prime numbers. Is the answer 1? "Sorry, wrong number." "Why?" "Here are some counter examples to prove that your answer is wrong. 11 and 31 are both prime numbers." Apart from 2, which number fits the description of x?

Answer: 5

Notice that 12, 22, 32, 42, 52, ... are all even numbers and hence, divisible by 2. In addition, 15, 25, 35, 45, 55, ... are all multiples of 5, so they are all composite numbers.
6. "How many weeks are there in 10! seconds?" "10! what?" "10 factorial, which means 10 x 9 x ... x 2 x 1." "That's a very large number, I would take a wild guess and say it's 100 weeks. Is the number 100?" "Sorry, wrong number." 10! seconds is equivalent to how many weeks? (Hint: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

Answer: 6

1 week = 7 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds

Using the four formulas above, and the fact that 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, we can convert the units easily.

(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / [60 x 60 x 24 x 7]
= (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / [(2 x 5 x 6) x (6 x 10) x (3 x 8) x 7]
(cancelling out the common terms)
= ( 9 x 4 ) / ( 6 )
= 36 / 6
= 6 weeks

It is interesting to note that a seemingly large number, 10!, can be reduced to an elegant integer, 6, using some common conversion units.
7. "Evaluate the square of the sum of the given two numbers, 11 and 19." "Oh, I can apply the formula that I have learned in my algebra class here. (a + b)^2 = a^2 + b^2. Here, a is 11 and b is 19. Is the answer 11^2 + 19^2 = 121 + 361 = 482?" "Sorry, wrong number." "But why?" "The formula that you used is incorrect." Using the correct formula, what is the square of the sum of 11 and 19?

Answer: 900

The formula (a + b)^2 = a^2 + b^2 is a very common misconception. The correct formula should be (a + b)^2 = a^2 + b^2 + 2ab.

Let a = 11 and b = 19. (11 + 19)^2 = 11^2 + 19^2 + 2x11x19 = 121 + 361 + 418 = 900. We can double check the answer: (11 + 19)^2 = 30^2 = 900.
8. "Find the least common multiple of the two given numbers 6 and 8". "Okay, I will just multiply the two numbers together. Easy peasy. Is 6 x 8 = 48 the correct answer?" "Sorry, wrong number." What number is actually the least common multiple of 6 and 8?

Answer: 24

A systematic way to determine the least common multiple (LCM) of any two integers is to list down all the multiples for each of the two numbers.

Multiples of 6: 6, 12, 18, 24, 30, 36...
Multiples of 8: 8, 16, 24, 32, 40, 48...

Observe that the number 24 appears in both the lists. So 24 is the LCM of 6 and 8.

Another more efficient way to find the LCM of two integers is by prime factorization.

Notice that 6 = 2 x 3 and 8 = 2 x 2 x 2 = 2^3. We first determine the highest power of all the prime numbers. Then, we multiply them to get the value of the LCM. In this case, we have 2^3 x 3 = 24.

Simply multiplying the given two numbers together will not necessarily give the LCM of the two numbers. 6 x 8 = 48. 48 is a common multiple of 6 and 8 but it is not the least common multiple.

However, in a more specific case where both the given numbers are prime numbers, we can simply multiply the two numbers together to get the LCM. For example, the LCM of 5 and 7 is simply 5 x 7 = 35.
9. "Find the greatest 3-digit number that ends in the digit 8 such that the number is divisible by 3." "That's an easy one. Is the number 998?" "Sorry, wrong number." "Why?" "998 is not divisible by 3. A simple way to determine if a number is divisible by 3 is to find the sum of the individual digits. The number is divisible by 3 if the sum is divisible by 3. 9 + 9 + 8 = 26. 26 is not divisible by 3." "Ah, I see." What is the greatest 3-digit number that ends in the digit 8 and is divisible by 3?

Answer: 978

Here's a simple example to show why the rule "if the sum of all the individual digits of a number is divisible by 3, then the number itself is also divisible by 3" is true for any number.

We will use a 3-digit number to show how this works, but the result can be generalized to any other numbers.

Let's try with the number 432. We can decompose the number into 4 x 100 + 3 x 10 + 2 x 1. We can then rewrite it as 4 x (99 + 1) + 3 x (9 + 1) + 2 = (4 x 99) + (3 x 9) + (4 + 3 + 2). Notice that 99 and 9 are multiples of 3, which implies that 4 x 99 and 3 x 9 are both divisible by 3. This leaves us with the operation 4 + 3 + 2. If the sum is also divisible by 3, then the number 432 is also divisible by 3. 4 + 3 + 2 = 9 is divisible by 3. So we conclude that the number 432 is divisible by 3.

A more rigorous mathematical proof involves the concept of modulo arithmetic. Any number in the form of 10^n is equivalent to 1 modulo 3, where n is any positive integer. In layman's terms, for n = 1, when you divide 10 by 3, you will obtain a remainder of 1. In fact, you will get the same remainder when you perform the division operation on 10^2 = 100, 10^3 = 1000, ... , 10^n. This property is based on the fact that 10^n = 99...99 + 1, and the term 99...99 is divisible by 3.

To find the greatest 3-digit that ends in 8 that is divisible by 3, we know that the number takes the form of 9_8. The number 998 might seem to be answer but 9 + 9 + 8 = 26 implies that 998 is not divisible by 3. We proceed to the next possible value, which is 988, but again, 9 + 8 + 8 = 25 is not divisible by 3. We then try the number 978. The sum of its digits, 9 + 7 + 8 = 24 is a multiple of 3. So the number 978 is the number that fits the given criteria.
10. "Given the four values 1, 2, 3, and 4, form two 2-digit numbers such that the product of the two numbers is as big as possible." "Hm, let's see. I will tackle the problem by forming two numbers. Let's try with 42 x 31 = 1302. Is the greatest possible product 1302?" "Sorry, wrong number." "Wrong number? I am pretty sure 1302 is the greatest number that I can form..." Which multiplication operation actually gives the greatest value?

Answer: 41 x 32

From the given four values, namely 1, 2, 3, and 4, we know that in order to make the product as big as possible, the two numbers should be in the form of 4_ and 3_. Now we need to consider where to put the remaining two numbers, 1 and 2. The two possible combinations are 41 x 32 and 42 x 31. Observe that 41 x 32 = 1312 > 42 x 31 = 1302.

A more challenging question requires you to determine the largest product that you can obtain by forming two values from the given nine numbers, 1 until 9. Using the concept of rearrangement inequality, the answer is 9642 87531 = 843973902.
Source: Author Matthew_07

This quiz was reviewed by FunTrivia editor WesleyCrusher before going online.
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