A multiple-choice quiz
by iggy4.
Estimated time: 22 mins.

Quiz Answer Key and Fun Facts

Answer:
**3**

If two of the numbers in the digit are the same, and the sum equals 17, the possible digits are 449, 557, 665, 773, and 881. Now you must subtract the unique digit from one of the other digits to get a positive even number. 449 and 557 result in negative numbers, so neither of them can be the answer. 665 results in 1, 773 results in 4, and 881 results in 7. 4 is the only one that is even, therefore, the digits have to be 7, 7, and 3.

If two of the numbers in the digit are the same, and the sum equals 17, the possible digits are 449, 557, 665, 773, and 881. Now you must subtract the unique digit from one of the other digits to get a positive even number. 449 and 557 result in negative numbers, so neither of them can be the answer. 665 results in 1, 773 results in 4, and 881 results in 7. 4 is the only one that is even, therefore, the digits have to be 7, 7, and 3.

Answer:
**Statement 4**

Statement 1 cannot be true because then the sum of the false statements would equal 9, not 8. Statement 3 cannot be true since that would make Statement 1 true. Statement 2 cannot be true because the sum of the false statements would equal 8, and that would result in Statements 1 and 3 being true also. Since we know Statement 2 is false, we know Statement 4 is true, because it says that Statement 2 is false.

Statement 1 cannot be true because then the sum of the false statements would equal 9, not 8. Statement 3 cannot be true since that would make Statement 1 true. Statement 2 cannot be true because the sum of the false statements would equal 8, and that would result in Statements 1 and 3 being true also. Since we know Statement 2 is false, we know Statement 4 is true, because it says that Statement 2 is false.

Answer:
**Kate**

Since their houses are 1 mile away, it would take Connor 12 minutes to jog to Kate's house, and it would take Kate 10 minutes to jog to Connor's house. After 6 minutes, Kate would be 60% of the way to Connor's house, and Connor would be 50% of the way to Kate's house.

This means Connor would be half a mile from his own house, but Kate is 60% of a mile away from her house, so she would only be 40% of a mile away from Connor's house.

Since their houses are 1 mile away, it would take Connor 12 minutes to jog to Kate's house, and it would take Kate 10 minutes to jog to Connor's house. After 6 minutes, Kate would be 60% of the way to Connor's house, and Connor would be 50% of the way to Kate's house.

This means Connor would be half a mile from his own house, but Kate is 60% of a mile away from her house, so she would only be 40% of a mile away from Connor's house.

Answer:
**0**

In these equations, L represents the larger number and S represents the smaller number. (L-S)/2 must equal L+S, which means 2L+2S equals L-S. Add S to both sides and we get 2L+3S = L. Subtract L from both sides and we get L+3S = 0. This means that the larger number is three times the smaller number (3S=L).

This means that (3S-S)/2 = L+S. Multiply both sides by two and we get 3S-S = 2L+2S. Subtract 2S from both sides and we get 3S-3S = 2L, or 0 = 2L. This means that L equals 0, and S equals 0.

In these equations, L represents the larger number and S represents the smaller number. (L-S)/2 must equal L+S, which means 2L+2S equals L-S. Add S to both sides and we get 2L+3S = L. Subtract L from both sides and we get L+3S = 0. This means that the larger number is three times the smaller number (3S=L).

This means that (3S-S)/2 = L+S. Multiply both sides by two and we get 3S-S = 2L+2S. Subtract 2S from both sides and we get 3S-3S = 2L, or 0 = 2L. This means that L equals 0, and S equals 0.

Answer:
**27**

Let's call the number N, and the digits are X and Y. X+Y = N/3. We can change N to 10X+Y, so X+Y =(10X+Y)/3. Simplified we get X+Y = 3.333X + 0.333Y. Subtract Y from both sides and we get X = 3.333X - 0.667Y. Subtract X from each side and we get 0 = 2.333X - 0.667Y. Add 0.667Y to each side and we get 0.667Y = 2.333X. Divide each side by 0.667, and we get Y = 3.5X, so the digit in the one's place is 3.5 times larger than the digit in the tens' place. Since digits must be integers, the digit in the tens' place has to be even (0, 2, 4, 6, or 8). If it was 4 or greater, then the digit in the one's place would be larger than 9, which is impossible for a digit. The digit must be lower than 4 (either 0 or 2). Since the answer is not 0, it must be 2. 2 times 3.5 equals 7.

27's digits add up to 9, which is a third of the number.

Let's call the number N, and the digits are X and Y. X+Y = N/3. We can change N to 10X+Y, so X+Y =(10X+Y)/3. Simplified we get X+Y = 3.333X + 0.333Y. Subtract Y from both sides and we get X = 3.333X - 0.667Y. Subtract X from each side and we get 0 = 2.333X - 0.667Y. Add 0.667Y to each side and we get 0.667Y = 2.333X. Divide each side by 0.667, and we get Y = 3.5X, so the digit in the one's place is 3.5 times larger than the digit in the tens' place. Since digits must be integers, the digit in the tens' place has to be even (0, 2, 4, 6, or 8). If it was 4 or greater, then the digit in the one's place would be larger than 9, which is impossible for a digit. The digit must be lower than 4 (either 0 or 2). Since the answer is not 0, it must be 2. 2 times 3.5 equals 7.

27's digits add up to 9, which is a third of the number.

Answer:
**55**

55 * 10 = 550, minus square digits equals 55.

55 * 10 = 550, minus square digits equals 55.

Answer:
**Statement 4**

If Statement 4 was false, then Statement 2 would be true, and Statement 3 would be true. The sum of the true statements would be 5. If Statement 1 was true, then the sum of the true statements would be 6, which would make Statement 1 false. If Statement 1 is false, then the sum of the true statements would be 5, which means that Statement 1 is true. Statement 1 does not have a non-contradictory answer, so Statement 4 is absolutely not false. Statement 4 has to be true.

If you said the answer was (Statements 4 & 1), this is not true because since we know Statement 4 is true, we can safely say that Statements 2 & 3 are false. Whether or not Statement 1 is true or false, it will not have a non-contradictory answer, we are still unsure if Statement 1 is true or false.

If Statement 4 was false, then Statement 2 would be true, and Statement 3 would be true. The sum of the true statements would be 5. If Statement 1 was true, then the sum of the true statements would be 6, which would make Statement 1 false. If Statement 1 is false, then the sum of the true statements would be 5, which means that Statement 1 is true. Statement 1 does not have a non-contradictory answer, so Statement 4 is absolutely not false. Statement 4 has to be true.

If you said the answer was (Statements 4 & 1), this is not true because since we know Statement 4 is true, we can safely say that Statements 2 & 3 are false. Whether or not Statement 1 is true or false, it will not have a non-contradictory answer, we are still unsure if Statement 1 is true or false.

Answer:
**30 seconds**

Sam and Chris can crush 70 cans together in a minute, and 140 cans in 2 minutes. This means there will only be 10 cans left after 2 minutes. Joe can crush 20 cans in a minute, so he can crush 10 cans in half a minute. If he works for 30 seconds and then leaves, Sam and Chris will be 10 cans ahead, and have 150 cans crushed by the time the 2 minutes is up.

Sam and Chris can crush 70 cans together in a minute, and 140 cans in 2 minutes. This means there will only be 10 cans left after 2 minutes. Joe can crush 20 cans in a minute, so he can crush 10 cans in half a minute. If he works for 30 seconds and then leaves, Sam and Chris will be 10 cans ahead, and have 150 cans crushed by the time the 2 minutes is up.

Answer:
**Tito**

Captain Cannon and Rafael both run at 8 miles an hour, so both of them will have ran 0.8 miles after 6 minutes. They will both be 0.2 miles away from the center, so they will be 0.4 miles away from each other.

Tito runs at 7 miles an hour, so he will have ran 0.7 miles after 6 minutes, and will be 0.3 miles away from the center. Remember, Tito is not directly across from Rafael, so he is actually closer to him than Captain Cannon is. The approximate distance is about 0.36 miles, (you can use the Pythagorean Theorem on a calculator to get the exact distance), which is closer than 0.4 miles.

Captain Cannon and Rafael both run at 8 miles an hour, so both of them will have ran 0.8 miles after 6 minutes. They will both be 0.2 miles away from the center, so they will be 0.4 miles away from each other.

Tito runs at 7 miles an hour, so he will have ran 0.7 miles after 6 minutes, and will be 0.3 miles away from the center. Remember, Tito is not directly across from Rafael, so he is actually closer to him than Captain Cannon is. The approximate distance is about 0.36 miles, (you can use the Pythagorean Theorem on a calculator to get the exact distance), which is closer than 0.4 miles.

Answer:
**30 minutes**

Before they start running, they are exactly 1 mile away from each other. Natalie can run a mile in 7:30 minutes, and Emily can run 75% of a mile in 7:30 minutes. Every 7.5 minutes, Natalie gets a quarter of a mile closer to Emily. This will take 4 sets of 7.5 minutes.

After 30 minutes, both of them will be at the same point.

That's a long time to run that fast!

Before they start running, they are exactly 1 mile away from each other. Natalie can run a mile in 7:30 minutes, and Emily can run 75% of a mile in 7:30 minutes. Every 7.5 minutes, Natalie gets a quarter of a mile closer to Emily. This will take 4 sets of 7.5 minutes.

After 30 minutes, both of them will be at the same point.

That's a long time to run that fast!

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

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