Math and Logic Puzzles

It is logically impossible to cross the 'last' person in a race because to cross someone, you must be behind them. If you are behind the last person, you are the last person yourself. Thus, 'none' of the positions apply.

If you overtake the person in second place, you take their position, making you the new second-place runner. You have not yet overtaken the person in first place. This is a common trick question where people instinctively answer 'first'.

This is a common riddle. Your name belongs to you, but other people use it much more frequently than you do when they address or refer to you. Books and money are used by the owner more often than by others.

If you cross the first person in a race, you take their spot, meaning you are now in the first position. This is a classic logic puzzle. Crossing the first person implies you have overtaken everyone else.

By definition, 1 is the only positive integer that is neither prime nor composite. 2, 13, and 17 are all prime numbers because they have exactly two distinct factors. 1 has only one factor.

In 856973, the digit 6 is in the thousands place, so its place value is 6000. The face value of any digit is the digit itself, which is 6. The difference is $6000 - 6 = 5994$. Other options represent incorrect place value calculations.

A number is divisible by 3 if and only if the sum of its digits is divisible by 3. For example, 123 is divisible by 3 because 1+2+3=6, which is divisible by 3. This rule works for all positive integers.

One second equals 1/3600 of an hour (60 seconds × 60 minutes = 3600 seconds per hour). Therefore, 1 ÷ 3600 = 0.000277... The correct answer 0.00027 is a reasonable approximation to two significant decimal places.

To check divisibility by 11, calculate the alternating sum of digits. For 415624: 4-1+5-6+2-4 = 0. Since the result is 0 (which is divisible by 11), the number 415624 is divisible by 11. The other options fail this test.

A prime number is defined as a natural number greater than 1 with exactly two distinct positive divisors: 1 and itself. The number 1 has only one divisor, so it is not prime. Two is the smallest prime number.

97 is a prime number as it has no divisors other than 1 and 97. 33 is divisible by 3 and 11; 81 is divisible by 3 and 9; 93 is divisible by 3 and 31. Thus, 97 is the only prime in the list.

A prime number has only two factors: 1 and itself. 31, 61, and 71 are prime. However, 91 is composite because $7 \times 13 = 91$. Therefore, 91 is the correct choice as it is not a prime number.

The smallest 3-digit number is 100. Checking numbers upwards: 101 is prime. Since 101 is not listed in the options (103, 107, 109), 'None' is the correct choice. 103, 107, and 109 are primes, but they are larger than 101.

We need a number consisting only of 3s that is divisible by 7. Testing 333, 3333, 33333, and 333333, we find $333333 / 7 = 47619$. This is the smallest such integer. Other options like 47719 or 48619 do not result in a product of all 3s when multiplied by 7.

The total weight increase for 10 men is $10 \times 1.5 = 15$ kg. Since the new man replaced a man weighing 68 kg, his weight must be $68 + 15 = 83$ kg. Options like 82 or 81 do not account for the total weight shift correctly.

The parents' statement that 'a dog would not be happy in an apartment' directly implies that they currently live in an apartment. This is the only conclusion that necessarily follows from the given information. We cannot conclude whether they prefer birds over dogs, whether Erin dislikes birds, or whether they want to move.

The passage explicitly states that 'When they heard news of the hurricane, Maya and Julian decided to change their vacation plans.' This makes option D necessarily true. We cannot infer that they always take beach vacations, that the spa is overpriced, or that six-month advance booking is usually necessary - these are assumptions not supported by the given information.

To solve this question, the user needs to carefully read and analyze the information provided. The statement that must be true according to the given information is option B, "One way to increase seahorse populations is to ban the fishing of seahorses." This conclusion can be drawn from the information that seahorse populations have declined everywhere that seahorses are fished, and that biologists met to discuss what might be done to reverse this trend. If seahorse populations have decreased by 50% in the past five years, it suggests that current methods of fishing and seahorse conservation are not working. Therefore, it is reasonable to assume that banning the fishing of seahorses could help to increase populations. Option A is incorrect because the information does not provide evidence that seahorses are likely to become extinct within five years. Option C is incorrect because the information does not indicate that biologists from all over the world are working to save the seahorses. Option D is incorrect because the information does not mention the opinions of seahorse fishermen.

The Answer is: B

The passage states that Thomas 'lives on the same street' as Vincent, which means they live in the same neighborhood. This is the only statement that must be true. We have no information about how long Thomas takes, whether it's dark during deliveries, or whether Thomas wants his own route.