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# Answers to Logical & Mathematical IQ Quiz

1. 2 2/3 miles. The trains are exactly 4 miles apart. Their combined speed is 15 miles/hour, so it will take them 16 minutes to collide. The first train will have travelled 1 1/3 miles, so 1/3 mile of it will be out of the tunnel in front, & 2/3 mile of it will be out in the back on collision. The other mile of it will be in the tunnel. The second train will have travelled 2 2/3 miles, so only 1/3 mile of it will still be in the tunnel, so 1 2/3 miles of it will be out of the tunnel.

2. Let's number the boxes 1 through 5. The number of arrangements can be found by counting out all of the possible arrangements of the numbers 1, 2, 3, 4, & 5, but only for those numbers that are in ascending order (1, 2, 3, 4, 5, 12, 13, 14, 15, 23, 24, 25, 34, 35, etc.), for a total of 31 different arrangements.

3. 63.

4. 30. In each set, the difference between the two leftmost numbers is divided by two, and then multiplied by the sum of the two rightmost numbers. The product is written in the middle for each set.

5. 359. If you answered 358, you must remember that the fence must begin & end with a post, & dividing 1,432 by 4 leaves one end without a post.

6. This was a tricky problem. The answer is 17625. In the first situation, you take 7, which leaves you with 1625 (taking the in the sense of removing it, & not subtracting it from the number as a whole), subract 17, & you have 1608, then take 8, which leaves you with 160. For the second situation, you take 6 from 17625, which leaves you with 1725. Subtract 17, & you now have 1708, & if you remove the 8, you have 170. In the last situation, remove 1, so you have 7625. Subtract 4, & you have 7621. Remove the 1, & you have 762. This may be the most difficult puzzle on the quiz by far!

7. 10.5. You divide the number shown & then add 5 for each step in the sequence.

8. 986. The sequence goes multiply by 1 & then add 1, multiply by 2 & then add 2, multiply by 3 & add 1, multiply by 1 & add 2, multiply by 2 & add 1, multiply by 3 & add 2, & then the sequence repeats.

9. The sequence goes divide by 3, then multiply by pi, divide by 3, multiply by pi, etc. But only the first 2 numbers following the decimal are written down, & used for the next step in the sequence.

10. 5. The numbers shown are the digits following the decimal when you divide 12 by 17.

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