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# Logical & Mathematical IQ Quiz

By William F. Bultas

See how many of these brain teasers you can solve. When you're finished, you can rank yourself with the scale below. This isn't an actual IQ test, but should give you an idea of how sharp your math & logic skills are. You can improve these skills by practicing with puzzles like these, which can be useful when for taking standardized tests, & for real life situations. You'll find the answers on this page. Work those mathematical & logical neurons, & have fun!
```
Number Correct         Logic & Math IQ
0-1                    Need Improvement (IQ < 90)
2-3                    Average (IQ 90-110)
4-5                    Above Average (IQ 110-130)
10                     Genius (IQ 150+)
```

1. Two trains, each two miles long, enter two one mile long tunnels that are two miles apart from one another on the same track. The trains enter the tunnels at exactly the same time. The first train is going 5 miles/hour, and the second train is going 10 miles/hour. What is the sum of the lengths of the two trains that will protrude from the tunnels at the exact moment that they collide, assuming that neither train changes its speed prior to collision? The trains are on the same track headed in opposite directions (i.e. directly toward one another).

2. You have a box that fits inside of a box that fits inside of a box that fits inside of a box that fits inside of a box, for a total of 5 boxes. Assume that no two boxes can fit inside of a box, unless one is inside of the other (e.g. the two smallest boxes could not fit inside of the largest box, unless the smallest box was inside of the second smallest box), & the boxes cannot be altered (e.g. folded, cut, or torn). Using only these 5 boxes, how many different arrangements are there to place a gift in the boxes, if the gift can only be inside of the smallest box that is being used? Example: The gift in the second smallest box inside of the largest box would be 1 arrangement.

3. Solve the preceding problem for 6 boxes.

4. If the same functions are applied to reach the results in each of the three sets of numbers, find what number should replace the ? in the last set:
```
21  5        28  13        16 2
24           30            ?
17  7        25  7         10 8
```

5. You have 1,432 feet of fence that must be strung out in a straight line. A fence post must be placed for every 4 feet of fence, so how many fence posts will be needed?

6. If you take 7, then 17, & then 8 from me, you have 160. But if you take 6, then 17, then 8 from me, you have 170. Finally, if you take 1, then 4, then 1 from me, you have 762. What am I?

For problems 7-10, replace the ? in each series of numbers with the most appropriate number.

7. 18, 14, 12, 11, ?, 10.25

8. 11, 12, 26, 79, 81, 163, 491, 492, ?

9. 4, 1.33, 4.17, 1.39, 4.36, 1.45, ?

10. 7, 0, 5, 8, 8, 2, 3, ?

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