The Spectrum-155 Reasoning Set (Test with Answers)

By E.W. Arden

Instructions 

There is no enforceable time limit, and be aware that some of these puzzles may take a while to solve, so the more time you spend working on them, the higher your score is likely to be. The use of reference aids is both encouraged and allowed; you can use books or any reference materials you think might help, except online resources, computer programs, or consulting other people and/or AI (This test is meant to capture reasoning skills, not googling skills). The ranking scale below is designed for entertainment purposes only, but it should give you a general idea of how well you have performed. Once you are done, you can look at the answers at the end of the test (resist the temptation to go straight to them before you're ready!).

Verbal Problems

Each analogy consists of a pair of related words or concepts followed by a blank space. Your task is to determine the relationship between the first two words or concepts in the analogy and then identify the word(s) or concept(s) that best complete the analogy. These analogies were written using the equation form A : B :: C : D. You would read this as “A is to B as C is to D.” For instance, the analogy "TASTE : GUSTATORY :: SMELL:  " should be read as "Taste is to gustatory as smell is to.... (the best answer being olfactory).

1. VULPINE : SLY :: LUPINE : ____

2. ICONOCLAST : TRADITION :: HERETIC : ____

3. HEMOGLOBIN : OXYGEN :: CHLOROPHYLL : ___

4. MYOPIA : NEARSIGHTEDNESS :: HYPEROPIA : ____

5. 1 : 100 :: AUREUS : ____

6. EUPHEMISM : OFFENSIVE :: DIRECT : ____

7. EQUIVALENCE RELATION : PARTITION OF A SET :: ELEMENT : ____

8. BITTERSWEET: OXYMORON : YOU CANNOT STEP INTO THE SAME RIVER TWICE :

9. OBSCURE : CRYPTIC :: DIAPHANOUS  : ____

10. SERRATED : EDGE :: BARBED : ____

11. ANVIL : BLACKSMITH :: LOOM : ____

12. EQUIVOCAL : AMBIGUITY :: LACONIC : ____

Spatial & Numerical Problems

13. If today is Tuesday, what day of the week will it be exactly \(1,000\) days from now?

14. What is the total number of faces of the resulting solid below if two holes go all the way through the cube, and the third only goes halfway?

15. A box contains three coins. Two of them are regular, fair coins (each being heads on one side and tails on the other), while the other has both sides as heads. One coin is selected from the box at random, and the face of one side is observed. If the face is heads, what is the probability that the other side of the coin is tails?

16.  Given \(5\) distinct books, \(2\) of which are red, and the remaining \(3\) are blue, in how many different ways can the books be arranged such that the red books are not contiguous with each other?

17. To the nearest whole percent, the probability that any one person selected at random was born on Friday is 14%. What is the probability, to the nearest whole percent, that of any seven persons chosen at random, exactly one was born on Friday?

18.  What is the maximum number of pieces (i.e., completely bounded areas), not further subdivided, that can be formed when a square and two triangles all intersect, counting only the sides of these three figures as boundaries?

19. Two trains, each measuring three kilometers in length, are set to enter two one-and-a-half-kilometer-long tunnels that are positioned three kilometers apart on the same track. The trains enter the tunnels simultaneously. The first train is traveling at a speed of \(8\) kilometers per hour, while the second train is moving at \(12\) kilometers per hour. What is the total length of the two trains that will protrude from the tunnels at the exact moment they collide, assuming that neither train alters its speed before the collision? The trains are on the same track and are headed directly toward one another.

20. On the ceiling is a mobile, made of rods and strings of negligible mass (i.e., massless). By assigning the correct weights, this mobile achieves perfect equilibrium. What are the values ​​of the masses of the three missing weights: \(x\), \(y\), and \(z\)?

21. Imagine you have a marker and you start at a corner of a regular dodecahedron (i.e., perfectly symmetrical). What is the maximum number of edges you can trace across if you never trace across the same edge twice, always keep the marker on the dodecahedron, and can only trace along the corners and edges?

22. In a research facility, there are \(150\) containers with particles. Among these containers:

• \(57\) contain alpha particles.
• \(73\) contain beta particles.
• \(54\) contain gamma particles.
• \(26\) containers have both alpha and beta particles.
• \(27\) containers have both beta and gamma particles.
• \(20\) containers have both alpha and gamma particles.
• \(27\) containers have none of the particles (neither alpha, nor beta, nor gamma).

How many containers have alpha, beta, and gamma particles?

23. Four perfectly rational human prisoners are being examined by malevolently curious aliens. The aliens place a colored hat on each prisoner's head, using exactly two red hats and two green hats (and everyone knows this). The prisoners are arranged on a vertical observation rig so that they can only see the hats of people below them, and nobody can see behind their own head.

Call the prisoners \(A\), \(B\), \(C\), and \(D\) from top to bottom.

• \(A\) stands at the highest platform and can see the hats on \(B\) and \(C\).

• \(B\) stands below \(A\) and can see only \(C\)'s hat.

• \(C\) stands below \(B\) and cannot see anyone's hat (\(D\) is tucked into a blind recess).

• \(D\) is hidden in that blind recess: nobody (\(A\), \(B\), or \(C\)) can see \(D\), and \(D\) cannot see anyone.

The four are fully conscious, perfectly logical, and hear every public statement. The aliens will let them go back to earth if at least one of them correctly pronounces the color of their hand; otherwise, they will all be disintegrated by a powerful laser. Humans are not allowed to say or do anything except state the color of their hats; otherwise, they will all be disintegrated as well. Is it possible for all of them to be liberated? Which prisoner will be the first to correctly announce the color of his own hat (if any)?

What number should come next in the following sequences?

24. \(3, 4, 12, 39, 103, 228,\) ?

25. \(750, 21, 264, 183, 210, 201,\) ?

ANSWERS