Solutions To Brain Busters #1 ('Logical Labyrinth')

 (1) We already know C is at zero degrees Celsius (O C) so all we have to do is correctly compute the total difference in temp. to object O. This is just: dT = 2F + 1.8C . Thus, we know O is at a temperature of more than 1.8C. Now how many C degrees in 2F? The hint provides the basis for deducing the answer (if one didn't already know it) so 1 C = 1.8F 

Then logically, 2F = 1C + 0.2F, and for 0.2F: 

0.2F/ (1.8 F/C) = 1/9 of a Celsius degree = 0.11 C

Therefore, 2F = 1.11 C

So O is at a temperature of: 1.11C + 1.80 C = 2.91 C 

Which is answer (C)

(2) This is straightforward. Obviously, a consecutive clockwise and counter-clockwise rotation of 60 degrees cancel each other. Then, rotating the triangle through 360 degrees clockwise simply turns it through a full circle - bringing it to its original position. Thus, the answer is: (A) the same as the original orientation.


(3) We know A and B choices are immediate conditions based on the information. Since we already have more than one choice, the answer has to be (D) - all the preceding may apply.

(4) A straightforward logical regression and deduction exercise:   (D)

(5) We have consecutive operations such that: operations: addition by 1 is denoted by A; multiplication by 2 is denoted by S; division by 4 is denoted by F, and subtraction by 1 is denoted by T.

Then: 28 SFATS -> (28)x 2 = 56 and 56/4 = 14 and (14 + 1) = 15 and (15 - 1) = 14 and finally 14 x 2 = 28

So the answer is: (B)

(6) This references a series of operations on a square whose top left corner is A, and the other corners (going clockwise) are: B, C and D. The operation sequence is: R2 M1 M3, where,

R2: rotation clockwise by 180 degrees

M1: Mirrors corners exactly through the midline of the square

M3: Mirrors two opposing corners in the opposite sense to M2

Now, performing operation R2 first, causes the square to rotate so that 'A' ends up where C is in the original orientation. (Fig. 1(A)) Operation M1 then causes all the existing corners to be mirrored through the midline of the square. Thus, Fig 1 (B) shows the orientation after M1.

The last operation, M3, mirrors two opposing diagonal corners: from top right to bottom left (e.g. opposite to the sense of M2) This will yield the result shown in Fig. 2 which is DABC or (C). 

(7) The key is to carefully read the conditions proposed for affecting the rate of synthesis, and to note that the density of the proteins will have nothing to do with this rate. All "an increased density of the proteins" means is that more will be there to be synthesized but this doesn't affect the rate applied to each of the proteins proper. (Of course the total time to complete the task will be longer but this is only because there will be 1000 times more to be synthesized!) Thus, galactoside at half the original concentration means the rate of synthesis slows by a factor of two, so we can expect only 500 molecules (as opposed to one thousand) to be synthesized for every five generations. Thus, the answer is: (B). 

(8) The next step in the sequence is easy to figure out once one identified the key components of the previous sequence of 4 and how they are changing. This is in the direction of increasing white squares and reducing the orange. Since the algorithmic sequence requires at least two whites for the next step, this automatically eliminates options (A), (C) and (D), leaving answer (B). 

(9) The key for this question's response is not to be fooled by the 'easy pop-up answer' which is (D). Clearly, on careful reading he has invented an  ad hoc law to permit miracles and that contradicts laws of logic and the general law.   The key sentences that give it away?  "A miracle is an exception to physical law but not to logical or ethical law. As such it does not contradict the general law "

BUT - if it contradicts the physical law, it also contradicts the general law- by his own definition.

Hence, answer is (C).

(10) In the case of this answer, the conclusion allows for a multiple points of view and this definitely prescribes answer (D): He has committed all the above.

(11) Ditto with respect to the author's reference to a "general law", i.e. he's committed all the following logical errors:

i) He has conflated "general law" with laws of thought, without defining the former.

ii) He has committed the "one True Scotsman" fallacy, i.e. asserting a certain association always trumps any other associations by virtue of having some special dispensation or quality (usually an appeal to "authority" or an undefined God).

iii) He has erred in extrapolating from the particular to the general.