Aptitude Tests 4 Me

Basic Numeracy/Quantitative Aptitude

Detailed Solution

20. a: You can find the integers which when divided by 5 have a remainder 2 by adding 2 to all multiples of 5. So we have n = 9 , 12, 17, 22 etc. From this series we can see that n does not have to be odd. Also n + 1 can be a prime because, for example, 12 + 1 = 13 and (n + 2) / 7 has a remainder 2 in some cases but not all. Remember the question asks us for what MUST be true, and we see that none of the statements are true in all cases.

21. c: When the larger cube is cut into smaller cubes, the corner cubes will have paint on three sides. The cubes in the middle of the faces will have paint on only one side, but the cubes cut from the edges will have paint on two sides. In this case, there will be only one cube one each edge (excluding the corners), and since there are 12 edges, there will be 12 cubes with paint on two sides. (Drawing a diagram will make this much clearer.)

22.

23. d: Let E2 = Event of getting ‘2’ balls are blue and ‘1’ is red.
= Total no. of ways -> n(E2) = 8C2 x 6C1
= 8/ (2x 6) x 6/ (1x 5)
= (8 x 7) / 2 x 6 / 1 = 168
P(E2) = 168 / 816 = 7/34

24. b: n(S) = Total number of ways of selecting 1 card out of 52 cards.
= 52C1 = 52
n(E) = Total number of selections of a card, which is either a kind or a queen.
= 4C1 + 4C1 = 4 + 4 = 8
P(E) = n(E) / n(S) = 8 / 52 = 2 / 3

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