Basic Numeracy/Quantitative Aptitude

Detailed Solution

99. The correct answer is (b + 8)(b - 2)
Once again, look at your middle term. You want factors of -16 that add up to be positive 6. You see that 8 and -2 add up to 6, and write your answer as (b + 8)(b - 2). Distributing it out, you get b^2 + 8b - 2b - 16. Combine your "b" terms to get b^2 + 6b - 16

100. The correct answer is 4(b + 2)^2
Right from the start, you notice a common factor of 4 in each term. Factor it out to get 4(b^2 + 4b + 4) Factor the trinomial down further to (b + 2)(b + 2). Your final answer would be 4(b + 2)^2. The reason (4b + 8)(b + 2) or (2b + 4)^2 won't work is that they still have a number that can be factored out of them

101. The best answer is D.
There are three different arrangements of a boy and two girls:(boy, girl, girl), (girl, boy, girl), (girl, girl, boy). Each has a probability of (1/2)3. The total is 3*(1/2)3=3/8.

102. The best answer is D.
Treat the three that sit together as one person for the time being. Now, you have only 6 people (5 and the three that act as one) on 6 places: 6!=720. Now, you have to remember that the three that sit together can also change places among themselves:
3! = 6. So, The total number of possibilities is 6!*3!= 4320.

103. The best answer is C.
First, check Suzan: she has 4 seats left (7 minus the one in the middle and the two ends), After Suzan sits down, the rest still have 6 places for 6 people or 6! Options to sit. The total is Suzan and the rest: 4*6! = 2880.

104. The best answer is C.
The worst case is that we take out seven balls of each color and still do not have 8 of the same color. The next ball we take out will become the eighth ball of some color and our mission is accomplished. Since we have 4 different colors: 4*7(of each) +1=29 balls total. Of course you could take out 8 of the same color immediately, however we need to make sure it happens, and we need to consider the worst-case scenario.

105. The best answer is D.
The worst case would be to take out 21 white balls, 22 green and 22 blue balls and still not having 23 of the same color. Take one more ball out and you get 23 of either the green or the blue balls. Notice that you cannot get 23 white balls since there are only 21, however, you must consider them since they might be taken out also. The total is: 21+22+22+1= 66.

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