5. The angles in a triangle are x, 3x, and 5x degrees. If a, b and c are the lengths of the sides opposite to angles x, 3x, and 5x respectively, then which of the following must be true?this means, that c >b>aI. c>a+b
nope. since in a triangle any side cant be more than the sum of the rest sidesII. c^2>a^2+b^2
it is possible! for example- the sides are 4 2 5 . then 25>16+4 25>20 III. c/a/b=10/6/2
hmm bad idea. let c=10 a=6 b=2 then again c >a+b. and it is not right (as mentioned above)
the answer is B. II only
6. Anna has 10 marbles: 5 red, 2 blue, 2 green and 1 yellow. She wants to arrange all of them in a row so that no two adjacent marbles are of the same colour and the first and the last marbles are of different colours. How many different arrangements are possible?hm have doubts, but will choose E as an answer. if it is a right answer, I can explain my logic
E. 480
7. After 2/9 of the numbers in a data set A were observed, it turned out that 3/4 of those numbers were non-negative. What fraction of the remaining numbers in set A must be negative so that the ratio of negative numbers to non-negative numbers be 2 to 1?D. 3/7 is the answer
let assume that total=18, then observed=2/9*18=4 non-negative of observed =3/4*4=3
negative/3=2/1 negative =6
6/(18-4)=6/14=3/7
9. Julie is putting M marbles in a row in a repeating pattern: blue, white, red, green, black, yellow, pink. If the row begins with blue marble and ends with red marble, then which of the following could be the value of M?it means that we have 5*7 (blue, white, red, green, black, yellow, pink)+3 ( blue, white, red)=38
the answer is C
10. If n is an integer and \frac{1}{10^{n+1}}<0.00737<\frac{1}{10^n}, then what is the value of n?
B is the answer
0.001<0.00737<0.01
11. The numbers {1, 3, 6, 7, 7, 7} are used to form three 2-digit numbers. If the sum of these three numbers is a prime number p, what is the largest possible value of p?A. 97
B. 151
C. 209
D. 211
E. 219
D is the answerfrom answer choices we can assume, that the last digit of the sum of 3 numbers could be 7,1,9.
for the last digit being 7- 13 +67 +37=157 (not mentioned in the answ. choices.so eliminate it)
for the last digit being 1 - 17+67+37=121 61+77+13=151 (not mentioned in the answ. choices.so eliminate it)
77+71+63=211(bingo!)
for the last digit being 9 -couldnt find any number.
12. If {-\frac{1}{3}}\leq{x}\leq{-\frac{1}{5}} and {-\frac{1}{2}}\leq{y}\leq{-\frac{1}{4}}, what is the least value of x^2*y possible?1/25<=x^2<=1/9 -1/2<=y<-1/4
to find min number we need to multiply min number of y and max number of x^2, i.e. (-1/2)*1/9=-1/18
D is the answer _________________
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