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21 Jan 2012, 06:10
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1. There are 5 pairs of white, 3 pairs of black and 2 pairs of grey socks in a drawer. If four socks are picked at random what is the probability of getting two socks of the same color?
A. 1/5
B. 2/5
C. 3/4
D. 4/5
E. 1
2. If x is an integer and 9<x^2<99, then what is the value of maximum possible value of x minus minimum possible value of x?
A. 5
B. 6
C. 7
D. 18
E. 20
3. Fanny and Alexander are 360 miles apart and are traveling in a straight line toward each other at a constant rate of 25 mph and 65 mph respectively, how far apart will they be exactly 1.5 hours before they meet?
A. 25 miles
B. 65 miles
C. 70 miles
D. 90 miles
E. 135 miles
4. If -3<x<5 and -7<y<9, which of the following represent the range of all possible values of y-x?
A. -4<y-x<4
B. -2<y-x<4
C. -12<y-x<4
D. -12<y-x<12
E. 4<y-x<12
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?
I. c>a+b
II. c^2>a^2+b^2
III. c/a/b=10/6/2
A. I only
B. II only
C. III only
D. I and III only
E. II and III only
6. Anna has 10 marbles: 5 identical red, 2 identical blue, 2 identical green, and 1 yellow. She wants to arrange all of them in a row such that no two adjacent marbles are of the same color, and the first and last marbles are of different colors. How many different arrangements are possible?
A. 30
B. 60
C. 120
D. 240
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 total ratio of negative numbers to non-negative numbers be 2 to 1?
A. 11/14
B. 13/18
C. 4/7
D. 3/7
E. 3/14
8. There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?
A. 3
B. 5
C. 6
D. 16
E. 19
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?
A. 22
B. 30
C. 38
D. 46
E. 54
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?
A. 1
B. 2
C. 3
D. 4
E. 5
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
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?
A. -1/100
B. -1/50
C. -1/36
D. -1/18
E. -1/6
The solutions can be found below on this page.
A. 1/5
B. 2/5
C. 3/4
D. 4/5
E. 1
2. If x is an integer and 9<x^2<99, then what is the value of maximum possible value of x minus minimum possible value of x?
A. 5
B. 6
C. 7
D. 18
E. 20
3. Fanny and Alexander are 360 miles apart and are traveling in a straight line toward each other at a constant rate of 25 mph and 65 mph respectively, how far apart will they be exactly 1.5 hours before they meet?
A. 25 miles
B. 65 miles
C. 70 miles
D. 90 miles
E. 135 miles
4. If -3<x<5 and -7<y<9, which of the following represent the range of all possible values of y-x?
A. -4<y-x<4
B. -2<y-x<4
C. -12<y-x<4
D. -12<y-x<12
E. 4<y-x<12
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?
I. c>a+b
II. c^2>a^2+b^2
III. c/a/b=10/6/2
A. I only
B. II only
C. III only
D. I and III only
E. II and III only
6. Anna has 10 marbles: 5 identical red, 2 identical blue, 2 identical green, and 1 yellow. She wants to arrange all of them in a row such that no two adjacent marbles are of the same color, and the first and last marbles are of different colors. How many different arrangements are possible?
A. 30
B. 60
C. 120
D. 240
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 total ratio of negative numbers to non-negative numbers be 2 to 1?
A. 11/14
B. 13/18
C. 4/7
D. 3/7
E. 3/14
8. There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?
A. 3
B. 5
C. 6
D. 16
E. 19
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?
A. 22
B. 30
C. 38
D. 46
E. 54
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?
A. 1
B. 2
C. 3
D. 4
E. 5
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
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?
A. -1/100
B. -1/50
C. -1/36
D. -1/18
E. -1/6
The solutions can be found below on this page.
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25 Jan 2012, 04:33
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6. Anna has 10 marbles: 5 identical red, 2 identical blue, 2 identical green, and 1 yellow. She wants to arrange all of them in a row such that no two adjacent marbles are of the same color, and the first and last marbles are of different colors. How many different arrangements are possible?
A. 30
B. 60
C. 120
D. 240
E. 480
Seems tough and complicated, but if we read the stem carefully, we find that the only way both conditions can be met for the 5 red marbles, which are half of the total marbles, is that they can be arranged in only two ways: R*R*R*R*R* or *R*R*R*R*R.
Here comes the next good news: in these cases, BOTH conditions are met for all other marbles as well. No two adjacent marbles will be of the same color, and the first and the last marbles will be of different colors.
Now, it's easy: 2 blue, 2 green, and 1 yellow marble can be arranged in 5 empty slots in \(\frac{5!}{2!*2!}=30\) ways (this is the permutation of 5 letters BBGGY, out of which 2 B's and 2 G's are identical). Finally, as there are two cases (R*R*R*R*R* and *R*R*R*R*R), the total number of arrangements is \(30*2=60\).
Answer: B
Answer: B.
A. 30
B. 60
C. 120
D. 240
E. 480
Seems tough and complicated, but if we read the stem carefully, we find that the only way both conditions can be met for the 5 red marbles, which are half of the total marbles, is that they can be arranged in only two ways: R*R*R*R*R* or *R*R*R*R*R.
Here comes the next good news: in these cases, BOTH conditions are met for all other marbles as well. No two adjacent marbles will be of the same color, and the first and the last marbles will be of different colors.
Now, it's easy: 2 blue, 2 green, and 1 yellow marble can be arranged in 5 empty slots in \(\frac{5!}{2!*2!}=30\) ways (this is the permutation of 5 letters BBGGY, out of which 2 B's and 2 G's are identical). Finally, as there are two cases (R*R*R*R*R* and *R*R*R*R*R), the total number of arrangements is \(30*2=60\).
Answer: B
Answer: B.
25 Jan 2012, 04:23
Kudos
Bookmarks
SOLUTIONS:
Notice that most of the problems have short, easy and elegant solutions, since you've noticed a trick/trap hidden in the questions.
1. There are 5 pairs of white, 3 pairs of black and 2 pairs of grey socks in a drawer. If four socks are picked at random what is the probability of getting two socks of the same color?
A. 1/5
B. 2/5
C. 3/4
D. 4/5
E. 1
No formula is need to answer this one. The trick here is that we have only 3 different color socks but we pick 4 socks, which ensures that in ANY case we'll have at least one pair of the same color (if 3 socks we pick are of the different color, then the 4th sock must match with either of previously picked one). P=1.
Answer: E.
Notice that most of the problems have short, easy and elegant solutions, since you've noticed a trick/trap hidden in the questions.
1. There are 5 pairs of white, 3 pairs of black and 2 pairs of grey socks in a drawer. If four socks are picked at random what is the probability of getting two socks of the same color?
A. 1/5
B. 2/5
C. 3/4
D. 4/5
E. 1
No formula is need to answer this one. The trick here is that we have only 3 different color socks but we pick 4 socks, which ensures that in ANY case we'll have at least one pair of the same color (if 3 socks we pick are of the different color, then the 4th sock must match with either of previously picked one). P=1.
Answer: E.
