After posting some 700+ questions, I've decided to post the problems which are not that hard. Though each question below has a trap or trick so be careful when solving. I'll post OA's with detailed solutions after some discussion. Good luck.

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

Solution: 12-easy-pieces-or-not-126366.html#p1033919

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

Solution: 12-easy-pieces-or-not-126366.html#p1033921

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

Solution: 12-easy-pieces-or-not-126366.html#p1033924

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

Solution: 12-easy-pieces-or-not-126366.html#p1033925

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

Solution: 12-easy-pieces-or-not-126366.html#p1033930

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 color and the first and the last marbles are of different colors. How many different arrangements are possible?
A. 30
B. 60
C. 120
D. 240
E. 480

Solution: 12-easy-pieces-or-not-126366.html#p1033932

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

Solution: 12-easy-pieces-or-not-126366.html#p1033933

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

Solution: 12-easy-pieces-or-not-126366.html#p1033935

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

Solution: 12-easy-pieces-or-not-126366.html#p1033936

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

Solution: 12-easy-pieces-or-not-126366.html#p1033938

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

Solution: 12-easy-pieces-or-not-126366-20.html#p1033939

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

Solution: 12-easy-pieces-or-not-126366-20.html#p1033949

Please read the whole thread before posting a question. Chances are that your doubt has been already addressed.

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2 ) For x to be integer, maximum value of x^2 should be a perfect square i.e 81 and minimum value of x^2 16

so maximim value ox x^2 = 81 , hence x = 9
similarly minimum value of x^2 = 16 hence x = 4
maximim value ox x^2 - minimum value of x^2 = 9-4 =5

Answer A

3 ) Since Fanny and alexander are travelling towards each other they travel for the same amount of time say 't' and sum of the distance traveled by them is equal to 360

hence 65t+25t = 360
90t = 360
t = 4 hrs

hence when they meet each would have traveled for 4 hrs. 1.5 hrs before they meet, each would travel for 2.5 hrs.

distance traveled by Fanny in 2.5 hrs= 25* 5/2 = 125/2 miles
distance traveled by Alex in 2.5 hrs= 65* 5/2 = 325/2 miles

therfore 1.5 hrs before they meet, distance traveled by them is
125/2+325/2 = 450/2 = 225 miles

Hence they will be 360-225 = 135 miles apart

Answer E

4) we can find the values of y-x at the boundaries of the given inequality

x=-3 y=-7 y-x = -7-(-3) = -4
x=5 y=-7 y-x = -7-5 = -12
x=-3 y=9 y-x = 9-(-3) = 12
x=5 y=9 y-x = 9-5 =4

minimum value of y-x is greater than -12 and maximim value less than 12

Answer D

7) Lets say set A has 36 numbers

2/9*36 = 8 numbers were 'observed' and remaining 36-8 = 28 numbers 'not observed'

3/4*8 = 6 of the 'observed' numbers were non negative.
Hence 8-6 =2 of the 'observed' numbers were negative

Ratio of Negative numbers/Non-negative numbers = 2/1
So out of 36 numbers 2/3 rd should be negative i.e 2/3*36 = 24 negative numbers

Total negative numbers in set A= 24

2 of the observed numbers are negative , hence from the remaining 'not observed' numbers 22 should be negative

fraction of the remaining numbers in set A that must be negative = 22/28 = 11/14
Answer A

8) there are 15 black chips and 5 white chips lets say first chip picked is black. second one is white..

hence third pick (either black or whote)would gurantee that 2 chips are of same color
Answer A

9) the pattern is blue, white, red, green, black, yellow, pink (total 7 colors)

Since the row begins with blue marble and ends with red marble the number of marbles would repeat for every 7th marble from red

3 10 17 24 31 38 45

Hence D

12) To find minimum value of x^2*y , both x^2 and y should be minimum

minimum value of y is -1/2
since x^2 is positive , minimum value of x^2 would be when x is -1/5

hence x^2 = (-1/5)^2*-1/4 = 1/25*-1/2 = -1/50

Answer B

Great! 2/3 of the questions answered correctly. Would you like to provide explanations along with answers?
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lets start
I will answer slowly
1 E
2!(5C2*3C1*2C1+3C2*5C1*2C1+2C2*3C1*5C1)/10C4=1
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3. is already answered. no need to write down the same

4. If -3<x<5 and -7<y<9, which of the following represent the range of all possible values of y-x?
(y-x )min=Y min -Xmax =-7-5=-12
(y-x )max=Y max -Xmin =9-(-3)=12

D. -12<y-x<12 is the answer
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2-d
3-e
4-d
5-b
6-d
7-d
8-c
9-c
10-b
11-d
12-d

Still working on the 1st one...plz check

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

Also tricky. Notice that \(x\) can take positive, as well as negative values to satisfy \(9<x^2<99\), hence \(x\) can be: -9, -8, -7, -6, -4, 4, 5, 6, 7, 8, or 9. We asked to find the value of \(x_{max}-x_{min}\), ans since \(x_{max}=9\) and \(x_{min}=-9\) then \(x_{max}-x_{min}=9-(-9)=18\).

Answer: D.
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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

To get max value of y-x take max value of y and min value of x: 9-(-3)=12;
To get min value of y-x take min value of y and max value of x: -7-(5)=-12;

Hence, the range of all possible values of y-x is -12<y-x<12.

Answer: D.
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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

If choose variable for set A there will be too many fractions to manipulate with, so pick some smart #: let set A contain 18 numbers.

"2/9 of the numbers in a data set A were observed" --> 4 observed and 18-4=14 numbers left to observe;
"3/4 of those numbers were non-negative" --> 3 non-negative and 1 negative;
Ratio of negative numbers to non-negative numbers to be 2 to 1 there should be total of 18*2/3=12 negative numbers, so in not yet observed part there should be 12-1=11 negative numbers. Thus 11/14 of the remaining numbers in set A must be negative.

Answer: A.
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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

There are total of 7 different color marbles in a pattern. Now, as the row begins with blue marble and ends with red marble (so ends with 3rd marble in a pattern) then M=7k+3. The only answer choice which is multiple of 7 plus 3 is 38=35+3.

Answer: C.
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