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12 Easy Pieces (or not?) [#permalink]
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21 Jan 2012, 06:10
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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: 12easypiecesornot126366.html#p10339192. 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: 12easypiecesornot126366.html#p10339213. 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: 12easypiecesornot126366.html#p10339244. If 3<x<5 and 7<y<9, which of the following represent the range of all possible values of yx?A. 4<yx<4 B. 2<yx<4 C. 12<yx<4 D. 12<yx<12 E. 4<yx<12 Solution: 12easypiecesornot126366.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: 12easypiecesornot126366.html#p10339306. 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: 12easypiecesornot126366.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 nonnegative. What fraction of the remaining numbers in set A must be negative so that the total ratio of negative numbers to nonnegative numbers be 2 to 1?A. 11/14 B. 13/18 C. 4/7 D. 3/7 E. 3/14 Solution: 12easypiecesornot126366.html#p10339338. 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: 12easypiecesornot126366.html#p10339359. 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: 12easypiecesornot126366.html#p103393610. 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: 12easypiecesornot126366.html#p103393811. The numbers {1, 3, 6, 7, 7, 7} are used to form three 2digit 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: 12easypiecesornot12636620.html#p103393912. 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: 12easypiecesornot12636620.html#p1033949Please read the whole thread before posting a question. Chances are that your doubt has been already addressed.
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22 Jan 2012, 11:17
Ans 1E 2A 3E 4D 5B 6C 7A 8A 9C 10D 11D 12B



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22 Jan 2012, 12:10



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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 = 94 =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 360225 = 135 miles apart
Answer E
4) we can find the values of yx at the boundaries of the given inequality
x=3 y=7 yx = 7(3) = 4 x=5 y=7 yx = 75 = 12 x=3 y=9 yx = 9(3) = 12 x=5 y=9 yx = 95 =4
minimum value of yx 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 368 = 28 numbers 'not observed'
3/4*8 = 6 of the 'observed' numbers were non negative. Hence 86 =2 of the 'observed' numbers were negative
Ratio of Negative numbers/Nonnegative 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
Last edited by anuu on 22 Jan 2012, 15:38, edited 1 time in total.



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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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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 I didnt get why everyone solved for x^2 we are asked to find XmaxXmin, not x^2 my choice is D
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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 yx? (yx )min=Y min Xmax =75=12 (yx )max=Y max Xmin =9(3)=12 D. 12<yx<12 is the answer
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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 nonnegative. What fraction of the remaining numbers in set A must be negative so that the ratio of negative numbers to nonnegative numbers be 2 to 1?D. 3/7 is the answer let assume that total=18, then observed=2/9*18=4 nonnegative of observed =3/4*4=3 negative/3=2/1 negative =6 6/(184)=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 2digit 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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2d 3e 4d 5b 6d 7d 8c 9c 10b 11d 12d
Still working on the 1st one...plz check



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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.
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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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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 According to the relationship of the sides of a triangle: the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides. Thus I and III can never be true: one side (c) can not be larger than the sum of the other two sides (a and b). Note that III is basically the same as I: if c=10, a=6 and b=2 then c>a+b, which can never be true. Thus even not considering the angles, we can say that only answer choice B (II only) is left. Answer: B.Now, if interested why II is true: as the angles in a triangle are x, 3x, and 5x degrees then x+3x+5x=180 > x=20, 3x=60, and 5x=100. Next, if angle opposite c were 90 degrees, then according to Pythagoras theorem c^2=a^+b^2, but since the angel opposite c is more than 90 degrees (100) then c is larger, hence c^2>a^+b^2.
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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 colours. 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 to be met for 5 red marbles, which are half of total marbles, they can be arranged only in 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 can be arranged in 5 empty slots in 5!/(2!*2!)=30 ways (permutation of 5 letters BBGGY out of which 2 B's and 2 G' are identical). Finally as there are two cases (R*R*R*R*R* and *R*R*R*R*R. ) then total # of arrangement is 30*2=60. Answer: B.
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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 nonnegative. What fraction of the remaining numbers in set A must be negative so that the total ratio of negative numbers to nonnegative 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 184=14 numbers left to observe; "3/4 of those numbers were nonnegative" > 3 nonnegative and 1 negative; Ratio of negative numbers to nonnegative 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 121=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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Re: 12 Easy Pieces (or not?)
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25 Jan 2012, 04:43



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