gmat quant topic 2 statistics solutions

... differences: 10 2 + 9 2 + 8 2 + 7 2 + 6 2 + 5 2 + 4 2 + 3 2 + 2 2 + 1 2 + 0 2 + (-1) 2 + ( -2) 2 (-3) 2 + (-4) 2 + (-5) 2 + (-6) 2 (-7) 2 + (-8) 2 + (-9) 2 + (-10) 2 = 770. Average ... volume of 25 oz: Let n = number of 40 oz. bottles ( 12) (20 ) + ( n )(40) n + 12 = 25 ( 12) (20 ) + 40 n = 25 n + ( 12) (25 ) 15 n =...

Ngày tải lên: 14/05/2014, 16:55

... (a + b) 2 a 2 2ab b 2 (15 + 1) 2 225 2( 15)1 =30 1 2 (15 + 2) 2 225 2( 15 )2 =60 2 2 (15 + 3) 2 225 2( 15)3 =90 3 2 . . . . . . . . . . . . (15 + 15) 2 225 2( 15)15 =450 15 2 TOTALS = 15 (22 5)=3375 ... S 2 = 2( 3) – 2 = 4 S 3 = 2( 4) – 2 = 6 S 4 = 2( 6) – 2 = 10 S 5 = 2( 10) – 2 = 18 S 6 = 2( 18) – 2 = 34 S 7 = 2( 34) – 2 = 66 S...

Ngày tải lên: 14/05/2014, 16:55

... b ) 2 (6) ( a + b ) 2 = c 2 + 24 c Substitute (1) and (2) into right side of (5) (7) (60 – c ) 2 = c 2 + 24 c Substitute ( a + b ) = 60 – c from (3) (8) 3600 – 120 c + c 2 = ... (x + 4)(x - 4), or x 2 - 16. Their combined area is 2( x 2 - 16), or 2x 2 _ 32. Since we know that 2x 2 = 968, the combined area of the two white rectangles is 968 - 32, o...

Ngày tải lên: 14/05/2014, 16:55

... are: 1 2 + 2 2 + 3 2 + 4 2 +5 2 +6 2 + 5 2 + 4 2 + 3 2 + 2 2 + 1 2 = 146. Therefore, there are 129 6 – 146 = 1150 non-ties. Since this is a symmetric problem, Jane will win 1150 /2 or ... 41/50 39. 1 /22 1 40. 1/1770 41. 2/ 9 42. 1 /21 6 43. 3 /25 44. $3.6 45. 7/8 46. 9/10 47. 143/1 52 48. 13/14 49. 13/18 50. 0 51. 1/5 52. 27 1/1000 53. 7 /21 6 54. 2/ 25 55. ½...

Ngày tải lên: 14/05/2014, 16:55

... = (2/ 3)h, we can solve for h: (1/3)h + (2/ 3)h + h + l = 20 00 (1/3)h + (2/ 3)h + h + (2/ 3)h = 20 00 (8/3)h = 20 00 h = 20 00(3/8) h = 750 If h = 750, l = (2/ 3)h = 500. (2) SUFFICIENT: If m = s + 25 0, ... equations from the two data points given: p (2) = 41 = r (2) – 5 (2) 2 + b 41 = 2 r – 20 + b 61 = 2 r + b p (5) = 26 = r (5) – 5(5) 2 + b 26 = 5 r – 125 + b...

Ngày tải lên: 14/05/2014, 16:55

... 75 pink roses and 25 red roses. Now we can fill out the rest of the double-set matrix: Red Pink White TOTAL Long- stemmed 20 60 0 80 Short- stemmed 5 15 20 40 TOTAL 25 75 20 120 Now we can answer ... English) we get: a + e + f + 2b +2c +2d + 9 = 84. Taking this equation and subtracting the 4 th equation (Total students) yields the following: a + e + f + 2b + 2c +2d + 9 = 84 –[ a + e...

Ngày tải lên: 14/05/2014, 16:55

... insufficient. (2) INSUFFICIENT: Let's factor the left side of the given inequality: - 12 y 2 – y 2 x + x 2 y 2 > 0 y 2 (- 12 – x + x 2 ) > 0 y 2 ( x 2 – x – 12) > 0 y 2 ( x ... AND (2) SUFFICIENT: We can combine the two expanded forms of the equations from the two statements by adding them: x 2 + 2 xy + y 2 = 9 a x 2 – 2 xy + y...

Ngày tải lên: 14/05/2014, 16:55

... whether r ^2+ s ^2= u ^2+ v ^2 or not. From statement 2, u ^2+ v ^2= (1-r) ^2+ (1-s) ^2= r ^2+ s ^2+ 2 -2( r+s) Combined statement 1, r+s=1, we can obtain that r ^2+ s ^2= u ^2+ v ^2. Answer is C. 6. y=kx+b 1). k=3b 2) . -b/k=-1/3 ... Then the answer is x = 2 / 3 . e. Solve 3x 2 + 4x + 2 = 0. Here's the graph: f. Solve x 2 + 2x = 1. Here's the graph:...

Ngày tải lên: 14/05/2014, 16:55

... 5 C 4 × 2 = 20 19. (3 ! × 2 ! × 3 !) × 3 ! 20 . 3 ! × 2 ! 21 . 1 × 10 × 10 × 5 22 . 5 C 3 × 4 C 3 23 . 5 ! × 2 ! 24 . 5 C 3 + 5 C 4 25 . 3 C 2 × 1 × 3 C 2 26. 3 ! × 2 ! × 2 ! × 2 ! 27 . TTTHHH, ... 4 28 . The only combination of odd is 5 × 5 × 5. So total required = 3 × 3 × 3 – 1 = 26 . 29 . 6 P 4 × 2 = 720 30. 2 × 2 × 2 × 4 × 4 – 2 × 1 × 1 × 4...

Ngày tải lên: 14/05/2014, 16:55

... use :2^ 1 +2^ 2+ +2^ n = [2^ (n+1)] – 2, where n equals to number of terms. question is: 2+ 2+ (2^ 2)+ (2^ 3)+ (2^ 4)+ (2^ 5)+ (2^ 6)+ (2^ 7)+ (2^ 8) this can be written as : 2+ (2^ 1)+ (2^ 2)+ (2^ 3)+ (2^ 4)+ (2^ 5)+ (2^ 6)+ (2^ 7)+ (2^ 8) ... are 2^ 2 + 2^ 2. this is 2( 2 ^2) , or (2^ 1) (2^ 2), or 2^ 3. now, using this combined term as the "first term", the first t...

Ngày tải lên: 14/05/2014, 16:55