gmat quant topic 4 - numbers solutions

... be 40 Answer: 2+2^2+2^3+2 ^4+ 2^5+2^6+2^7+2^8 is a geometric progression S=(A1+An*q )/(1-q) =-2 +2^9 2+S=2^9 8. T= 1/ 2-1 /2^2+1/2^3 1/2^10 = 1 /4+ 1 /4^ 2+1 /4^ 3+1 /4^ 4+1 /4^ 5 Notice that 1 /4^ 2+1 /4^ 3+1 /4^ 4+1 /4^ 5 ... integer, then 4 a will always have a units digit of 4 or 6. We can show this by listing the first few powers of 4: 4 1 = 4 4 2 = 16 4 3 = 64 4...

Ngày tải lên: 14/05/2014, 16:55

... 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 + (-1 0) 2 = 770. Average of the sum ... The correct answer is D. 18. Range before transaction: 112 -4 5 =67 Range after transaction: ( 94+ 24) -( 5 6-2 0)=11 8-3 6=82 The difference is: 8 2-6 7...

Ngày tải lên: 14/05/2014, 16:55

... each other, are each x + 4 units long and x - 4 units high. Therefore, the area of either rectangle is (x + 4) (x - 4) , or x 2 - 16. Their combined area is 2(x 2 - 16), or 2x 2 _ 32. Since ... the hypotenuse = 4/ 5. For ABD , the ratio of the longer leg to the hypotenuse = 5/ AB . Thus, 4/ 5 = 5/ AB , or AB = 25 /4 = 6.25 (2) SUFFICIENT: If DE = 4, then BDE...

Ngày tải lên: 14/05/2014, 16:55

... D. 38. 41 /50 39. 1/221 40 . 1/1770 41 . 2/9 42 . 1/216 43 . 3/25 44 . $3.6 45 . 7/8 46 . 9/10 47 . 143 /152 48 . 13/ 14 49. 13/18 50. 0 51. 1/5 52. 271/1000 53. 7/216 54. 2/25 55. ½ 56. 8/25 57. 1/ 24 58. ... assume the players have the numbers 1, 2, 3, and 4. There are 24 ways to arrange these 4 numbers: 12 34, 1 243 , 13 24, 1 342 , 142 3, 143 2, . . . , etc. Only one o...

Ngày tải lên: 14/05/2014, 16:55

... be, x-1, x-2, x-3, x -4 , x-5 So, 38+x+x-1+x-2+x-3+x -4 + x-5=90 6x=67 x=67/6>11 32. Let attend fee be x, number of person be y: Form 1, (x-0.75)(y+100)=xy 100x-0.75y-75=0 From 2, (x+1.5)(y-100)=xy ... for four days: $0 .4+ $0.3=$0.7, as it is less than $0 .4* 2 Answer is B 41 . Let x be the height of the tree increase each year, then: [4+ 6x- (4+ 4x)]/ (4+ 4x) = 1/5 10x = 4+ 4x x=...

Ngày tải lên: 14/05/2014, 16:55

... have a queen-sized bed, while 25 have a king-sized bed. Of the non-smoking rooms (let's call this unknown n), 60% or .6n have queen-sized beds. 10 rooms are non-smoking with king-sized beds. Let's ... right-handed, then three of them must be left-handed. Add that to the three left-handed girls, and we know that a total of 6 students are left-handed. GIRLS BOYS TOTALS LEFT-HANDED 3...

Ngày tải lên: 14/05/2014, 16:55

... correct answer is D. 25. X-2Y < -6 => -X + 2Y > 6 Combined X - Y > -2 , we know Y > 4 X - Y > -2 => -2 X + 2Y < 4 Combined X - 2Y < -6 , we know -X < -2 => X > 2 Therefore, ... 0-1 0 1 0-2 0 2 0-3 0 30 -4 0 40 -5 0 5 0-6 0 60+ speed And since Missile 2's rate doubles every 10 minutes, Missile 2 will be tra...

Ngày tải lên: 14/05/2014, 16:55

... of -1 . (A) (8 – 9) ÷ (5 – 4) = -1 /1 = -1 . (B) (-1 – (-2 )) ÷ (3 – 4) = 1/ (-1 ) = -1 . (C) (6 – 9) ÷ (-1 – ( -4 ) ) = -3 /3 = -1 . (D) (5 – 2) ÷ (2 – (-3 )) = 3/5. (E) (1 – 2) ÷ (7 – 6) = -1 /1 = -1 . The ... the y-coordinate. (A) (- 14, 10) y = -5 /7 (- 14) + 5 = 15; this does not match the given y-coordinate. (B) (-7 , 5) y = -5 /7...

Ngày tải lên: 14/05/2014, 16:55

... victory circles: Albert-GOLD, Cami-GOLD, Bob-GOLD. Bob-GOLD, Albert-GOLD, Cami-GOLD. Bob-GOLD, Cami-GOLD, Albert-GOLD. Cami- GOLD, Albert-GOLD, Bob-GOLD. Cami-GOLD, Bob-GOLD, Albert-GOLD. Each unique ... P&C / Page 14 of 4 1. 4! , 8!/2! 2. 7 P 4 3. 4 P 2 + 4 P 3 + 4 P 4 4. 4! /2! 5. 10 P 2 + 10 P 3 6. ( 10 P 8 + 10 P 9 + 10 P 10 ) × 12 seconds 7. 6! – 5! × 2! 8. 7...

Ngày tải lên: 14/05/2014, 16:55

... devoted to math. Solutions to Try-It Problems If you haven't tried to solve the first three Try-It problems on page 14, then go back and try them now. Think about how to get your Top-Down brain ... PATTERNS In Action Problems Solutions 6. COMMON TERMS & QUADRATIC TEMPLATES In Action Problems Solutions 7. VISUAL SOLUTIONS In Action Problems Solutions Solution to Try-It #0...

Ngày tải lên: 05/12/2013, 08:40