gmat quant topic 3 (inequalities + absolute value) solutions

... for the absolute value expression | x + 3| . If x > -3, making ( x + 3) positive, we can rewrite | x + 3| as x + 3: x + 3 < 4 x < 1 If x < -3, making ( x + 3) negative, ... solution: |2 + 3| = 4(2) – 3 |5| = 8 – 3 5 = 5 Now let's consider what happens when x + 3 is negative. To do so, we multiply x + 3...

Ngày tải lên: 14/05/2014, 16:55

... discussion. Answer is C 2. From 1, a+b=-1. From 2, x=0, so ab=6. (x+a)*(x+b)=0x^ 2+( a+b)x+ab=0 So, x= -3, x=2 The answer is C. 3. ( 0+6 +x) /3= 3,x =3 ( 0+0 +y) /3= 2,y=6 Answer is B 4. Just image that, ... 2x + y = px + 7 yields y = 2x + 7 (B) 2x + y = –px yields y = –6x (C) x + 2y = px + 7 yields y = (3/ 2)x + 7/2 (D) y – 7 = x ÷ (p – 2) yields y = (1/2...

Ngày tải lên: 14/05/2014, 16:55

... 0.1(F + G + C) 10C = F + G + C 9C = F + G The pure Fujis plus the cross pollinated ones total 187 (4) F + C = 187 3/ 4 of his trees are pure Fuji (5) F = (3/ 4)(F + G + C) (6) 4F = 3F + 3G + 3C (7) ... gives us: (11) (3G + 3C) + C = 187 (12) 3G + 4C = 187 ( 13) 9G + 12C = 561 Substituting equation (10) into ( 13) gives: (14) 9G + 8G...

Ngày tải lên: 14/05/2014, 16:55

... Is ( c + d )/2 > ( a + b + c + d + e + f )/6 ? Is 3( c + d ) > a + b + c + d + e + f ? Is 3 c + 3 d > a + b + c + d + e + f ? Is 2 c + 2 d > ... the set. Therefore, ( x + y + x + y + x – 4 y + xy + 2 y ) 6 = y + 3...

Ngày tải lên: 14/05/2014, 16:55

... 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 ... = 3 Odd 1 t 1 = 3 + 1 = 4 Even 2 t 2 = 4 + 2 = 6 Even 3 t 3 = 6 + 3 = 9 Odd 4 t 4 = 9 + 4 = 13 Odd...

Ngày tải lên: 14/05/2014, 16:55

... + y = s + q . Since x + y + z = 180 and since q + s + r = 180, it must be true that z = r . We can now look at the statements. Statement (1) tells us that xq + sy + sx + ... ( 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...

Ngày tải lên: 14/05/2014, 16:55

... getting a 2, 3, and 5, in any order, can be calculated as follows (remember, when calculating probabilities, OR means add): (1 /33 6) + (1 /33 6) + (1 /33 6) + (1 /33 6) + (1 /33 6) + (1 /33 6) = 6 /33 6 Now, let’s ... to know is R>W. For 1, R/(B+W)> W/(B+R)=>R/(B+W)-W/(B+R) >0 [ R(B+R)-W(B+W)]/(B+W)(B+R) >0 (R-W)(R+W+B)/(B+W)(B+R) >0 As (R+W+B)>0,...

Ngày tải lên: 14/05/2014, 16:55

... = (2 /3) h, we can solve for h: (1 /3) h + (2 /3) h + h + l = 2000 (1 /3) h + (2 /3) h + h +( 2 /3) h = 2000 (8 /3) h = 2000 h = 2000 (3/ 8) h = 750 If h = 750, l = (2 /3) h = 500. (2) SUFFICIENT: If m = s + 250, ... Captured Ticks Awarded Berks Captured 1 3, 4 or 5 77 30 8, 30 9, 31 0, or 31 1 7 21, 22, or 23 11 44, 45, 46 or 47 11 33 , 34 , or 35 7 28, 2...

Ngày tải lên: 14/05/2014, 16:55

... required = 3 × 3 × 3 – 1 = 26. 29. 6 P 4 × 2 = 720 30 . 2 × 2 × 2 × 4 × 4 – 2 × 1 × 1 × 4 × 4 = 96 31 . 10 32 . 3 ! × 3 ! = 36 33 . 6 C 2 × 9 × 3 = 405 seconds 34 . 9 ! / 5! × 4! 35 . 6 × 2 × 1 × 3 × 2 ... So, 2 6+2 6 2 +2 6 3 , the units digit is 8. Answer is E 62. C(4,1)C(6,2)+C(4,2)C(6,1)+C(4 ,3) =60 +3 6 +4 =100 63. C(9,1)C(9,1)C(8,1)C(7,1)=4 536 64....

Ngày tải lên: 14/05/2014, 16:55

... = 3 20 – 3 17 = 3 17 (3 3 – 1) = 3 17 (27 – 1) = 3 17 (26) = 3 17 ( 13) (2) Now we have what we need: the prime factorization of x. We can see that x has three different prime factors: 2, 3, ... x: x = (3 2 ) 10 – 3 17 = 3 20 – 3 17 Now, we still have not expressed x as a product of prime numbers. We need to pull out a common factor from both terms. The largest...

Ngày tải lên: 05/12/2013, 08:40