sat suite question viewer

Problem-Solving and Data Analysis / Percentages Difficulty: Hard

The number $a$ is $70 percent sign$ less than the positive number $b$ . The number $c$ is $60 percent sign$ greater than $a$ . The number $c$ is how many times $b$ ?

Back question 32 of 78 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

Explanation

The correct answer is $.48$ . It's given that the number $a$ is $70 percent sign$ less than the positive number $b$ . Therefore, $a = (1 - \frac{70}{100}) b$ , which is equivalent to $a = (1 - 0.70) b$ , or $a equals 0.30 b$ . It's also given that the number $c$ is $60 percent sign$ greater than $a$ . Therefore, $c = (1 + \frac{60}{100}) a$ , which is equivalent to $c = (1 + 0.60) a$ , or $c equals 1.60 a$ . Since $a equals 0.30 b$ , substituting $0.30 b$ for $a$ in the equation $c equals 1.60 a$ yields $c equals 1.60 left parenthesis 0.30 b right parenthesis$ , or $c equals 0.48 b$ . Thus, $c$ is $0.48$ times $b$ . Note that .48 and 12/25 are examples of ways to enter a correct answer.