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Problem-Solving and Data Analysis / Percentages Difficulty: Hard

The number $a$ is $190 percent sign$ greater than the number $b$ . The number $b$ is $80 percent sign$ less than $24$ . What is the value of $a$ ?

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Explanation

Choice B is correct. It's given that the number $b$ is $80 percent sign$ less than $24$ . It follows that $b$ is equal to $24$ minus $80 percent sign$ of $24$ , which can be written as $b = 24 - (\frac{80}{100}) 24$ . This is equivalent to $b = 24 - 0.8 (24)$ , or $b equals 4.8$ . It's also given that the number $a$ is $190 percent sign$ greater than the number $b$ . It follows that $a$ is equal to $b$ plus $190 percent sign$ of $b$ . Since $b equals 4.8$ , this can be written as $a = 4.8 + (\frac{190}{100}) 4.8$ . This is equivalent to $a = 4.8 + 1.9 (4.8)$ , or $a equals 13.92$ .

Choice A is incorrect. This would be the value of $a$ if $a$ were $190 percent sign$ of $b$ , not $190 percent sign$ greater than $b$ .

Choice C is incorrect. This is $left parenthesis 190 minus 80 right parenthesis percent sign$ of $24$ .

Choice D is incorrect. This would be the value of $a$ if $b$ were $80 percent sign$ of $24$ , not $80 percent sign$ less than $24$ , and $a$ were $190 percent sign$ of $b$ , not $190 percent sign$ greater than $b$ .