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Physicians often estimate the adult height \(c\), in inches,

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Physicians often estimate the adult height \(c\), in inches,

by swerve » Sat Jul 13, 2019 9:10 am

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Physicians often estimate the adult height \(c\), in inches, of a female child by using the inequalities

\(\frac{m+f-13.2}{2}\leq c \leq \frac{m+f-2.8}{2}\)

where \(m\) represents the mother's adult height and \(f\) represents the father's adult height, both measured in inches. If Rachel is a 5-year-old girl, what is her maximum adult height that will satisfy these inequalities?

1. Rachel's height at age 5 is 44 inches.
2. Rachel's mother's adult height is 62 inches and Rachel's father's adult height is 71 inches.

The OA is B

Source: GMAT Prep
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Jul 15, 2019 9:29 pm

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swerve wrote:Physicians often estimate the adult height \(c\), in inches, of a female child by using the inequalities

\(\frac{m+f-13.2}{2}\leq c \leq \frac{m+f-2.8}{2}\)

where \(m\) represents the mother's adult height and \(f\) represents the father's adult height, both measured in inches. If Rachel is a 5-year-old girl, what is her maximum adult height that will satisfy these inequalities?

1. Rachel's height at age 5 is 44 inches.
2. Rachel's mother's adult height is 62 inches and Rachel's father's adult height is 71 inches.

The OA is B

Source: GMAT Prep
Given \(\frac{m+f-13.2}{2}\leq c \leq \frac{m+f-2.8}{2}\), we find that the estimated adult height of a female child is a function of mother's and father's heights and is not a function of female child's current height; thus, Statement 1 is of no use. We see that Statement 2 provides the required data, thus, it is sufficient to answer the question.

Maximum height a female child can attain = \(\frac{m+f-2.8}{2} = \frac{71+62-2.8}{2}\) = a unique value. Suffiicent.

The correct answer: B

Hope this helps!

-Jay
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by deloitte247 » Fri Jul 19, 2019 9:09 pm

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$$\frac{\left(m+f-13.2\right)}{2}\le c\le\frac{\left(m+f-2.8\right)}{2}$$
m = mother's adult height
f = father's adult height
c = adult's height

Statement 1: Rachel height at age 5 was 44 inches. The inequality given does not require child's height. Hence, statement 1 is NOT SUFFICIENT

Statement 2: Rachel's mother's adult height is 62 inches and Rachel's father's adult height is 71 inches.
m = 62 inches, f = 71 inches
Since the greater part of the inequality is
$$\frac{\left(m+f-2.8\right)}{2},$$
we can get the minimum adult height <c>;
$$c=\frac{\left(m+f-2.8\right)}{2}$$
$$c=\frac{62+71-2.8}{2}\ \ =\ 65.1$$
Statement 2 alone is SUFFICIENT. The correct answer is option B
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