If d = (a + b)/(1 + ab/c^2), a = c/2, and b = 3c/4, what is

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

If d = (a + b)/(1 + ab/c^2), a = c/2, and b = 3c/4, what is

by BTGmoderatorDC » Sun Dec 15, 2019 6:42 pm

If \(d = \frac{a + b}{1 + \frac{ab}{c^2}}\), \(a = \frac{c}{2}\), and \(b = \frac{3c}{4}\), what is the value of d in terms of c ?

A. 10c/11
B. 5c/2
C. 10c/3
D. 10/(11c)
E. 5/(2c)

OA A

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Sun Dec 15, 2019 6:42 pm

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by [email protected] » Mon Dec 16, 2019 1:53 pm

Hi All,

We're given 3 equations to work with (which I'm going to order from least-to-most complicated):
1) A = C/2
2) B = 3C/4
3) D = (A+B)/(1 + (AB)/C^2))

We're asked for the value of D in terms of C. Under most circumstances, the phrase "in terms of" is a big hint to just do Algebra. However, this question can be solved rather easily by TESTing VALUES.

IF... C=4, then A=2 and B=3. Plugging those values in, we can solve for D:

D = (5)/(1 + 6/16) = 5/(22/16) = 80/22 = 40/11

Thus, we're looking for an answer that equals 40/11 when C=4. Based on how the answers are written, the correct answer should be really easy to find...

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jan 10, 2020 1:05 pm

BTGmoderatorDC wrote:If \(d = \frac{a + b}{1 + \frac{ab}{c^2}}\), \(a = \frac{c}{2}\), and \(b = \frac{3c}{4}\), what is the value of d in terms of c ?

A. 10c/11
B. 5c/2
C. 10c/3
D. 10/(11c)
E. 5/(2c)

OA A

Source: Official Guide

First, let's express a + b and ab in terms of c:

a + b = c/2 + 3c/4 = 2c/4 + 3c/4 = 5c/4 and ab = (c/2)(3c/4) = 3c^2/8

Therefore, d, in terms of c, is:

d = (a + b) / (1 + ab / c^2) = (5c/4) / (1 + (3c^2/8) / c^2) = (5c/4) / (1 + 3/8) = (5c/4) / (11/8) = 10c/11

Answer: A

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Founder and CEO
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