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

Question

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)

PS93502.01

CareerGeek · Accepted Answer

a + b = c/2 + 3c/4 = 5c/4

ab/c^2 =   = 3/8
--> 1 + ab/c^2 = 1 + 3/8 = 11/8

--> d = (5c/4)/(11/8) = 5c/4*8/11 = 10c/11

IMO Option A

Pls Hit kudos if you like the solution

Archit3110 · Answer

d = \frac{a + b}{1 + \frac{ab}{c^2}}

D=C/2+3C4 * C^2/ C^2+C/2*3C/4
SOLVE
10C/11
IMO A

EMPOWERgmatRichC · Answer

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

DeeptiManyaExpert · Answer

Plugging in can be super useful and a faster way of solving some Algebra questions where too many variables are involved. Try c = 4. Use 2 and 4 in the denominators to decide the value for c.

c = 4
a = 2
b = 3

Target answer: d = 40/11 (circle it)

Note: You should feel elated if you get the target answer in the fraction form as it means that you need to check the denominators of the answer choices first. Eliminate all answer choices which are not the multiples of the denominator of your target answer. In this case, only A and D qualify the criteria.

Now, plug the value of the variables in A and D options. Only option A will match.

Thus, the answer is A.

Hope this helps

bumpbot · Answer

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards