If x/4 + 24/x = 5, what are the values of 3x - 7?

Question

A. 8
B. 8 and 24
C. 17
D. 12 and 29
E. 17 and 29

BumblebeeMan · Answer

FYI, this really should be posted in the Math Questions section.

4x(x/4 + 24/x = 5)
x^2 + 96 = 20x
x^2 - 20x + 96 = 0
(x-8)(x-12) = 0
x = 8 or 12

If f(x) = 3x-7
f(8) = 3*8 - 7 = 17
f(12) = 3*12 - 7 = 29

Answer number 5 is correct.

nakib77 · Answer

I got the same thing E is the answer 29 or 17

Bhai · Answer

x^2 - 20x + 96 = 0 
(x-8)(x-12) = 0 
x = 8 or 12 


substituting these values in 3x - 7 gives us answer choice 5.

TeHCM · Answer

x/4 + 24/x = 5 => x^2-20x+96 = 0

x could be either 12 or 8

thus 3x-7 could be either 29 or 17

E

krisrini · Answer

solving for x and substituing in 3x-7 would give the answer E.

PareshGmat · Answer

\frac{x}{4} + \frac{24}{x} = 5

\frac{x^2+96}{4x} = 5

x^2 - 20x + 96 = 0

x = 12 OR x = 8

3x-7 = 17 OR 29

Answer = E

deepthit · Answer

given expression can bededuced to x^2 -20x+96 =0 => x values are 8 and 12

substituting 8 and 12 in the 3x-7 gives 17 and 29 respectively

chetan2u · Answer

Hi,
Another way for those who have difficulty in factorising..
Check for values of 3x-7..
A) 3x-7=8....x=5 substitute in the equation..
You don't get 5 ..
B) same as A..
C) 17=3x-7.....x=8
Substitute in equation..
8/4 + 24/8 = 2+3=5.. correct.
SO 17 is correct and thus we can check for choices where 17 is a choice..
So we can skip D
D) 12=3x-7... substitute and you don't get 5
E) 17 is correct,lets check 29..
3x-7=29...x=12..
Substitute in equation 12/4 + 24/12 = 3+2=5.. correct

E

EgmatQuantExpert · Answer

Solution

Given:  
 • x/4 + 24/x = 5

To find:  
• We need to find the value of 3x-7.

Approach and Working:   
 • x/4 + 24/x = 5 
 o x2+96/4x= 5
o x2+96-20x=0
o (x-12)(x-8)=0
o Thus, x=12 and 8

• For x= 12
 o 3x-7= 29

• For x= 8
 o 3x-7= 17

Hence, the correct answer is option E.

Answer: E

chetan2u · Answer

Responding to a PM

\frac{x}{4} + \frac{24}{x} = 5 ...
Get the LCM of denominators of two fractions - 4 and x, so LCM is 4x...
so LHS =  \frac{x}{4} + \frac{24}{x} = \frac{x*x+4*24}{4x}=\frac{x^2+96}{4x}=5  = RHS
now multiply both sides by 4x...
 \frac{x^2+96}{4x}=5............\frac{x^2+96}{4x}*4x=5*4x.........x^2+96=20x...........x^2-20x+96=0............x^2-12x-8x+96=0...........x(x-12)-8(x-12)=0............(x-12)(x-8)=0 , so x can be 12 or 8
1) x=12, 3x-7=3*12-7=36-7=29
2) x=8, 3x-7=3*8-7=24-7=17
so E

KarishmaB · Answer

We can eliminate options by back solving. The good thing is that multiple options have the same value so it makes the process faster. But mind you, all calculations I am showing below need to be done orally. Else, this method is not worth it and you might as well make a quadratic and solve.

The options give the values of 3x - 7.

If 3x - 7 = 8, x = 5 
5/4 + 24/5 do not give an integer. Hence eliminate (A) and (B)

If 3x - 7 = 17, x = 8
8/4 + 24/8 = 5 (Fits)

If 3x - 7 = 29, x = 12
12/4 + 24/12 = 5 (Fits)

Answer (E)

shashankism · Answer

x/4 + 24/x = 5
 x^2 + 96 = 20x 
 x^2 - 20x + 96 = 0 
 x^2 - 12x - 8x + 96 = 0 
 (x - 12) (x - 8) = 0 
x = 12,8

3x - 7 = 29, 17

Answer E

If x/4 + 24/x = 5, what are the values of 3x - 7?

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GMAT Problem Solving (PS) Questions

If x/4 + 24/x = 5, what are the values of 3x - 7?

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