An electric company charges its commercial customers according the

Question

An electric company charges its commercial customers according the number of kilowatts of electricity they use per hour. The price charged is determined by the formula 2 + $\frac{5}{\sqrt{3-x}}$ dollars per hour, where x is the number of kilowatts used and 0 < x < 3. Which of the following is the closest to the value of x to the nearest 0.1 kilowatt if the amount charged per hour of use is $9.00 ?

(A) 1.4
(B) 2.0
(C) 2.3
(D) 2.5
(E) 2.7

(A) 1.4
(B) 2.0
(C) 2.3
(D) 2.5
(E) 2.7

sahilvermani · Answer

D

2 + 5/root(3-x) = 9

5/root(3-x) = 7

root(3-x) = 5/7

3 - x = 25/49

x = 3 - 25/49 = 122/49 = 2.5

AndrewN · Answer

An alternative approach  - Use the answers. Any  which of the following  question about  a single unknown  lends itself to back-solving, and (B) and (D) are excellent targets, since either one of them will be the answer or, through testing both, will point you to the correct answer (either higher or lower than the last value tested). In this case, (B), 2.0, makes a logical entry point, since the denominator would then be easy to work with:

2 + \frac{5}{\sqrt{3-(2)}}

2 + \frac{5}{\sqrt{1}}

2 + \frac{5}{1}

2 + 5 = 7

Since our target value is 9 and we know that dividing by a larger square root will only make the value smaller, we need to go higher. Try (D):

2 + \frac{5}{\sqrt{3-(2.5)}}

2 + \frac{5}{\sqrt{0.5}}

2 + 5*\frac{\sqrt{2}}{1}

2 + 5\sqrt{2}

Now, this is the point at which knowing certain common root values can help with timing. For instance, √2 is about 1.4, and that is just what we want. (√3 also comes up fairly frequently, and that one is closer to 1.7.)

2 + 5*1.4

2 + 7 = 9

You cannot get any closer, even though the actual value of √2 is closer to 1.41. (Note that we could logically eliminate (E), since it would have to be higher.) If you had time to kill, you could check (C), but if we appreciate that the +0.5 jump between answers (B) and (D) led to a difference between a derived value of 7 versus one of 9, we can estimate that a number that falls between them, almost in the middle, would likely lead to an answer closer to 8 than to 9.

GMAT™ Quant tests analytical reasoning as much as it does mathematical prowess. Once the basics are there, you can be flexible with your approach. Not only does this increase the likelihood of your arriving at the correct answer (instead of hitting the panic button if you cannot remember a formula), but you will probably go through the questions more efficiently as well.

Good luck with your studies.

- Andrew

siddhantmittal · Answer

Equating 9= 2 +  \frac{5}{\sqrt{3-x}}  
Solving we get  \sqrt{3-x}= \frac{5}{7}

Squaring both sides and solving, we get

x= 3 -  \frac{ 25}{49 }

Now, we can estimate the fraction part to be ~0.5

x= 3-0.5=2.5  OPTION D

Budhaditya_Saha · Answer

Can anyone please explain, what does this line mean?

"Which of the following is the closest to the value of  x  to the nearest 0.1 kilowatt if the amount charged per hour of use is $9.00 ?"

Is it only me, or is this line actually difficult to comprehend?

Bunuel · Answer

It just means find x when the price is $9 per hour, then round x to 1 decimal place. When we solve, we get x = 122/49 ≈ 2.489..., which to the nearest 0.1 is 2.5.

egmat · Answer

Let's solve this step by step.

We're told the price formula is  2  +  5 /√( 3  - x), and the price charged is  $9 . We need to find x.

Step 1:  Set the formula equal to  9 .
 9  =  2  +  5 /√( 3  - x)

Step 2:  Subtract  2  from both sides.
 7  =  5 /√( 3  - x)

Step 3:  Solve for the square root. Flip both sides to isolate it.
√( 3  - x) =  5 / 7

Step 4:  Square both sides to remove the  square root .
 3  - x = ( 5 / 7 )2 =  25 / 49

Step 5:  Solve for x.
x =  3  -  25 / 49 
x =  147 / 49  -  25 / 49 
x =  122 / 49 
x ≈  2.49

Rounded to the nearest  0.1 , that's  2.5 .

Answer: D

Common mistake : Some students try to square the entire equation before isolating the square root term, which creates a messy expression and leads to errors.   Key principle   here is:  always isolate the square root on one side FIRST, then square both sides . This keeps the algebra clean and avoids introducing extraneous terms.

GSV · Answer

9 = 2+ ( 5 / sqrt(3-x))
7 = 5 / sqrt(3-x)
sqrt(3-x) = 5/7 
3-x = 25/49
x= 3- (25/49)
x= 122/49 = 2.4897 ~ 2.5

An electric company charges its commercial customers according the

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

An electric company charges its commercial customers according the

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards