The cost C, in dollars, of producing x units per day of a certain

Question

The cost C, in dollars, of producing x units per day of a certain commodity is given by

\(C= 3x^2 + 5x + 20\).

If the number of units produced per day is increased from 50 to 60, what is the corresponding increase in the production cost, in dollars?

A. 370

B. 380

C. 1,150

D. 3,310

E. 3,350

Hello, people! For this question, one way you could start is by inputting the values of 50 and 60 into seperate expressions and subtracting them from one another.

\(3 (60)^2 + 5(60) + 20\) - [\(3 (50)^2 + 5(50) + 20\)]

3(3600) + 5(60) + 20 - 3(2500) - 5(50) - 20

3(1100) + 5(10)

3300 + 50

3350

Bunuel · Answer

Essentially we need to find the value of:

(3*60^2 + 5*60 + 20)- (3*50^2 + 5*50 + 20) =

= 3*60^2 + 5*60 - 3*50^2 - 5*50 =

= 3*(60^2 - 50^2) + 50 =

= 3*(1,100) + 50 =

= 3,350

Answer: E.

DanTheGMATMan · Answer

Just plug in 60 and 50 for x. Little shortcut noticing a difference of squares:

https://www.youtube.com/watch?v=c5VEg92dOhE

rak08 · Answer

Understood this but just wanted to know when we calculate for just the incremental why does it seem to be wrong

like 3(10)^2 + 5(10) + 20

Bunuel · Answer

The rate of increase in a quadratic function is not constant. This means the increase from 1 to 2 is not the same as from 2 to 3. For example, in the basic quadratic f(x) = x^2, the increase from f(1) to f(2) is 3, but from f(2) to f(3) it's 5. So in the original question, f(10) does not correspond to the increase from f(50) to f(60).

GMATinsight · Answer

@x=50,  C_1 = 3(50)^2 + 5(50) + 20 .
@x=60,  C_2 = 3(60)^2 + 5(60) + 20 .

c_2 - c_1 = 3(60)^2 + 5(60) + 20 - 3(50)^2 - 5(50) - 20 =3,350

Answer: Option E

GmatKnightTutor · Answer

The cost C, in dollars, of producing x units per day of a certain commodity is given by

C= 3x^2 + 5x + 20 .

If the number of units produced per day is increased from 50 to 60, what is the corresponding increase in the production cost, in dollars?

A. 370

B. 380

C. 1,150

D. 3,310

E. 3,350

Hello, people! For this question, one way you could start is by inputting the values of 50 and 60 into seperate expressions and subtracting them from one another.

3 (60)^2 + 5(60) + 20  -  3 (50)^2 + 5(50) + 20 ]

3(3600) + 5(60) + 20 - 3(2500) - 5(50) - 20

3(1100) + 5(10)

3300 + 50

3350

bhanu29 · Answer

If u want to simplify the calculation(less multiplicatio), u can simplify the difference expression first .

C1 = 3(x1)^2 + 5x1 + 20 
 C2 = 3(x2)^2 + 5x2 + 20

x1 = 50, x2 = 60 here

C2-C1 = 3((x2)^2 - (x1)^2) + 5(x2-x1) 
Take x2-x1 common

C2-C1 = (x2-x1)*(3*(x2+x1) +5)

Now substitute x2-x1 = 10 x2+x1 =110

C2-C1 = 10*(3*110 +5) 
 C2-C1 = 3350

Correct Answer  E. 3,350

I find big multiplications very tedious and time consuming, if u are like me you might find this helpful, otherwise u can perform the calculation from word go.

This saved me sometime too ~30s

The cost C, in dollars, of producing x units per day of a certain

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

The cost C, in dollars, of producing x units per day of a certain

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