How to do some calculation fast

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Hi,
Please suggest some quicker way to solve practice questions Q#135 and #182 of Problem Solving in OG 13th Edition.

As per the explanation of Q.135, they have done calculations:
207/1.15=180 how can we do this calculation fast.

In Q.182 explanation also some lengthy calculations have been done, which takes time.

Please suggest some tips for such questions.

Thanks!

[rintoo22]

Hi Depali,

Please post the questions.

[srcc25anu]

1.15 * 2 = 2.30
so 2.07 * 100 / 1.15 = (Slightly less than 2) * 100

[GMATGuruNY]

PS182 in the OG13:

A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer's initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer's initial cost for the 60 cameras?
A.7% loss
B.13% loss
C.7% profit
D.13% profit
E.15% profit

54 cameras yield a 20% profit, while 6 cameras suffer a 50% loss.
Average for all 60 cameras = (54*20 - 6*50)/60 = 13.

The correct answer is D.

[GMATGuruNY]

PS135 in the OG13:

The price of lunch for 15 people was $207.00,
including a 15 percent gratuity for service. What was
the average price per person, EXCLUDING the
gratuity?

(A) $11.73
(B) $12.00
(C) $13.80
(D) $14.00
(E) $15.87

We can plug in the answers, which represent the cost per person.
Given that the total cost is an INTEGER, the correct answer is almost certainly an integer itself.
Answer choice D is too great, since 15 people paying $14 each = 15*14 = 210 -- a value beyond the total cost of 207.

Answer choice B: $12 per person without gratuity
Total price for 15 people = 15*12 = 180.
Price + gratuity = 180 + .15(180) = 180+27 = 207.
Success!

The correct answer is B.

[Anju@Gurome]

207/1.15=180 how can we do this calculation fast.

Prime factorization.
207 = 3*69 = 3*3*23
115 = 5*23

So, 207/1.15 = 207*100/115 = 9*100/5 = 180

[rintoo22]

The price of lunch for 15 people was $207.00,
including a 15 percent gratuity for service. What was
the average price per person, EXCLUDING the
gratuity?

(A) $11.73
(B) $12.00
(C) $13.80
(D) $14.00
(E) $15.87

x+15/100(x)= 207
x=180
180/15 = 12 ... Ans B.

[bharat.bondalapati]

For fast calculations, learn squares and cubes upto 30, multiplication tables atleast upto 20 and also learn to quickly factorize larger numbers. Hope that helps.