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# If w widgets cost d dollars, then at this rate how many dollars will 2

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Math Expert
Joined: 02 Sep 2009
Posts: 50000
If w widgets cost d dollars, then at this rate how many dollars will 2  [#permalink]

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20 May 2017, 06:31
00:00

Difficulty:

25% (medium)

Question Stats:

82% (00:50) correct 18% (00:32) wrong based on 21 sessions

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If w widgets cost d dollars, then at this rate how many dollars will 2000 widgets cost?

(A) wd/2000

(B) 2000w/d

(C) 2000d/w

(D) d/(2000w)

(E) 2000/(wd)

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Re: If w widgets cost d dollars, then at this rate how many dollars will 2  [#permalink]

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20 May 2017, 06:49
Cost of w widgets = d dollars
Cost of 1 widget = d/w

Thus, cost of 2000 widgets = 2000d/w

Hence C
Senior SC Moderator
Joined: 22 May 2016
Posts: 2034
Re: If w widgets cost d dollars, then at this rate how many dollars will 2  [#permalink]

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21 May 2017, 08:07
Bunuel wrote:
If w widgets cost d dollars, then at this rate how many dollars will 2000 widgets cost?

(A) wd/2000

(B) 2000w/d

(C) 2000d/w

(D) d/(2000w)

(E) 2000/(wd)

Probably not as quick as algebraic method but perhaps helpful to some: Choose smart numbers and plug into answer choices.

Let original number of widgets, w = 2
Let original total cost, d = $10 1. Do the mental math.$10 for 2 items means $5 per item.$5 per item * 2000 items = $10,000; OR 2. Unit cost for w is total cost / # of items = $$\frac{10}{2}$$=$5 per w or $$\frac{5}{w}$$

$$\frac{5}{w}$$ * 2000w = $10,000 3. Plug w = 2 and d = 10 into answer choices, don't worry about the$5 unit cost, just look for $10,000 as the answer*: (A) wd/2000 =2*10/2000 = 20/2000 ... no need to calculate. Too small. Eliminate (B) 2000w/d = 2000*2/10 = 4000/10 =$400. Eliminate

(C) 2000d/w = 2000*10/2 = 20,000/2 = $10,000. Correct (D) d/(2000w) = 10/2000*2 = 10/4000 . . . no need to calculate. Too small. Eliminate (E) 2000/(wd) = 2000/2*10 = 2000/20 =$100. Eliminate

*If you scan the answers quickly, with these chosen small values for w and d, it's immediately clear that A and D, with small values in numerator and large values in denominator, will yield an answer that is too small. Similarly, with E, you might notice that the denominator is too big, even with the relatively small numbers chosen for w and d. Now you're down to (B) and (C).
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Re: If w widgets cost d dollars, then at this rate how many dollars will 2 &nbs [#permalink] 21 May 2017, 08:07
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