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If w widgets cost c cents, how many widgets can you get for d dollars?

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If w widgets cost c cents, how many widgets can you get for d dollars?  [#permalink]

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New post 04 Sep 2018, 22:10
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A
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C
D
E

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  35% (medium)

Question Stats:

66% (01:23) correct 34% (01:19) wrong based on 93 sessions

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If w widgets cost c cents, how many widgets can you get for d dollars?


(A) \(\frac{100dw}{c}\)

(B) \(\frac{dw}{100c}\)

(C) \(100cdw\)

(D) \(\frac{dw}{c}\)

(E) \(cdw\)

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Re: If w widgets cost c cents, how many widgets can you get for d dollars?  [#permalink]

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New post 05 Sep 2018, 00:00
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Bunuel wrote:
If w widgets cost c cents, how many widgets can you get for d dollars?


(A) \(\frac{100dw}{c}\)

(B) \(\frac{dw}{100c}\)

(C) \(100cdw\)

(D) \(\frac{dw}{c}\)

(E) \(cdw\)


Unit cost of widgets=\(\frac{c}{w}\) cents
Or, \(\frac{c}{100w}\) dollars are required to purchase 1 widget
Or, $1 is required to purchase \(\frac{100w}{c}\)widgets
hence $d is required to purchase \(\frac{100dw}{c}\)

Ans. (A)
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Re: If w widgets cost c cents, how many widgets can you get for d dollars?  [#permalink]

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New post 05 Sep 2018, 00:30
For c cents, w widgets can be bought

......1 cent.., \(\frac{w}{c,}\) widgets can be bought

.......100d cents...., \(\frac{w}{c}\)*100d widgets can be bought

= \(\frac{100dw}{c}\)

Answer: A.
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If w widgets cost c cents, how many widgets can you get for d dollars?  [#permalink]

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New post 15 Sep 2018, 07:40
One of my favorite approaches for questions with all variables is plug-in method.

Let w=100 pcs, c=100 cents, d = $1 (actually d=c, so for 'd' we can buy the same number of 100 pcs - now we have to find an option that will give us the same 100 pcs.). Only option A gives us 100. Hence this is the right choice.

Now if you wonder how efficient this method is: 01:10 for the question above and I got the right answer, with my brain in a low level of energy consumption mode. Belive me, the saved brain stamina will be very useful for hard level questions later on the test. I highly recommend to use algebra only in cases in which it is really necessary.
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Re: If w widgets cost c cents, how many widgets can you get for d dollars?  [#permalink]

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New post 15 Sep 2018, 07:51
Bunuel wrote:
If w widgets cost c cents, how many widgets can you get for d dollars?


(A) \(\frac{100dw}{c}\)

(B) \(\frac{dw}{100c}\)

(C) \(100cdw\)

(D) \(\frac{dw}{c}\)

(E) \(cdw\)


1 Dollar = 100 Cents

So, d Dollar = 100 d Cents

For c cents w widgets can be bought

So, For 1 cents \(\frac{w}{c}\) widgets can be bought

Thus, for 100 d Cents \(\frac{100dw}{c}\) widgets can be bought, Answer must be (A)
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Re: If w widgets cost c cents, how many widgets can you get for d dollars?   [#permalink] 15 Sep 2018, 07:51
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