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If b percent of c percent of d percent of b/c

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by Brent@GMATPrepNow » Thu Feb 02, 2017 9:45 am
Another question I made up. Difficulty-wise, I'd say this is in the 600 to 650 range.
If b percent of c percent of d percent of b/c equals 1/c percent of b percent of 100,000, then what is the value of bcd?

A) 10^6
B) 10^7
C) 10^8
D) 10^9
E) 10^10
Answer: B
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by Matt@VeritasPrep » Thu Feb 02, 2017 5:40 pm
Oh yeesh!

I'd use the definition p% = p/100, then apply it to each term here, giving me

(b/100) * (c/100) * (d/100) * b/c = (1/c)/100 * (b/100) * 100000

Divide both sides by (b/100):

(c/100) * (d/100) * b/c = (1/c)/100 * 100000

Multiply both sides by 100 * 100:

c * d * b/c = (1/c) * 100 * 100000

The c's cancel on the left:

d * b = (1/c) * 100 * 100000

Then multiply both sides by c:

c * d * b = 100 * 100000

And we're done!
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by Brent@GMATPrepNow » Fri Feb 03, 2017 10:38 am
Brent@GMATPrepNow wrote:If b percent of c percent of d percent of b/c equals 1/c percent of b percent of 100,000, then what is the value of bcd?

A) 10^6
B) 10^7
C) 10^8
D) 10^9
E) 10^10
x percent = x/100

So, we can translate the given information as follows:
(b/100)(c/100)(d/100)(b/c) = [(1/c)/100](b/100)(100,000)
Evaluate each side: b²cd/1,000,000c = 100,000b/10,000c
Simplify each side: b²d/1,000,000 = 10b/c
Multiply both sides by 1,000,000 to get: b²d = 10,000,000b/c
Multiply both sides by c to get: b²cd = 10,000,000b
Divide both sides by b to get: bcd = 10,000,000
In other words, bcd = 10^7

Answer: B

Cheers,
Brent
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by GMATGuruNY » Sat Feb 04, 2017 1:49 pm
If b percent of c percent of d percent of b/c equals 1/c percent of b percent of 100,000, then what is the value of bcd?

A) 10^6
B) 10^7
C) 10^8
D) 10^9
E) 10^10
Alternate approach:
Plug in values for b and c and solve for d.

Let b=100 and c=100, with the result that b/c = 1.
The questions stem becomes:
If 100% of 100% of d percent of 1 equals 1/100% of 100% of 100,000, then what is the value of bcd?
More simply:
If d% of 1 equals (1/100)% of 100,000, then what is the value of bcd?

Translating the blue portion into math, we get:
(d/100)(1) = (1/100)/100 * 100,000
d/100 = 10
d = 1000.
Thus, bcd = 100*100*1000 = 10�.

The correct answer is B.
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