If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of

m=an/100
n=bp/100
m=abp/10000
p*100/m=1000000/ab
hence E

Pick numbers, in stages. If there are three integers to be compared, I start with the second to avoid generating numbers that are too large or too small.

For percents, I avoid 100% when choosing values for "a" and "b" percents. Choosing 50% or 10% usually keeps arithmetic simpler.

Assign
n = 40
a% = 50

Calculate
m is a% percent of n

m is 50% of 40

m = 20

Assign
b = 50%

Calculate
n is b% of p

40 is 50% of 80 --> p = 80

p = 80
m = 20

p is \(\frac{80}{20}\) * 100 = 400% of m

a = 50
b = 50

All the answer choices contain ab, which = 2,500

Now the process goes very quickly.

We know ab = 2,500

We need the answer choice that yields the raw number 400. "Percent" is already in the prompt's last clause: do not divide 400 by 100 (nor "move the decimal left two places") - that trap is in the answer choices.

Answer choices

Eliminate A and B without calculation. They're huge.

Eliminate C without calculation. It's a fraction whose numerator is smaller than denominator - much too small.

D. 10,000/(ab)? No.
(10,000/2,500) = 4. We need 400. D is the trap answer here.

E. 1,000,000/2,500 = 400. Correct.

Answer E

We can create the following equations:

m = (a/100)(n)

and

n = (b/100)(p)

Thus:

m = (a/100)(b/100)(p)

m = (ab/10,000)(p)

m(10,000/ab) = p

p = m x (1,000,000/ab)/100

Thus, p is 1,000,000/ab percent of m.

Answer: E

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