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

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

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01 Jul 2017, 00:26
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46% (02:12) correct 54% (01:57) wrong based on 102 sessions

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

A. 10,000ab

B. 1,000,000ab

C. 100/(ab)

D. 10,000/(ab)

E. 1,000,000/(ab)

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Re: If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of  [#permalink]

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01 Jul 2017, 00:53
Bunuel wrote:
If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of a and b, p is what percent of m?

A. 10,000ab

B. 1,000,000ab

C. 100/(ab)

D. 10,000/(ab)

E. 1,000,000/(ab)

$$m = an/100$$
$$n = bp/100$$ ===> $$p = 100n/b$$

$$(p/m)*100 = ((100n/b)/(an/100))*100$$

$$= (10^6)/ab$$
E
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If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of  [#permalink]

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01 Jul 2017, 01:27
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Bunuel wrote:
If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of a and b, p is what percent of m?

A. 10,000ab

B. 1,000,000ab

C. 100/(ab)

D. 10,000/(ab)

E. 1,000,000/(ab)

$$m = a$$ % of $$n = \frac{a}{100}*n$$-------- (i)

$$n = b$$ % of $$p = \frac{b}{100} * p$$ ------- (ii)

Substituting value of $$n$$ from (ii) to (i), we get;

$$m = \frac{a}{100}*\frac{b}{100}*p$$ ------------- (iii)

Required percent is $$p$$ is what % of $$m$$. Let the unknown percent be $$x$$.

$$p = \frac{x}{100}*m$$-------- (iv)

Substituting value of $$m$$ from (iii) to (iv), we get;

$$p = \frac{x}{100}* \frac{a}{100}*\frac{b}{100}*p$$

$$1 = \frac{x}{100}* \frac{a}{100}*\frac{b}{100}$$

$$x = \frac{1,000,000}{ab}$$

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Re: If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of  [#permalink]

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01 Jul 2017, 02:36
m=an/100
n=bp/100
m=abp/10000
p*100/m=1000000/ab
hence E
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If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of  [#permalink]

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24 Jul 2017, 18:05
Bunuel wrote:
If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of a and b, p is what percent of m?

A. 10,000ab

B. 1,000,000ab

C. 100/(ab)

D. 10,000/(ab)

E. 1,000,000/(ab)

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.

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.

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Re: If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of  [#permalink]

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26 Jul 2017, 16:10
Bunuel wrote:
If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of a and b, p is what percent of m?

A. 10,000ab

B. 1,000,000ab

C. 100/(ab)

D. 10,000/(ab)

E. 1,000,000/(ab)

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.

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Re: If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of  [#permalink]

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30 Jul 2018, 10:29
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Re: If a>0 and b>0, and if m is a% of n and n is b% of p, then in terms of &nbs [#permalink] 30 Jul 2018, 10:29
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