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If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the

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If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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If mn ≠ 0 and 25 percent of n equals \(37\frac{1}{2}\) percent of m, what is the value of \(\frac{12n}{m}\)?

A) 18

B) \(\frac{32}{3}\)

C) 8

D) 3

E) \(\frac{9}{8}\)


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Originally posted by AbdurRakib on 15 Jun 2016, 01:25.
Last edited by Bunuel on 03 Oct 2017, 01:58, edited 3 times in total.
Edited the question.
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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New post 15 Jun 2016, 07:59
Given : 25 percent of n equals 37(1/2) percent of m => (25/100)*n = (75/200)*m => 2n = 3m.
12n/m = 6*2n/m = 6*3m/m = 18. Hence A.
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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New post 21 Jun 2016, 11:39
I'm totally stuck with arithmetic in this question. I will be very grateful for explanation why exactly I get another result. Can't see it on my own.
I start with (1/4)*n=(37/100)*(1/2)*m and get (1/4)*n=(37/200)*m. Then I continue with 200n=37*4*m and divide both sides by 2 and get 100n=75n. This equation I divide by 100, resulting in n=(3/4)m. Here I substitude for m and get that 12n=12*(3/4)m=9m, and it comes that 9m/m=9.
Where am I lost?
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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MannyOliveira wrote:
I'm totally stuck with arithmetic in this question. I will be very grateful for explanation why exactly I get another result. Can't see it on my own.
I start with (1/4)*n=(37/100)*(1/2)*m and get (1/4)*n=(37/200)*m. Then I continue with 200n=37*4*m and divide both sides by 2 and get 100n=75n. This equation I divide by 100, resulting in n=(3/4)m. Here I substitude for m and get that 12n=12*(3/4)m=9m, and it comes that 9m/m=9.
Where am I lost?


37(1/2) % of m = 37.5 % of m = 75/2 * of m

You have incorrectly assumed it to be (37/100)*(1/2)*m = 18.5% of m.

Hope this helps.
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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AbdurRakib wrote:
If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the value of 12n/m?

A) 18
B) \(\frac{32}{3}\)
C) 8
D) 3
E) \(\frac{9}{8}\)


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-------------------------------------------------------------------------------------------------------------

25 % of n = 37 (1/2) % of m , this means n>m

n/m > 1 ; 12 (n/m) > 12

there is only 1 option greater than 12. i.e 18

Answer = 18
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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AbdurRakib wrote:
If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the value of 12n/m?

A) 18
B) \(\frac{32}{3}\)
C) 8
D) 3
E) \(\frac{9}{8}\)



Useful conversions:
25% = 1/4
37.5% = 3/8


25 percent of n equals 37(1/2) percent of m
In other words, 1/4 of n equals 3/8 of m
We get: n/4 = 3m/8

What is the value of 12n/m?
Take n/4 = 3m/8
Cross-multiply to get: (8)(n) = (3m)(4)
Simplify: 8n = 12m
Divide both sides by m to get: 8n/m = 12 [ALMOST THERE!!!]
Multiply both sides by 1.5 to get: 12n/m = 18

Answer:
[Reveal] Spoiler:
A


Cheers,
Brent
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Originally posted by GMATPrepNow on 10 Aug 2016, 11:59.
Last edited by GMATPrepNow on 30 Nov 2016, 13:54, edited 1 time in total.
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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AbdurRakib wrote:
If mn ≠ 0 and 25 percent of n equals \(37{}^1/_2\) percent of m, what is the value of \(\frac{12n}{m}\)?

A) 18
B) \(\frac{32}{3}\)
C) 8
D) 3
E) \(\frac{9}{8}\)


We are given that 25 percent of n = 37 1/2 percent of m. So we have:

(25/100)n = (37.5/100)m

We can multiply both sides by 100:

25n = 37.5m

We can multiply both sides by 10:

250n = 375m

We can divide both sides by 25:

10n = 15m

2n = 3m

We can multiply both sides by 6 to get the 12n in the numerator of (12n)/m:

12n = 18m

Finally, divide both sides by m, obtaining the value of (12n)/m:

(12n)/m = 18

Answer: A
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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25n/100 = 37.5m/100
25n = 37.5m
25n/m = 37.5
12.5n / m = 18.45
12n/m = 18 (no need to calculate all other option not at all close to 18)
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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New post 02 Oct 2017, 09:01
1/4(N)=3/8(M)
N=12/8(M)
N/M=12/8
12N/M = 18
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If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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New post 01 Mar 2018, 06:10
FacelessMan wrote:
Given : 25 percent of n equals 37(1/2) percent of m => (25/100)*n =(75/200)*m => 2n = 3m.
12n/m = 6*2n/m = 6*3m/m = 18. Hence A.


hello FacelessMan with brains :)

can you please explain why are you dividing 75 by 200 and not by 100 like you did here (25/100)

thanks! :)
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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New post 01 Mar 2018, 06:16
GMATPrepNow wrote:
AbdurRakib wrote:
If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the value of 12n/m?

A) 18
B) \(\frac{32}{3}\)
C) 8
D) 3
E) \(\frac{9}{8}\)



Useful conversions:
25% = 1/4
37.5% = 3/8


25 percent of n equals 37(1/2) percent of m
In other words, 1/4 of n equals 3/8 of m
We get: n/4 = 3m/8

What is the value of 12n/m?
Take n/4 = 3m/8
Cross-multiply to get: (8)(n) = (3m)(4)
Simplify: 8n = 12m
Divide both sides by m to get: 8n/m = 12 [ALMOST THERE!!!]
Multiply both sides by 1.5 to get: 12n/m = 18

Answer:
[Reveal] Spoiler:
A


Cheers,
Brent


Useful conversions:
25% = 1/4
37.5% = 3/8


Hello GMATPrepNow,

what if dont know that 37.5% is 3/8. How can i convert 37.5% into 3/8 manually with pen and paper ? :)

please explain :-)
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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dave13 wrote:

Useful conversions:
25% = 1/4
37.5% = 3/8


Hello GMATPrepNow,

what if dont know that 37.5% is 3/8. How can i convert 37.5% into 3/8 manually with pen and paper ? :)

please explain :-)


We can first write 37.5 as a fraction over 100, and then simplify that fraction.

So, 37.5% = 37.5/100 = 375/1000 = 75/200 = 15/40 = 3/8

Cheers,
Brent
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If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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Quote:
what if dont know that 37.5% is 3/8. How can i convert 37.5% into 3/8 manually with pen and paper ?


I hope you know 1/2 = 50%

So 1/8 will 50/4 or 12.5%

Multiply numerator by 3 to get 37.5%.

Have attached chart besides your bed too :-)

Hope this helps.
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Re: If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the [#permalink]

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New post 19 Mar 2018, 12:57
If mn ≠ 0 and 25 percent of n equals 37.5 percent of m, what is the value of 12/m?

We can solve it by direct calculation or through plugging numbers

Solution 1:
25 % of n is equal to 37.5% of m

so 100% of n = 150% of m
N = 1.5M
12N = 18M

Ans: A

Solution 2:

Plugging in a number that is easy to calculate both 25% and 37.5%. Let's take 60 as N.
N = 60
25% Of N = 15

Now 15 is 37.5% of M. So 100 % of M is = 40. [37.5% is 15 , then 75% is 30 , which gives us 100% = 40]

Now we got N=60 , M = 40

Coming to our problem = 12n/m = \(\frac{60*12}{40}\) = 18

Ans: A
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