If m pencils cost the same as n pens, and each pencil costs 20 cents,

Question

If m pencils cost the same as n pens, and each pencil costs 20 cents, what is the cost, in dollars, of 10 pens, if each pen costs the same amount? (100 cents = 1 dollar)

A. 200n/m

B. 2n/100m

C. 2m/n

D. 2n/m

E. 200nm

cbh · Answer

equality
20*m=n*x (x price of pens)
multiply the equality by 10
10*20*m=10*n*x
200m=10nx
10x=200m/n or in dollars 2m/n

varun4s · Answer

Let cost of each pen= y
No of pens= n
Total cost of pen= ny

Cost of each pencil= 20 cents
No of pencils= m
Total cost of pencil= 20m

Total cost of m pencils= Total cost of n pens
20m=ny
Multiply both sides by 10
200m= 10ny
10y = \frac{200m}{n} 
10y=  \frac{2m}{n}  (100cents= 1 dollar)
cost of 10 pencils= 10y

Answer:C.

Kudos please if you like my explanation!

niks18 · Answer

Given:  n  pens  = m  pencils

=>  1  pen  = \frac{m}{n}  pencils

therefore  10  pens  = \frac{10m}{n}  pencils

Given cost of  1  pencil =  20  cents

therefore cost of  m  pencils  = 20m  cents

hence cost of  10  pens in  $ = \frac{(10*20m)}{n}*\frac{1}{100} = \frac{2m}{n}

Option  C

pushpitkc · Answer

The cost of m pencils is the same as the cost of n pens.
Assume m = 5 and n = 4
Let x be the cost of a pen.

Given data:   Cost of a pencil - 20 cents

20m = nx
20*5 = 4*x => x = 5*5 = 25 cents
Therefore, if each pencil costs 20 cents, the pens cost 25 cents.

We have been asked to find the cost of 10 pens in dollars, 
the cost of 10 pens will be 250 cents or 2.5$

Putting the values of m and n in the answer options, we will be able to arrive at the solution

A.  \frac{200n}{m} = \frac{200*4}{5} = 250 $(wrong)
B.  \frac{2n}{100m} = \frac{2 * 5}{100 * 4} = \frac{1}{40} = 0.25 $(wrong)
C.  \frac{2m}{n} = \frac{2*5}{4} = 2*1.25 = 2.5 $(correct)

Hence,  Option C  is the correct answer option.

PKN · Answer

Given the unit cost of pencil=20 cents=$0.2. Let the unit cost of pen $x.
Given, m pencils cost the same as n pens.
So, 0.2*m=n*x
Or, x= \frac{0.2m}{n}

Ans. (C)

So, cost of 10 pens=unit cost of pen * no of pens=x*10= \frac{0.2m}{n}*10 = \frac{2m}{n}

AashiS · Answer

Why both sides are multiplied by 10??

uttam94317 · Answer

=> 11 pen

therefore 1010 pens

Given cost of 11 pencil

therefore cost of mm pencils =20m=20m cents

Option C

ScottTargetTestPrep · Answer

We can let p = the cost of a pen, in cents and we can create the equation:

20m = pn

20m/n = p

So the cost of each pen, in dollars, is (20m/n)/100 = 20m/100n = m/5n.

So 10 pens cost:

10 x m/5n = 2m/n dollars.

Alternate Solution:

We are told that m pencils cost the same as n pens, and pencils cost 20 cents (0.20 dollars) each, so we have:

0.20m = n

We see that n pens cost 0.20m, so the cost of one pen can be obtained by dividing by n, so we get:

0.20m/n = n/n

0.20m/n = 1

Since 1 pen costs 0.20m/n dollars, then 10 pens costs (0.20m/n) x 10 = 2m/n dollars.

Answer: C

sahilkak · Answer

pencil costs-20 cents
we have m pencils, so m pencil total cost=20m cents

20 m cost=n x - where n is no of pens

so 1 pen cost-20m/n cents
10-pen cost-200m/n cents
 1 dollar=100 cents

so 10 pen cost-200m/n * 1/100=20m/n

correct OA:C

Archit3110 · Answer

let cost of each pencil be x cents and that of pens by x cents
given
m*x*100 = n*100*y
given x = 2000 
m*2000 = n*100*y
cost of 10 pens 
2000*m= 1000*n*y
y = 2m/n
option C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If m pencils cost the same as n pens, and each pencil costs 20 cents,

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If m pencils cost the same as n pens, and each pencil costs 20 cents,

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards