M04-33

Question

Brittany bought a total of 17 pens, of the following three types: ball pens, gel pens, and ink pens costing $0.05, $0.10, and $0.25 each, respectively. If Brittany paid a total of $2.05, and bought twice as many gel pens as ink pens, how many ball pens did she buy?

A. 4
B. 5
C. 7
D. 8
E. 10

A. 4
B. 5
C. 7
D. 8
E. 10

Raihanuddin · Accepted Answer

Let, ink pens be x
 Gel pen = 2x 
and ball pen = (17-3x)

Now, 25x+20x+(17-3x)5 = 205
Solving we get x=4

Therefore ball pen = 17-3*4 =5

Bunuel · Answer

Official Solution:

Brittany bought a total of 17 pens, of the following three types: ball pens, gel pens, and ink pens costing $0.05, $0.10, and $0.25 each, respectively. If Brittany paid a total of $2.05, and bought twice as many gel pens as ink pens, how many ball pens did she buy?

A. 4
B. 5
C. 7
D. 8
E. 10

A. 4
B. 5
C. 7
D. 8
E. 10

Let's denote each type of pen with the first letter of its kind and build a system of equations:
  
• The total amount Brittany paid in cents was 205, which can be represented as  5B+10G+25I=205 .
 
• Brittany bought 17 pens in total, which can be represented as:  B+G+I=17 .
 
• Brittany bought twice as many gel pens as ink pens, which can be represented as  G=2I .
  
Now let's solve the above system of equations:
 
From  5B+10G+25I=205  and  G=2I , we get  5B+10*(2I)+25I=205 , which simplifies to  5B+45I=205  and further to  B+9I=41 .
 
Given  B+G+I=17  and  G=2I , we can substitute and get  B+3I=17 .
 
Finally, subtract the equation  B+3I=17  from  B+9I=41  to get  6I=24 , and then solve for  I  to get  I=4 . This gives us  B=5 .

Answer: B

AneesShaik · Answer

I think this is a  high-quality  question and I agree with explanation.

neilchettri · Answer

I think this is a  high-quality  question and I agree with explanation.

NandishSS · Answer

HI  GMATGuruNY ,  MentorTutoring  , GMATBusters   GMATinsight

This question took me four minutes to solve. Can you please me how to solve these kind of problem in 2 min?

GMATGuruNY · Answer

We can PLUG IN THE ANSWERS, which represent the number of ball pens.
When the correct answer is plugged in, the total cost = 205 cents.

B: 5 ball pens
Since gel:ink = 2:1 = 4:2 = 8:4, the remaining 12 pens are composed of 8 gel pens and 4 ink pens.
Total cost for 5 5-cent ball pens, 8 10-cent gel pens, and 4 25-cent ink pens = (5*5) + (8*10) + (4*25) = 25 + 80 + 100 = 205 cents.
Success!

B

AndrewN · Answer

Sure thing,  NandishSS . This is an easy problem to work backwards from in a time-efficient manner. Well, it looks like  GMATGuruNY  beat me to the punch. I concur with that assessment.

- Andrew

GMATinsight · Answer

NandishSS

You can either plug in the values of simply make equation. Either way it's not going to take 4 min. If it's taking this long then it only means that you haven't practiced enough to deal with algebra.

b + g + i =17----(1)

ball pens, gel pens, and ink pens, which cost $0.05, $0.10 and $0.25 each.

i.e 5b + 10g + 25i = 205----(2)

Also, g = 2*i

I.e 5b + 10*(2i) + 25i = 205
i.e. b + 9i = 41-----(3)

and 
i.e. b+3i = 17----(4) From eq. (1)

Solving (3) and (4) we get

6i = 41-17 = 24

i.e. i = 4
i.e. g = 2*4 = 8
i.e. b = 17-(4+8) = 5

Answer: Option B

RayyanTanvir · Answer

Any one Please teach me the technique to understand this

"If Brittany bought twice as many gel pens as ink pens"

Sentence properly.

Posted from my mobile device

AndrewN · Answer

Hello,  RayyanTanvir . The phrase  twice as many X as Y  is the same as  two times more X than Y . In the sentence at hand, we could reinterpret it as saying,

Brittany bought  two times more  gel pens  than  ink pens .

I hope that helps. Good luck with your studies.

- Andrew

mSKR · Answer

usually i end up in doing mistake as Y= 2X is there any other way to express

x X xx Y i.e. 2y= X what could be other words to express the same meaning?

AndrewN · Answer

Hello,  sushilr . I understand about misinterpreting counting words. It happens all the time with percent increase/decrease questions, at least I encounter the situation a lot in my tutoring. Are there other ways of expressing 2y = x? Sure there are. In addition to the above, you could add just about anything numerical to compare the two unknowns. The following are some more common ways that could fit into certain question types (algebraic, mixtures, and so on):

double the number of y as x
half the number of x as y
100 percent more y than x (this one gets people a lot)
half as many/much x as y
50 percent as many/much x as y

Of course, there could be an infinite number of ways to use multiple steps to arrive at the same conclusion. For instance, you might see the following question stem in a mixture problem:

If the amount of y is one-third as much as six times the amount of x...

A good rule of thumb for straightening out these comparisons is to remember that the second item, the one following as/than, is the one being used as the basis for comparison. In other words, you can think of that second item as having a coefficient of 1 unless some other number is offered.

I hope that helps. If you have further questions, let me know.

- Andrew

I hope that helps. If you have further questions, let me know.

- Andrew

NandishSS · Answer

HI  MentorTutoring  (Andrew)

Can you show some examples. Sometimes it is bit tricky.

- Brittany bought twice as many gel pens as ink pens

- Twice as many cats as dogs

AndrewN · Answer

Hello,  NandishSS . Translating the two sentences into mathematical language, we get the following:

1) Brittany bought twice as many gel pens (G) as ink pens (I) → 2G per 1I or 2G:I; e.g., if given 20 ink pens,

2G:I

2G*20:I*20

40G:20I

That is 40 gel pens for every 20 ink pens.

2) Twice as many cats (C) as dogs (D) → 2C per 1D or 2C:D; e.g., if given 80  cats ,

2C:D

(2*40)C:(1*40)D

80C:40D

There are 40 dogs for every 80 cats.

3) Seven times as many ants (A) as wasps (W) → 7A per 1W or 7A:W; e.g., if given 45 wasps,

7A:W

7A*45:W*45

315A:45W

There are 315 ants for every 45 wasps.

I hope that helps clarify. Understand, the variables I use above are stand-ins for  words , not numbers. If you have further questions, just let me know. Thank you for tagging me.

- Andrew

dmk0909 · Answer

I think this is a  high-quality  question and I agree with explanation. I AGREE WITH THE SOLUTION.. BUT EFFICIENT APPROACH TO THIS IS BACK SOLVE. I've realised in GMAT If something is taking time then there has to be a faster way that would take less than 2 mins.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

vn049636 · Answer

I think this is a  high-quality  question and I agree with explanation.

705in11112025 · Answer

I answered this by spotting the answer choice that will satisfy the condition " bought twice as many gel pens as ink pens" only 5 will fit the criteria.

M04-33

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