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# M04-33

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Math Expert
Joined: 02 Sep 2009
Posts: 55277

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16 Sep 2014, 00:23
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6
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Difficulty:

35% (medium)

Question Stats:

77% (02:56) correct 23% (02:53) wrong based on 113 sessions

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In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05,$0.10 and $0.25 each. The total that Brittany paid was$2.05. If Brittany 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

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Joined: 02 Sep 2009
Posts: 55277

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16 Sep 2014, 00:24
1
2
Official Solution:

In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05,$0.10 and $0.25 each. The total that Brittany paid was$2.05. If Brittany 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

Denote each pen with the first letter of its kind and build a system of equations:

$$5B+10G+25I=205$$

$$B+G+I=17$$

$$G=2I$$

$$B+9I=41$$

$$B+3I=17$$

$$6I=24$$

$$I=4$$

$$B=5$$

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Joined: 21 May 2013
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24 Oct 2014, 23:52
Bunuel wrote:
Official Solution:

In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05,$0.10 and $0.25 each. The total that Brittany paid was$2.05. If Brittany 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

Denote each pen with the first letter of its kind and build a system of equations:
$$5B+10G+25I=205$$
$$B+G+I=17$$
$$G=2I$$
$$B+9I=41$$
$$B+3I=17$$
$$6I=24$$
$$I=4$$
$$B=5$$

Hi Bunuel,

Thanks for your explanation. Can you please clarify how you received the equation B +9I = 41? I understand how you received B +3I =17.

Thanks a lot!
Aram
Math Expert
Joined: 02 Sep 2009
Posts: 55277

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25 Oct 2014, 06:38
safaria25 wrote:
Bunuel wrote:
Official Solution:

In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05,$0.10 and $0.25 each. The total that Brittany paid was$2.05. If Brittany 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

Denote each pen with the first letter of its kind and build a system of equations:
$$5B+10G+25I=205$$
$$B+G+I=17$$
$$G=2I$$
$$B+9I=41$$
$$B+3I=17$$
$$6I=24$$
$$I=4$$
$$B=5$$

Hi Bunuel,

Thanks for your explanation. Can you please clarify how you received the equation B +9I = 41? I understand how you received B +3I =17.

Thanks a lot!
Aram

From $$5B+10G+25I=205$$ and $$G=2I$$ we get $$5B+10*(2I)+25I=205$$ --> $$5B+45I=205$$ --> $$B+9I=41$$.

Hope it's clear.
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Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
GMAT 1: 650 Q39 V41
WE: Analyst (Commercial Banking)

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04 Nov 2014, 21:12
1
To solve this we need to set up a system of equations.

Equation 1: B+G+i=17; where B,G, and i, are the number of each type pen purchased, respectively.
Equation 2: 5B +10G+25i=205; reduce by dividing each term by 5 --> *B+2G+5i=41* (this is the equation we'll use).
Equation 3: G=2i

Sub eq.3 into eq.2 --> B+2(2i)+5i=41 --> *B+9i=41*

We want to end up with a value for B, so isolate i -->9i=41-B --> *i=(41-B)/9*

Plug the value of i into eq1: B+G+i=17 --> (B)+((82-2B)/9)+((41-B)/9)=17 (The middle term is 2i, or twice the last term).

simplify: (9B/9)+((82-2B)/9)+((41-B)/9)=17

(9B+82-2B+41-B)/9=17

(9B+82-2B+41-B) = 17*9 = 153

6B+123=153

B=5
Manager
Joined: 11 Sep 2013
Posts: 142
Concentration: Finance, Finance

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09 Dec 2014, 08:40
1
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
Senior Manager
Joined: 12 Aug 2015
Posts: 284
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)

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23 Sep 2015, 00:40
an approach if you face time constraint:

1. b + g + i = 17

2. b + 2i + i= 17 (obviously g/i=2/1)

3. given the above only answer B and D suffice (the rest options do not result into integer values), i.e.

B. 5 + 3*4 = 17 (where g/i=8/4)
or
D. 8 + 3*3 = 17 (g/i=6/3)

4. from here you can play the game choose either after 30 secs or solve further using the given info re prices and spend additional 15 secs.

D. 8*$5 + 6*$10 + 3*$25 -> does not equal$205, hence wrong, ANSWER B should be correct. We are done.

Just to check:
B: 5*$5 + 8*$10 + 4*$25=$205. correct
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KUDO me plenty
Intern
Joined: 12 Oct 2014
Posts: 9
Location: India
GMAT 1: 700 Q48 V38
GPA: 3.2

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11 Sep 2016, 02:08
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 04 Aug 2018
Posts: 6

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31 Aug 2018, 12:42
Lets Say,

Ball PEN- BP,
Gel PEN- GP
Ink PEN- IP

Given :-

GP= 2IP (Brittany bought twice as many gel pens as ink pens)

BP + GP + IP = 17

Alternative Approach:-

BP + GP + IP = 17

BP + 2IP + IP =17 (using GP= 2 x IP )

BP + 3IP = 17

IP must be a integer. That makes 3IP , a multiple of 3.
chk for values of IP=1,2,3,4,5....
Use GP= 2IP as limiting condition to chk BP + GP + IP = 17.

The values that makes sense are 5 & 8 (Among options given)
Put the cost values & check.

Intern
Joined: 03 May 2017
Posts: 3

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22 Mar 2019, 21:05
I think this is a high-quality question and I agree with explanation.
Re M04-33   [#permalink] 22 Mar 2019, 21:05
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# M04-33

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