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M04-33

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M04-33  [#permalink]

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New post 16 Sep 2014, 00:23
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A
B
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Difficulty:

  35% (medium)

Question Stats:

79% (02:20) correct 21% (02:36) wrong based on 157 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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M04-33  [#permalink]

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New post 16 Sep 2014, 00:24
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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:


\(5B+10G+25I=205\)

\(B+G+I=17\)

\(G=2I\)

\(B+9I=41\)

\(B+3I=17\)

\(6I=24\)

\(I=4\)

\(B=5\)


Answer: B
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Re: M04-33  [#permalink]

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New post 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:
\(5B+10G+25I=205\)
\(B+G+I=17\)
\(G=2I\)
\(B+9I=41\)
\(B+3I=17\)
\(6I=24\)
\(I=4\)
\(B=5\)


Answer: B


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!
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Re: M04-33  [#permalink]

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New post 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:
\(5B+10G+25I=205\)
\(B+G+I=17\)
\(G=2I\)
\(B+9I=41\)
\(B+3I=17\)
\(6I=24\)
\(I=4\)
\(B=5\)


Answer: B


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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M04-33  [#permalink]

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New post 04 Nov 2014, 21:12
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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
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Re: M04-33  [#permalink]

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New post 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
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M04-33  [#permalink]

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New post 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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Re M04-33  [#permalink]

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New post 11 Sep 2016, 02:08
I think this is a high-quality question and I agree with explanation.
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Re: M04-33  [#permalink]

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New post 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.

      Answer:- 5
      Re: M04-33 &nbs [#permalink] 31 Aug 2018, 12:42
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