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605-655 Level|   Word Problems|            
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bmwhype2
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Three types of pencils, J,K, and L, cost $0.05, $0.10, and Updated on: 01 May 2014, 00:05
Originally posted by bmwhype2 on 22 May 2007, 00:14.
Last edited by Bunuel on 01 May 2014, 00:05, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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77% (02:57) correct 23% (03:04) wrong based on 1580 sessions

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Three types of pencils, J, K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40 and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?

(A) 6
(B) 12
(C) 14
(D) 18
(E) 20
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C
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Dek
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Three types of pencils, J,K, and L, cost $0.05, $0.10, and Updated on: 22 May 2007, 23:45
Originally posted by Dek on 22 May 2007, 01:03.
Last edited by Dek on 22 May 2007, 23:45, edited 3 times in total.
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14.

Total in the box = 32
so J+K+L = 32
we have K = 2L

so eq 1:
K+3L = 32
(oops! this eq. should be j+3L=32
sorry for the confusion)

Total price = 3.40 = 340 cents
so J5 + K10 + L25 = 340
J5 + 2L*10 + L25 = 340
5J + 45L = 340
divide both sides by 5
J + 9L = 68

so eq 2:
J + 9L = 68

Solve to get J = 14, K = 12 and L = 6
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Three types of pencils, J,K, and L, cost $0.05, $0.10, and 03 Apr 2011, 05:52
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Let the number of pencils are J, K and L correspondingly.
Then we need to solve the system in integer numbers, where J,K,L>=0

5J+10K+25L=340
J+K+L=32
K=2L

J+4L+5L=68
J+2L+L=32

J+9L=68
J+3L=32

6L=68-32=36

L=6
J=32-3L=32-18=14

The answer is C
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BrentGMATPrepNow
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Three types of pencils, J,K, and L, cost $0.05, $0.10, and 13 Apr 2022, 13:19
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bmwhype2
Three types of pencils, J, K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40 and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?

(A) 6
(B) 12
(C) 14
(D) 18
(E) 20
Show more

STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can test the answer choices, but it will take a bit of work doing so.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also solve the question via algebraic methods.
Which approach should we use?
Well, after reviewing the question, I now realize that 3 of the answer choices are disqualified, which means I need only test ONE answer choice.
Let's go!!

GMAT-specific approach: Testing the answer choices.
The answer choices tell us the number of J pencils in the box.
Since the box contains 32 pencils, knowing the number of J pencils will let me determine the total number of K- and L- pencils combined.
For example, if there are 6 J pencils (answer choice A), then the remaining 26 pencils must consist of K and L pencils.
Since there are twice as many K pencils as L pencils in the box, we need to divide the 26 pencils into a 2:1 ratio, but we can't do that since 26 isn't divisible by 3.
So, we can automatically eliminate choice A.

We can also eliminate choice B (12 J pencils) for the same reason.
If there are 12 J pencils, the remaining 20 K and L pencils must be divided into a 2:1 ratio, which is impossible to do with integer values.
Eliminate choice B.

Finally, we can eliminate choice D (18 J pencils) for the same reason.
If there are 18 J pencils, the remaining 14 K and L pencils must be divided into a 2:1 ratio, which is impossible to do with integer values.
Eliminate choice D.

So, by applying a little number sense, we are already down to answer choices C and E.
At this point, we need only test one of the remaining answer choices.
For example, if we test choice C, and it works, then the correct answer is C. If we test choice C, and it doesn't work, then the correct answer is E.

Let's test choice C . . .
C - 14. This tells us there are 14 J pencils, which means the remaining 18 pencils must be K and L pencils.
Since there are twice as many K pencils as L pencils, let's divide the 18 pencils into a 2:1 ratio, to get: 12:6
This tells us there are 12 K pencils, and 6 L pencils (and 14 J pencils!).
So, the total cost of the 32 pencils = ($0.05)(14) + ($0.10)(12) + ($0.25)(6) = $0.70 + $1.20 + $1.50 = $3.40 PERFECT!!

Answer: C

Conventional approach: Assign variables, create equations, solve equations, blah blah...
There are twice as many K pencils as L pencils in the box
Let x = the total number of L pencils
So, 2x = the total number of K pencils

There are 32 pencils in the box
So, the number of J pencils = 32 - (the total number of L and K pencils)
In other words: The number of J pencils = 32 - (x + 2x) = 32 - 3x

Three types of pencils, J, K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40
Since the total cost is $3.40, we can write: (0.05)(32 - 3x) + (0.10)(2x) + (0.25)(x) = 3.40
Expand: 1.6 - 0.15x + 0.2x + 0.25x = 3.40
Simplify: 0.3x + 1.6 = 3.40
Subtract 1.6 from both sides: 0.3x = 1.80
Solve: x = 1.80/0.3 = 6

Important: x does not represent the number of J pencils. x represents the number of L pencils. So do not choose choice A.

The number of J pencils = 32 - 3x
Now that we know x = 6, the number of J pencils = 32 - 3(6) = 32 - 18 = 14

Answer: C
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Three types of pencils, J,K, and L, cost $0.05, $0.10, and 29 Apr 2022, 04:25
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BrentGMATPrepNow
bmwhype2
Three types of pencils, J, K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40 and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?

(A) 6
(B) 12
(C) 14
(D) 18
(E) 20

STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can test the answer choices, but it will take a bit of work doing so.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also solve the question via algebraic methods.
Which approach should we use?
Well, after reviewing the question, I now realize that 3 of the answer choices are disqualified, which means I need only test ONE answer choice.
Let's go!!

GMAT-specific approach: Testing the answer choices.
The answer choices tell us the number of J pencils in the box.
Since the box contains 32 pencils, knowing the number of J pencils will let me determine the total number of K- and L- pencils combined.
For example, if there are 6 J pencils (answer choice A), then the remaining 26 pencils must consist of K and L pencils.
Since there are twice as many K pencils as L pencils in the box, we need to divide the 26 pencils into a 2:1 ratio, but we can't do that since 26 isn't divisible by 3.
So, we can automatically eliminate choice A.

We can also eliminate choice B (12 J pencils) for the same reason.
If there are 12 J pencils, the remaining 20 K and L pencils must be divided into a 2:1 ratio, which is impossible to do with integer values.
Eliminate choice B.

Finally, we can eliminate choice D (18 J pencils) for the same reason.
If there are 18 J pencils, the remaining 14 K and L pencils must be divided into a 2:1 ratio, which is impossible to do with integer values.
Eliminate choice D.

So, by applying a little number sense, we are already down to answer choices C and E.
At this point, we need only test one of the remaining answer choices.
For example, if we test choice C, and it works, then the correct answer is C. If we test choice C, and it doesn't work, then the correct answer is E.

Let's test choice C . . .
C - 14. This tells us there are 14 J pencils, which means the remaining 18 pencils must be K and L pencils.
Since there are twice as many K pencils as L pencils, let's divide the 18 pencils into a 2:1 ratio, to get: 12:6
This tells us there are 12 K pencils, and 6 L pencils (and 14 J pencils!).
So, the total cost of the 32 pencils = ($0.05)(14) + ($0.10)(12) + ($0.25)(6) = $0.70 + $1.20 + $1.50 = $3.40 PERFECT!!

Answer: C

Conventional approach: Assign variables, create equations, solve equations, blah blah...
There are twice as many K pencils as L pencils in the box
Let x = the total number of L pencils
So, 2x = the total number of K pencils

There are 32 pencils in the box
So, the number of J pencils = 32 - (the total number of L and K pencils)
In other words: The number of J pencils = 32 - (x + 2x) = 32 - 3x

Three types of pencils, J, K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40
Since the total cost is $3.40, we can write: (0.05)(32 - 3x) + (0.10)(2x) + (0.25)(x) = 3.40
Expand: 1.6 - 0.15x + 0.2x + 0.25x = 3.40
Simplify: 0.3x + 1.6 = 3.40
Subtract 1.6 from both sides: 0.3x = 1.80
Solve: x = 1.80/0.3 = 6

Important: x does not represent the number of J pencils. x represents the number of L pencils. So do not choose choice A.

The number of J pencils = 32 - 3x
Now that we know x = 6, the number of J pencils = 32 - 3(6) = 32 - 18 = 14

Answer: C
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Hi Brent,
I have been following your posts and I really find your strategies helpful in great many ways. I've noticed you mention "number sense" quite many times, could you please suggest ways that would help a test taker to develop this number sense or just a way of working around the numbers? Many Thanks sir.
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Three types of pencils, J,K, and L, cost $0.05, $0.10, and 29 Apr 2022, 10:34
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shantanugaware

Hi Brent,
I have been following your posts and I really find your strategies helpful in great many ways. I've noticed you mention "number sense" quite many times, could you please suggest ways that would help a test taker to develop this number sense or just a way of working around the numbers? Many Thanks sir.
Show more

It just so happens that, this morning, I posted this article that addresses number sense: https://gmatclub.com/forum/4-simplify-y ... 88909.html
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Three types of pencils, J,K, and L, cost $0.05, $0.10, and 24 Nov 2022, 08:37
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Three types of pencils, J, K, and L, cost $0.05, $0.10, and $0.25 each, respectively. If a box of 32 of these pencils costs a total of $3.40 and if there are twice as many K pencils as L pencils in the box, how many J pencils are in the box?

(A) 6
(B) 12
(C) 14
(D) 18
(E) 20

First eradicate decimal form of expression. multiply all costs by 100
5J + 10K + 25L = 340 (Divide all by 5)
J + 2K + 5L = 68
J + K + L = 32 ( Cost Equation)
32-3x : 2X : X (Quantity equation)
1(32 - 3X) + 2(2X) + 5(X) = 68
32 - 3X + 4X + 5X = 68
6X = 36 X =6
No of J pencils = 32 - 3x = 32 - 18 = 14
C
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Three types of pencils, J,K, and L, cost $0.05, $0.10, and 27 Nov 2024, 08:34
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