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Pencils Problem...Help me

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Pencils Problem...Help me

by kumard24 » Wed Mar 26, 2008 4:00 am
19. 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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by madhavi » Wed Mar 26, 2008 6:16 am
Total no of pencils sold = 32

So, J + K + L= 32

Also, K =2L --------1

J + 3L =32; L =(32-J)/3 -----------2

Now,

J(0.05)+K(0.10)+L(0.25)=3.40

5J + 20L +25L =340 (substituting K in terms of L from 1 )

5J + 45(32-J)/3=340 (substituting L in terms of J from 2)

Solving for J; J=14

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by kumard24 » Wed Mar 26, 2008 7:36 am
This is probably a stupid question but why is it K=2L and not L=2K???

I cant get my head round it!
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by madhavi » Wed Mar 26, 2008 7:45 am
This is one of the question models that appears in GMAT.

"as many as" construction is used to confuse test takers.

Correlate with the following:

[b] "There will be more than twice as many applicants in round two as there were in round one; and they will be competing for fewer open spots."[/b]

Hope this helps.

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by kumard24 » Wed Mar 26, 2008 8:24 am
Urrrmmmm....actually i still dont get it! Is there another to understand it?
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by madhavi » Wed Mar 26, 2008 8:46 am
I hope this article will be of help.

https://null706.mbablogs.businessweek.co ... 55eyl7naoz

He says, A phrase like"three times as many as John has" can be translated as 3j...
Applying to the prob here,

"AS MANY" k pencils "AS L PENCILS"

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by tmmyc » Wed Mar 26, 2008 9:08 am
Personally, I like to test using real numeric examples.

There are twice as many K pencils as L pencils in the box.

Assume you have four K pencils. These four K pencils are twice as many as L pencils.

L must be two.

These 4 pencils are twice as many as those 2 pencils in the box. Does that help?
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by kumard24 » Wed Mar 26, 2008 10:08 am
Really hate to say this but from the evidence you have given me it appears that Twice as many =2K=L.


Heeellp...this is driving me nuts
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by tmmyc » Wed Mar 26, 2008 12:41 pm
kumard24 wrote:Really hate to say this but from the evidence you have given me it appears that Twice as many =2K=L.


Heeellp...this is driving me nuts
I am assuming you understand my comment:

These 4 [K] pencils are twice as many as those 2 [L] pencils in the box. (because 4 is twice 2)

Essentially, we find that
K=4
L=2

Let's put it to the test.


You want to know if 2*K = L or K = 2*L.

2*K = L
2*4 = 2
8 = 2
This is not the correct interpretation.

K = 2*L
4 = 2*2
4 = 4
This must be the correct interpretation.
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by kumard24 » Thu Mar 27, 2008 12:07 am
Thats perfect. I finally get it. Apologies for beiing so silly. It seems obvious now. :D :D :D :D
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by kumard24 » Thu Mar 27, 2008 9:43 am
I lied...i get the twice as many concept but now dont understand

5J + 45(32-J)/3=340 (substituting L in terms of J from 2)

Solving for J; J=14

I get 5j +1440+45j=1020

and then from here i dont get J=14.

help
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by rros0770 » Thu Mar 27, 2008 11:08 am
1) Watch the + & - signs (you should have 1440 - 45J; NOT 1440 + 45J)
2) You're cross multiplying (3*340) when you should be dividing:

Step 1: You've gotten to this point already so you're good:

5J + {45(32 - J)/3} = 340

Step 2: We'll focus on the terms in these brackets { }

{((45 x 32)- (45 x J))/ 3}

which equals:

(1440-45J)/3

Dividing 1440 & 45J by 3 yields:

{480- 15J}; now plug this back into the whole equation:

5J + {480-15J} = 340

STEP 3: subtract 480 from 340 & 5J from -15J

-10J= -140

therefore J= 14
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wow

by resilient » Sun Mar 30, 2008 10:51 am
wow folks...what a thread. This is great. I learned how to translate math into english the manhattan gmat book (word translations) but i would get stuck on certain translations. THe test method works great by applying simple logical tests to prove your way.

Thanks a lot Kaunteya1
Appetite for 700 and I scraped my plate!
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