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SS2204 · 2009 June 19th, 04:08 AM

Hi guys,

I'm getting stuck on the following Kaplan question:

A wire is cut into three equal parts. The resulting segments are then cut into 4, 6 and 8 equal parts respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire?

a) 24
b) 36
c) 48
d) 54
e) 72

The answer to this is 72.

I found out the L.C.M for 3, 4, 6 and 8 and got 24. But apparently that's not correct....

abhishek_mumbai · 2009 June 19th, 08:07 AM

It is 72.. answer is correct..

there are three pieces of wires.. say A,B,C
and each of A, B and C is cut in 4,6,8 parts.. to have integer length of each sub-piece, the length of A, B, C should be LCM of 4,6,8 i.e. 24..

now as length of A,B and C are equal. total length of wire = 24 * 3 = 72

eravi11 · 2009 June 20th, 11:16 AM

Picking answer choices one by one and keeping in mind that mininum length of wire cut into 4,6 and 8 parts respectivley will be equal to 24. hence minimun length of the wire=24.3=72.

option E.

madhur_ahuja · 2009 June 21st, 10:35 AM

Agree with E

NYC_Kid · 2009 June 21st, 05:34 PM

I guess I'm Joe Bloggs in this situation. If they were cut in 4,6,8 , then I would assume they add up to 18 multiplied by 3 pieces which would equal to 54.

I still can't visualize or see why you would to LCM.

bkparikh · 2009 June 22nd, 05:35 AM

original wire length = x
after cut into three equal parts, each part = ^x/₃

part one is now cut into 4 parts, each part = ^x/₁₂
part two is now cut into 6 parts, each part = ^x/₁₈
part three is now cut into 8 parts, each part = ^x/₂₄

In order for ^x/₁₂, ^x/₁₈, and ^x/₂₄ to all be integers you must find the LCM or 12, 18, and 24

@NYC_Kid if the wire length was 54, the 4 parts in part one and 8 parts in part 3 would not be of integer values

spacepure · 2009 June 23rd, 10:18 AM

Yeah, I agree with abhishek_mumbai .
The length of each of the three parts should be the LCM of 4,6,8 (that is 24)..
And there are 3 parts..
Thus, the total length should be 24*3=72

lecast · 2009 June 29th, 08:49 AM

Or making in another problem:
¹/₃(¹/₄+¹/₆+¹/₈)=¹/₃(⁶/₂₄+⁴/₂₄+³/₂₄)=⁶/₇₂+⁴/₇₂+³/₇₂

gmat.raj · 2009 June 29th, 09:48 PM

yes E; abhishek mumbai & bkparikh explanations are good.

acrao80 · 2009 July 22nd, 05:55 AM

E seems to be the correct answer !

So for problems like this what is the best approach?

1) substituting giving options in the equation and checking OR

2) solving the math equation and getting the answer directly

I have just started my GMAT preparations so was curious on the best approach !

2009 June 19th, 04:08 AM	#1 (permalink)
SS2204 I JUST got here. Join Date: Nov 2008 Posts: 1	Arithmetic Question Hi guys, I'm getting stuck on the following Kaplan question: A wire is cut into three equal parts. The resulting segments are then cut into 4, 6 and 8 equal parts respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire? a) 24 b) 36 c) 48 d) 54 e) 72 The answer to this is 72. I found out the L.C.M for 3, 4, 6 and 8 and got 24. But apparently that's not correct....

2009 June 22nd, 05:35 AM	#6 (permalink)
bkparikh Magoosh, Co-Founder Join Date: Jun 2009 Posts: 134	original wire length = x after cut into three equal parts, each part = ^x/₃ part one is now cut into 4 parts, each part = ^x/₁₂ part two is now cut into 6 parts, each part = ^x/₁₈ part three is now cut into 8 parts, each part = ^x/₂₄ In order for ^x/₁₂, ^x/₁₈, and ^x/₂₄ to all be integers you must find the LCM or 12, 18, and 24 @NYC_Kid if the wire length was 54, the 4 parts in part one and 8 parts in part 3 would not be of integer values _ _ _ _ SIG _ _ _ _ Magoosh - Online GMAT Prep

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2009 June 19th, 08:07 AM	#2 (permalink)
abhishek_mumbai Done with GMAT - 700 Join Date: Apr 2009 Location: Pune, India Posts: 1,182	It is 72.. answer is correct.. there are three pieces of wires.. say A,B,C and each of A, B and C is cut in 4,6,8 parts.. to have integer length of each sub-piece, the length of A, B, C should be LCM of 4,6,8 i.e. 24.. now as length of A,B and C are equal. total length of wire = 24 * 3 = 72

2009 June 20th, 11:16 AM	#3 (permalink)
eravi11 So far So bad! Join Date: Feb 2009 Posts: 630	Picking answer choices one by one and keeping in mind that mininum length of wire cut into 4,6 and 8 parts respectivley will be equal to 24. hence minimun length of the wire=24.3=72. option E.

2009 June 21st, 10:35 AM	#4 (permalink)
madhur_ahuja TestMagic Guru Join Date: Feb 2007 Location: Hyderabad Posts: 1,674	Agree with E

2009 June 21st, 05:34 PM	#5 (permalink)
NYC_Kid I JUST got here. Join Date: Jun 2009 Posts: 13	I guess I'm Joe Bloggs in this situation. If they were cut in 4,6,8 , then I would assume they add up to 18 multiplied by 3 pieces which would equal to 54. I still can't visualize or see why you would to LCM.

2009 June 23rd, 10:18 AM	#7 (permalink)
spacepure Confident and Positive Join Date: Mar 2009 Posts: 59	Yeah, I agree with abhishek_mumbai . The length of each of the three parts should be the LCM of 4,6,8 (that is 24).. And there are 3 parts.. Thus, the total length should be 24*3=72

2009 June 29th, 08:49 AM	#8 (permalink)
lecast Eager! Join Date: Jun 2009 Posts: 53	Or making in another problem: ¹/₃(¹/₄+¹/₆+¹/₈)=¹/₃(⁶/₂₄+⁴/₂₄+³/₂₄)=⁶/₇₂+⁴/₇₂+³/₇₂

2009 June 29th, 09:48 PM	#9 (permalink)
gmat.raj Eager! Join Date: Jun 2009 Location: London, UK Posts: 94	yes E; abhishek mumbai & bkparikh explanations are good.

2009 July 22nd, 05:55 AM	#10 (permalink)
acrao80 I JUST got here. Join Date: Jul 2009 Posts: 8	E seems to be the correct answer ! So for problems like this what is the best approach? 1) substituting giving options in the equation and checking OR 2) solving the math equation and getting the answer directly I have just started my GMAT preparations so was curious on the best approach !

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