Confusing MATH Problem

[researchlove]

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this was from like an old diagnostic problem back in 2007..

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


Anwer is 72, but I'm not quite getting the wording in there.. what do you mean by having an integral length? so.. is it like


l----------l----------l----------l

　　　4　　　 　　6 　　　　　8　　　　 parts..? is that what it's saying?


help me pleaseee, thanks in advance!

 

[iwannabadentist]

integral length means that the length is an integer. so 1 or 2 or 3, no decimals. you need to find the least common multiple of 4 6 and 8, which is 24. then u multiple that by 3 so u get 72.
u need to find the least common multiple because each segment that was divided in either 8 6 or 4 parts had to be the same length before it was divided. and after division, for them to have an integral length, the size of the wire must be (at least) 24. so when its cut into 8 pieces, you have 8 segments of 3 units, 6 pieces = 6 segments of 4 units and 4 pieces = 4 segments of 6 units. then u gotta remember that originally, a BIG segment was equally cut into 3, so there must be 3 identical 24 unit segments. 24 times 3 is 72.

 

[Sugafoot79]

What is everyone still doing up in the wee hours of the morning? 😴 Man I can't wait till this test is over. All my friends are still out drinking and having a blast, while I cram I fell cracked out, haha!

Here is another confusing one:
Dr. Hagwood received a 25% reduction in his income
tax rate, which was 66 2/3%. By what percent did his
after-tax income increase?
A. 16 2/3%
B. 25%
C. 33 1/3%
D. 50%
E. 100%

The ans is D

are there any ways to do this problem in less than a minute? I'm seriously struggling with time management for QR.😡

 

[UCB05]

this was from like an old diagnostic problem back in 2007..

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


Anwer is 72, but I'm not quite getting the wording in there.. what do you mean by having an integral length? so.. is it like


l----------l----------l----------l

　　　4　　　 　　6 　　　　　8　　　　 parts..? is that what it's saying?


help me pleaseee, thanks in advance!

Poorly worded question. 72 if all 4 pieces were the same length (ie 6 unit lengths each), all 6 pieces were the same length (4 unit lengths each) and all 8 pieces were the same length (3 unit lengths each). As the original question never required each 1/3 segment to be divided equally into 4, 6, or 8 parts respectively, the answer could be 24 ( 4 pieces: 2/2/2/2, 1/1/3/3,1/1/2/4) the six (pieces could be 1/1/1/1/2/2), the eight (1/1/1/1/1/1/1/1).

 

[UCB05]

What is everyone still doing up in the wee hours of the morning? 😴 Man I can't wait till this test is over. All my friends are still out drinking and having a blast, while I cram I fell cracked out, haha!

Here is another confusing one:
Dr. Hagwood received a 25% reduction in his income
tax rate, which was 66 2/3%. By what percent did his
after-tax income increase?
A. 16 2/3%
B. 25%
C. 33 1/3%
D. 50%
E. 100%

The ans is D

are there any ways to do this problem in less than a minute? I'm seriously struggling with time management for QR.😡

You'll just have to think fast and recognize convenient numbers.

Instead of working with 66 2/3% and 25%, you can see his income is 1/3 or 2/6, and his tax is 2/3 (66 2/3%) or 4/6 of his total earnings. His tax rate decreases by 1/4(25%) of 4/6, or 1/6, down to 3/6, which means his new income is 1-3/6= 3/6.

2/6 -> 3/6 of his earnings represents a 50% increase. It would have taken me much longer to do this question if I had stuck with calculating using the % values given.