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# GMAT Diagnostic Test Question 45

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GMAT Diagnostic Test Question 45 [#permalink]

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07 Jun 2009, 00:13
GMAT Diagnostic Test Question 45
Field: algebra
Difficulty: 750
 Rating:

5 boxes are placed in a stack by weight from lightest to heaviest. If the heaviest box weighs $$x$$ kg, then the next heaviest weighs $$x%$$ less than the heaviest box. If this second-heaviest box weighs $$y$$ kg, then the next heaviest weighs $$y%$$ less than this second-heaviest box. And so on, for all 5 boxes. If the heaviest box weighs 10kg, approximately what percent less weight is the lightest box than the heaviest one?

A. 30
B. 40
C. 50
D. 60
E. 70

THIS QUESTION WAS REMOVED FROM THE TESTS
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Last edited by Bunuel on 16 Jun 2013, 21:30, edited 4 times in total.
Clarified the setup
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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14 Jun 2009, 09:53
Explanation
 Rating:

Official Answer: A

Given that the weight of the heaviest box = x kg = 10 kg
The weight of the second heaviest box = x – x% of x = 10 kg – 10% of 10 kg = 9 kg
The weight of the third heaviest box = 9 kg – 9% of 9 kg = 8.19 kg
The weight of the fourth heaviest box = 8.19 kg – 8.19 % of 8.19 kg = 7.52kg
The weight of the lightest box = 7.52 kg – 7.52% of 7.52 kg = 6.95 kg
The weight of the lightest box/ the weight of the heaviest box $$= 1 - \frac{6.95}{10} \approx 30%$$, which is A.
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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18 Jul 2009, 11:21
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The question says
Quote:
approximately what percent less weight is the lightest box than the heaviest one?

So 10 - 6.95 = 3.05 less weight = 30%, wich is Answer A.
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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18 Jul 2009, 12:20
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Seeing how it is being solved, I can tell that "same ratio" can be dubious.
For example, I "solved" it as 10*0.9^4
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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18 Jul 2009, 13:07
seofah wrote:
Seeing how it is being solved, I can tell that "same ratio" can be dubious.
For example, I "solved" it as 10*0.9^4

Thank you! I agree - rephrasing the question...
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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18 Jul 2009, 13:08
saruba wrote:
The question says
Quote:
approximately what percent less weight is the lightest box than the heaviest one?

So 10 - 6.95 = 3.05 less weight = 30%, wich is Answer A.

GMAT Tiger will answer this one.
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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18 Jul 2009, 21:02
Agreed and modified the OA accordingly.

Thanks for the suggestion.

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GMAT TIGER wrote:
Explanation
 Rating:

Official Answer: A

Given that the weight of the heaviest box = x kg = 10 kg
The weight of the second heaviest box = x – x% of x = 10 kg – 10% of 10 kg = 9 kg
The weight of the third heaviest box = 9 kg – 9% of 9 kg = 8.19 kg
The weight of the fourth heaviest box = 8.19 kg – 8.19 % of 8.19 kg = 7.52kg
The weight of the lightest box = 7.52 kg – 7.52% of 7.52 kg = 6.95 kg
The weight of the lightest box/ the weight of the heaviest box $$= 1 - \frac{6.95}{10} \approx 30%$$, which is A.

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Re: GMAT Diagnostic Test Question 45 [#permalink]

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24 Jul 2009, 05:09
The pdf and the excel sheet mention OA as E - It should be corected
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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14 Aug 2009, 20:05
I think this question is difficult from a time consuming stand point. Once a person understands what they need to do, the person just has to crunch the numbers and get close to 3 kgs less so they know A is the correct answer. I'm thinking this is about a 650-700 question. If you really wanted to make it a 750 question (in my opinion) make it a symbolism question.

I know a lot of people that are in the upper 600s that want to break through to the low 700s and into mid-700s have a very difficult time with symbolism.
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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15 Aug 2009, 16:50
Lets make it a little polished and improved:-

bb wrote:
5 boxes are placed in a stack by weight from lightest to heaviest. The heaviest box weighs $$x$$ kg and then next heaviest weighs $$x%$$ less than the heaviest box and the next heaviest box weighs $$x-x%$$ less than the next heaviest, and so on. Approximately what is the weight of the lightest box?

A. .3x
B. .4x
C. .5x
D. .6x
E. .7x

It is not an easy question because it, I mean the original ones as well, doesnot have any direct/quick way to get the answer. The calculation is cumbersome and time consuming. Its difficult to solve it in 2 minuets. This way it is 700+ or 750 level question.

In terms of solution, it may not be a 750 level question.
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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17 Aug 2009, 12:59
The question was a bit confusing for me:
The heaviest box weighs x kg and then next heaviest weighs x% less than the heaviest box and the next heaviest box weighs x-x% less than the next heaviest, and so on.

The heaviest box( top box ) weighs x kg and then next heaviest (top-1 box )weighs x% less than the heaviest box (top box) and the next heaviest box ( top-1/top-2? box ) weighs x-x% less than the next heaviest (top-1 ? ), and so on.
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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23 Aug 2009, 01:23
bb wrote:
5 boxes are placed in a stack by weight from lightest to heaviest. The heaviest box weighs $$x$$ kg and then next heaviest weighs $$x%$$ less than the heaviest box and the next heaviest box weighs $$x-x%$$ less than the next heaviest, and so on. If the heaviest box weighs 10kg, approximately what percent less weight is the lightest box than the heaviest one?

I think the question is a little bid confusingly made. It says that the heaviest box weighs x kg and that the value of this box is 10 kg, which means that x is 10. Thus we subtract 10%. But then x equals 9% then 8,19... guess somewhere should be indicated that the x% equals the values of the boxes, not exactly 10 but each box and x is not stable but changes every time we move to the next box. Let me know your thoughts
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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23 Aug 2009, 09:14
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bb wrote:
GMAT Diagnostic Test Question 45
Field: algebra
Difficulty: 750
 Rating:

5 boxes are placed in a stack by weight from lightest to heaviest. The heaviest box weighs $$x$$ kg and then next heaviest weighs $$x%$$ less than the heaviest box and the next heaviest box weighs $$x-x%$$ less than the next heaviest, and so on. If the heaviest box weighs 10kg, approximately what percent less weight is the lightest box than the heaviest one?

A. 30
B. 40
C. 50
D. 60
E. 70

"weighs $$x-x%$$ less than the next heaviest..."
it's not easy to know what this sentence mean...
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29 Oct 2009, 05:40
I think this question should not be on the real GMAT exam since the question itself is too confusing. I bet 90% of the people in this forum did find the expression x-x% confusing. Even someone know the concept and know what to do, it is still impossible to try to do all these calculation under 2 min without a calculator. Maybe there is another solution???
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21 Nov 2009, 08:18
I agree. Should not we do something to clarify the x-x%??
Since the box weighs x kg, people can assume that x=10 all through the calculation?
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29 Nov 2009, 01:44
the question is too confusing esp x - x%

if we say x - x%ofx then it would be better

or weight of (n-1)th box = Wn – (Wn % of Wn)

where Wn is the weight of nth box

not easy to phrase
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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30 Apr 2010, 13:03
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This is a badly-worded question.

bb wrote:
GMAT Diagnostic Test Question 45

5 boxes are placed in a stack by weight from lightest to heaviest. The heaviest box weighs $$x$$ kg and then next heaviest weighs $$x%$$ less than the heaviest box and the next heaviest box weighs $$x-x%$$ less than the next heaviest, and so on. If the heaviest box weighs 10kg, approximately what percent less weight is the lightest box than the heaviest one?

A. 30
B. 40
C. 50
D. 60
E. 70

"The heaviest box weighs $$x$$ kg and then next heaviest weighs $$x%$$ less than the heaviest box"
Except for the "then" typo, so far so good.

"the next heaviest box weighs $$x-x%$$ less than the next heaviest"
If I follow the OE, this is not written correctly.
First, it shouldn't say "than the next heaviest"; it should say "than the previous heaviest box".
Second, $$x-x%$$ makes no sense. The OE says "The weight of the second heaviest box = x – x% of x = 10 kg – 10% of 10 kg = 9 kg". In other words, the second-heaviest box should weigh $$x - x * x%$$. So the third-heaviest box should weigh $$(x - x * x%)%$$ less than $$x - x * x%$$.
Not only is this wrong, but it's way too complicated and the wording forces you to give part of the answer away.

I would simply write:
If the heaviest box weighs $$x$$ kg, then the next heaviest weighs $$x%$$ less than the heaviest box. If this second-heaviest box weighs $$y$$ kg, then the next heaviest weighs $$y%$$ less than this second-heaviest box. And so on, for all 5 boxes.
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Re: GMAT Diagnostic Test Question 45 [#permalink]

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17 May 2010, 05:05
I just worked on this question and x-x% also confused me. I used x as the original value (10) for all the boxes, not the previous weight.
Re: GMAT Diagnostic Test Question 45   [#permalink] 17 May 2010, 05:05

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