GMAT Diagnostic Test Question 45

Question

GMAT Diagnostic Test Question 45 
Field: algebra
Difficulty: 750
 Rating:  yellow/79377

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

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

THIS QUESTION WAS REMOVED FROM THE TESTS

GMAT TIGER · Answer

Explanation 
 Rating:  yellow/793772

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.

saruba · Answer

The question says

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

seofah · Answer

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

bb · Answer

Thank you! I agree - rephrasing the question...

bb · Answer

GMAT Tiger will answer this one.

GMAT TIGER · Answer

Agreed and modified the OA accordingly.

Thanks for the suggestion.

GT

shubhashreeb · Answer

The pdf and the excel sheet mention OA as E - It should be corected

jallenmorris · Answer

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.

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.

bb · Answer

Thanks!
By symbolism you mean "@"?

jallenmorris · Answer

@ would work. Anything actually. The more abstract the better. I think @ is used often so it would be a good choice. Of course, you don't have to change the question, it was just a suggestion.

GMAT TIGER · Answer

Lets make it a little polished and improved:- :-D

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.

Economist · Answer

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.

nauruz · Answer

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

flyingbunny · Answer

"weighs  x-x%  less than the next heaviest..." 
it's not easy to know what this sentence mean...

ezinis · Answer

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???

lonewolf · Answer

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?

kt780 · Answer

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 :lol:

AloneAndInsufficient · Answer

This is a badly-worded question.

"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.

oldguru82 · Answer

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.

GMAT Diagnostic Test Question 45

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