GMAT Diagnostic Test Question 19

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GMAT Diagnostic Test Question 19 [#permalink]

06 Jun 2009, 22:58

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GMAT Diagnostic Test Question 19
Field: word problems (min/max)
Difficulty: 650

Rating:

Ten suits, each priced at a whole number of dollars, have an average price of $350. If the five cheapest suits are priced at $200 or less with at least one of them costing $200, what is the maximum possible price of the most expensive suit?

A. $890
B. $1250
C. $1475
D. $1694
E. $2492
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Re: GMAT Diagnostic Test Question 19 [#permalink]

14 Aug 2009, 02:29

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BB, here's my attempt at rephrasing:
"Ten suits, each priced at a whole number of dollars, have an average price of $350. If the five cheapest suits are priced at $200 or less with atleast one of them costing $200, what is the maximum possible price of the most expensive suit?"

Pointer:
Based on the previously provided solution (OA), other than the 5 aforementioned 'cheap' suits which'll cost <=$200, 4 suits are assumed to cost $200. Again, this conflicts with the constraint that only 5 (cheapest) of these 10 suits will cost <=200.
Hence, here's my solution:
Out of the 5 'cheap' suits, atleast one costs $200. The remaining 4 cost $1 apiece, bringing the total to 200+1+1+1+1=$204.
Out of the remaining 5, we can assume that 4 of these cost $201 apiece (as opposed to $200 apiece, as that doesn't tie into the above constraint reg. 'cheapest' suits). Thus, these 4 suits cost 4X201=$804.

Thus, the most expensive suit costs: $3500-($204+$804)=$2492

What say??

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Re: GMAT Diagnostic Test Question 19 [#permalink]

15 Jul 2009, 09:26

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Hi there,
it's my first post but I'll leave presentations for later and will go straight to the point:

The PDF has different answers for question 19 than those of this post:
a) $890
b) $1250
c) $1475
d) $1696
e) $2691

Also the (my) explanation differs:

If the 5 cheapest suits cost $200 or less, then we can assume the 5 suits costs $1 each.
After that, we can also assume that 4 of the most expensive suits costs $201 each.
The sum equals a total of $809. Now, if we substract the price of the 10 suits ($3500-$809),
we get $2691 (D), which is the maximum price the suit can take.

Please verify which is the correct answer,
thank you so much for the test!
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Re: GMAT Diagnostic Test Question 19 [#permalink]

16 Jul 2009, 00:19

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This question has gone through a few revisions before it was published and one of the answer choices in the PDF must have survived. It has been corrected now and matches the answer on this page.

The question says: "are each priced at $200 or less" which implies that one of the suites has to be $200 - at least one.
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Re: GMAT Diagnostic Test Question 19 [#permalink]

02 Jul 2009, 03:36

Explanation:

Rating:

Official Answer: E

We can find the price of all suits by multiplying the number of suits (10) by the average price ($350). So the price of all suits is $3500. We know that 5 cheapest suits cost $200 or less. In order to maximize the possible price of the most expensive suit we need to keep the prices of other 9 suits as low as possible. So we might suppose that 1 of the 5 cheapest suits costs $200 and other 4 cheapest ones might cost $1 each as we know they should cost less than $200. Giving these 4 suits a price of $1 each we are considering the most favorable scenario for the maximum possible highest price of the most expensive suit. Other 4 suits might cost $201 each. Again, we're considering the most favorable outcome. Now we have to subtract the price of 9 suits from $3500 in order to find out the maximum possible price of the most expensive suit:

$3500 - $201*4 - $200 - $1*4 = $2492
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Re: GMAT Diagnostic Test Question 19 [#permalink]

24 Jul 2009, 12:28

Hi I did it another way and just would like to know if it sounds good :
actually we know that the cheapest is 200 or less. If we assume that cost is 200 :
then 9*200+1*X = 3500
X=1700
so X must be at least 1700 which leaves answer E

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Re: GMAT Diagnostic Test Question 19 [#permalink]

25 Jul 2009, 00:45

defoue wrote:

Hm... I don't think it works this way. I should say it worked for this problem, but don't think it will work for others...
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Re: GMAT Diagnostic Test Question 19 [#permalink]

14 Aug 2009, 01:44

In response to BB's point, I contend that the question needs to be re-phrased to ensure there's no ambiguity in its meaning. When you say "Each item costs $200 or less", this can be interpreted in two ways:
1)Owing to the usage of 'Each', it can be inferred that the cost of the 4 items is the same, and is dependent on the in/equality <=$200. In other words, it may be $1 apiece for the 4 items (in this case), or $200 for the 4 items. Instead, it could have read: Among the 4 least expensive items, all are priced at $200 or less with atleast one costing $200.
2)The second interpretation is along the lines of the solution provided by dzyubam.

Let me know what you make of it!

Thanks.

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Re: GMAT Diagnostic Test Question 19 [#permalink]

14 Aug 2009, 01:59

AspirationsSuccess wrote:

Thanks. I may be off, but I think it is a fairly "typical" language (there are other questions that have it) but I can see what you mean. Any suggestions how to rephrase???
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Re: GMAT Diagnostic Test Question 19 [#permalink]

04 Feb 2010, 18:32

i read the "with at least one costing $200" to mean that the 5 most expensive might cost $200.

so i have $1, $1, $1, $1, $200, and the last four $200 (not $201). obviously with this approach, I wouldn't be able to get to E. $2,492 but close at $2,496
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Re: GMAT Diagnostic Test Question 19 [#permalink]

11 Mar 2010, 20:25

adalfu wrote:

It says "at least one of them costing $200" , which means at least one of cheapest costing $200 and price for any of the cheapest suit can be max $200. And as you said last four (not cheapest suits) can be of $200, well they cant be because if any of them costs $200 then it would be included in the category cheapest suits and we'll have more than 5 cheapest suits which contradicts the information provided by question.
Hope it helps.
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Re: GMAT Diagnostic Test Question 19 [#permalink]

30 Apr 2010, 08:58

There are a couple of problems with this exercise.

Quote:

Question:
Ten suits, each priced at a whole number of dollars, have an average price of $350. If the five cheapest suits are priced at $200 or less with at least one of them costing $200, what is the maximum possible price of the most expensive suit?

A. $890
B. $1250
C. $1475
D. $1694
E. $2492

1) Wikipedia clearly states that "whole number" has an inconsistent decision; it could imply that the 4 cheapest suits are free, i.e. $0 instead of $1. (Search wikipedia for "whole number" -- I'm not allowed URLs to this forum yet)
I would change the question to: Ten suits, each priced at a positive integer number of dollars,

dzyubam wrote:

Explanation:
Official Answer: E

We can find the price of all suits by multiplying the number of suits (10) by the average price ($350). So the price of all suits is $3500. We know that 5 cheapest suits cost $200 or less. In order to maximize the possible price of the most expensive suit we need to keep the prices of other 9 suits as low as possible. So we might suppose that 1 of the 5 cheapest suits costs $200 and other 4 cheapest ones might cost $1 each as we know they should cost less than $200. Giving these 4 suits a price of $1 each we are considering the most favorable scenario for the maximum possible highest price of the most expensive suit. Other 4 suits might cost $201 each. Again, we're considering the most favorable outcome. Now we have to subtract the price of 9 suits from $3500 in order to find out the maximum possible price of the most expensive suit:

$3500 - $201*4 - $200 - $1*4 = $2492

2) Nothing in the problem states that the 5th cheapest suit ($200) is any cheaper than the 6th, 7th, 8th, 9th. This is analogous to a tie in a race or in a ranking; e.g. if I say I came in 2nd place, it doesn't mean that I'm the only one that came in 2nd place, and there could be in fact be other people in 2nd place. So 4 other suits should cost $200, not $201.

Assuming that "whole number" means "positive integer" (and not "non-negative integer), then the answer becomes: $3500 - $200*5 - $1*4 = $2496

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Re: GMAT Diagnostic Test Question 19 [#permalink]

05 Mar 2011, 07:26

Here is another attempt by plugging answer choices.

Sum of cost of 10 items = 3500
C1+C2+C3+C4+.....C10 = 3500
200+C2+C3+C4+....C10 =3500

Now look at the answer choices
A)890
200+C2+C3+C4+...+890=3500
C2+C3+C4+...C7+C8+C9 (sum of 8 items) = 3500-200-890=2410
Cost of each item =2410/8 = 301.25 Not a whole number (A whole number can’t be a fraction of a number)

B)1250
sum of 8 items = 3500-200-1250=2230
Cost of each item= 2230/8 = 278.75 Not a whole number

C)1475
sum of 8 items = 3500-200-1475 =1825
Cost of each item= 1825/8 Not a whole number

D)1694
sum of 8 items = 3500-200-1694 =1606
Cost of each item= 1606/8 Not a whole number

E)2492 -- Answer
sum of 8 items = 3500-200-2492 =808
Cost of each item= 808/8=101 ( a whole number )
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Re: GMAT Diagnostic Test Question 19 [#permalink]

06 Mar 2011, 20:38

defoue wrote:

Nice alternative, though I doubt its validity. A more structure approach would yield a more reliable answer.

Btw, in my opinion, you can have a set like this:

1,1,1,1, 200, 200, 200, 200, X

which leads to x= 2496 (close enough to guess the right answer). I would probably explicitly indicate, that there are 5 cheapest suits and the rest is more expensive. Just knit-picking

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Re: GMAT Diagnostic Test Question 19 [#permalink]

28 Oct 2011, 23:40

Ans is E

350*10 =3500
one is 200

so 3300
now 4 suits cost more than 200 so let us take them to be 201
so now 3300-201*4 = 2496

now 4 cheapest suits so 1*4 => 2496-4 = 2492 => most expensive one. Ans B

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Re: GMAT Diagnostic Test Question 19 [#permalink]

19 Jan 2012, 07:03

With the constraints-five cheapest suits are price $200 or less with atleast one costing $200", can't the prices be:
$1,$1,$1,$1,$200,$200,$200,$200,$200,$MAX
So $max = 3500-(4*1)-(200*5)=$2496??
If not, can someone explain why the above distribution is wrong?

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Re: GMAT Diagnostic Test Question 19 [#permalink]

29 Dec 2012, 15:29

I agree with two good points that others have brought up regarding this question:

A.) The use of the term "whole number" does not clearly indicate that the cheapest suit must be greater than or equal to $1. Some wording around this is needed to prevent readers from assuming that the four cheapest suits can be $0.

B.) It is unclear that the sixth through ninth cheapest suits must be $201 as opposed to $200. This is the part that messed me up - I kept getting $2496 as my final answer because I assumed that five of the suits were priced at $200. The sentence "the five cheapest suits are priced at $200, with at least one of them costing $200" does not preclude five of the suits costing $200.

I hope that the makers of this diagnostic test update question 19 accordingly. This is a really helpful test, and it would be great to update this question and make it even better.

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Re: GMAT Diagnostic Test Question 19 [#permalink]

30 Dec 2012, 07:03

bb wrote:

GMAT Diagnostic Test Question 19
Field: word problems (min/max)
Difficulty: 650

Rating:

This question was replaced by the following one:
A set of 11 different integers has a median of 25 and a range of 50. What is the greatest possible integer that could be in this set?

A. 65
B. 70
C. 75
D. 80
E. 85

Consider 11 numbers in ascending order to be x_1, x_2, x_3, ..., x_{11}.

The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is x_{6}=25;

The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is 50=x_{11}-x_{1} --> x_{11}=50+x_{1};

We want to maximize x_{11}, hence we need to maximize x_{1}. Since all integers must be distinct then the maximum value of x_{1} will be median-5=25-5=20 and thus the maximum value of x_{11} is x_{11}=50+20=70.

The set could be {20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 70}

Answer: B.
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Re: GMAT Diagnostic Test Question 19 [#permalink] 30 Dec 2012, 07:03

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