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If Bob produces 36 or fewer in a week, he is paid X dollars

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If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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If Bob produces 36 or fewer items in a week, he is paid X dollars per item. If Bob produces more than 36 items in a week, he is paid X dollars per item for the first 36 items and 3/2 times that amount for each additional item. How many items did Bob produce last week?

(1) Last week Bob was paid total of $480 for the items that he produced that week.

(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 May 2012, 05:27, edited 1 time in total.
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Re: Bob's produced items last week [#permalink]

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IMO E

we are having two variables no. of item is not known and price is x

with bth also we are not getting any thing

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Re: Bob's produced items last week [#permalink]

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If Bob produces 36 or fewer items in a week, he is paid X dollars per item. If Bob produces more than 36 items in a week, he is paid X dollars per item for the first 36 items and 3/2 times that amount for each additional item. How many items did Bob produce last week?

First let's set the equation for Bob's income:

\(I=nx\), when \(n<=36\),
OR
\(I=36x+(n-36)1.5x=1.5nx-18x\), when \(n>36\).

\(n=?\)

(1) Last week Bob was paid total of $480 for the items that he produced that week --> \(I=480\). Clearly insufficient.

Either: \(I=480=nx\) OR \(I=480=1.5nx-18x\)

(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week --> \(I'=510\), \(n'=n+2\). Clearly insufficient.

Either: \(I'=510=(n+2)x\) OR \(I'=510=1.5(n+2)x-18x\)


(1)+(2) We can have three system of equations:

\(480=nx\) and \(510=(n+2)x\), meaning that \(n+2<=36\). In this case \(x=15\) and \(n=32\).

OR:
\(480=nx\) and \(510=1.5(n+2)x-18x\), meaning that \(n+1<=36\) and \(n+2>36\) (\(n=35\)). In this case n has no integer value, so this system doesn't work;

OR:
\(480=1.5nx-18x\) and \(510=1.5(n+2)x-18x\), meaning that \(n>36\). In this case \(x=10\) and \(n=44\).

So we can have two values for n. Not sufficient.

Answer: E.

The last step can be done in another way:

We know that 2 more items resulted 30$ more.

If these two items were paid by 1.5x rate (n>=36) --> 1.5x+1.5x=30 --> x=10 and as n>=36, we should substitute this value in the second equation from (1), which gives n=44
If these two items were paid by x rate (n<=34) --> x+x=30 --> x=15 and as n<=34, we should substitute this value in the first equation from (1), which gives --> n=32
Already two different answers for n (no need to check for the third case when one item is paid by regular rate and another with overtime rate), hence insufficient.

Answer: E.
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Re: Bob's produced items last week [#permalink]

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E,...
combining two st... $30 is price of either both at x(no<=36),one at x ,other at 1.5x. or both at 1.5x.....
so one sol x=15...items 32...
2nd sol x=10....items 360/10+120/15=42.....
3rd sit of one of x and second at 1.5x not possible
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Re: Bob's produced items last week [#permalink]

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and E

if you assume the no of items is less than 36, you get

x* (no of items) = 480
x* (no of items + 2) = 510
==> no of items = 15

if you assume the no of items is more than 36, you get

36* x + ( no of items - 36)*(1.5x) = 480
36*x + (no of items + 2 - 36)*(1.5x) = 510
==> no of items = 44

clearly the same set of information leads to 2 possible solutions
therefore additional data is required

ans : E
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Re: Bob's produced items last week [#permalink]

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Why then the GMATPrep marks C as the correct answer?
I answered E but when I checked the solution, it was C...
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Re: Bob's produced items last week [#permalink]

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New post 02 Sep 2013, 19:45
Bunuel wrote:
Stiv wrote:
Why then the GMATPrep marks C as the correct answer?
I answered E but when I checked the solution, it was C...


Correct answer as well the answer given in GMAT Prep is E.


Just wanted to confirm,
by solving equations 1.5nx-18x=480 & 1.5nx-15x=510 (for n>36), if still we get non integer values for n,
would the answer be C?

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Re: Bob's produced items last week [#permalink]

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New post 03 Sep 2013, 02:11
jeetmech152 wrote:
Bunuel wrote:
Stiv wrote:
Why then the GMATPrep marks C as the correct answer?
I answered E but when I checked the solution, it was C...


Correct answer as well the answer given in GMAT Prep is E.


Just wanted to confirm,
by solving equations 1.5nx-18x=480 & 1.5nx-15x=510 (for n>36), if still we get non integer values for n,
would the answer be C?


If 2 out of 3 equations give non-integer values then only the third solution is valid and the answer would be C.
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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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New post 24 Oct 2013, 01:46
Its a pretty lengthy problem any other way to solve this under 2.5 mins?
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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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New post 26 Oct 2013, 07:14
fozzzy wrote:
Its a pretty lengthy problem any other way to solve this under 2.5 mins?


just as i saw the "65% difficulty" i chose most needing to explore answer, i.e. E. May be it is good strategy for complicated questions?

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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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New post 26 Oct 2013, 07:43
Temurkhon wrote:
fozzzy wrote:
Its a pretty lengthy problem any other way to solve this under 2.5 mins?


just as i saw the "65% difficulty" i chose most needing to explore answer, i.e. E. May be it is good strategy for complicated questions?


I honestly think this is a difficult question, look at the overall accuracy its not very high. But personally I think its a time consuming question rather than a difficult question since it has 2 scenarios. Regarding your strategy I don't think that's safe.
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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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Clearly each statement alone is NOT sufficient

Now, let's combine and see what happens

We have an extra US$30 revenue from the sale of two extra items. Now then, we could have two scenarios.

Original price 'x' equals to 15, then 2 extra items account for the US$30 difference (510 - 480). So we would have 480/15 = 32 items.

Or we could have that two items again represent US$30 but original price is in fact US$10 and US$15 are the 1.5x for each item > 36. Therefore, Maximum # with US$ 10 tag is 36=US$360. The rest is US$120 / 15 = 8 additional. So we would have a total of 36+8=44 items.

Two possible answers

Answer: E

Hope it clarifies
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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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New post 24 May 2014, 23:10
Let x be price per item and Y be total no of items produced
St 1- 36x + (y-36)* (1.5x)=480
St 2- 36x + (y+2-36)* (1.5x)= 510

Solving the 2 equations gives u X=10 and Y=32 as the unique ans. So according to me, ans should be C. Please let me know if I have made any mistake

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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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New post 17 Jan 2016, 08:37
I'm still not too clear on when it is appropriate to stop and be confident on the solution choice. I got to the part with the 2 equations combined, but then I selected "e", hoping there wasn't a constraint trick bc we clearly have too few equations and multiple unknowns. For some reason, I'm coming up on the 2 min mark after checking all of the previous out and it takes me another 2 mins (and a lot of energy) to find the exact #'s in Bunuel's solution. Is there a way to be confident without getting exact values for price and quantity in the combined statements case?

bump: MathRevolution, VeritasPrepKarishma, etc.

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jwamala wrote:
I'm still not too clear on when it is appropriate to stop and be confident on the solution choice. I got to the part with the 2 equations combined, but then I selected "e", hoping there wasn't a constraint trick bc we clearly have too few equations and multiple unknowns. For some reason, I'm coming up on the 2 min mark after checking all of the previous out and it takes me another 2 mins (and a lot of energy) to find the exact #'s in Bunuel's solution. Is there a way to be confident without getting exact values for price and quantity in the combined statements case?

bump: MathRevolution, VeritasPrepKarishma, etc.


Let me try to answer.

You have not completely figured out the main crux of the problem. You need to be absolutely sure of whether the items were \(\leq\) 36 or > 36 . This will determine (for example) in statement 1 you need to use I =nx or I=1.5x(n-36)+36x (lets calls them equations 1.a and 1.b respectively). So, you get 2 distinct equations with no basis to eliminate either one. Thus this statement is NOT sufficient.

You will be able to use I=nx if x \(\leq\) 36 but if it is > 36, then you must use I=1.5x(n-36)+36x. This ambiguity makes this statement NOT sufficient.

You can now see that there might be a catch in this question based on analysis of statement 1 alone. Now, go onto statement 2 and you will again realize that there is no basis to eliminate 1 of the 2 possible equations (lets calls them equations 2.a and 2.b respectively) as you still have not been provided any information about the number of the items. They can be \(\leq\) 36 but at the same time can also be >36. We have no justification to choose 1 option over the other.

Again, you get 2 more distinct equations , making statement 2 not sufficient alone.

For combining the 2 statements, you can now clearly see that you can have the following 2 sets of distinct equations:

1. 1.a and 2.a or
2. 1.b and 2.b

Either way, you will not be getting the same answer ---> E is thus the correct answer. But be careful about this step as if you do get the same result for 'x' or 'n' from the 2 systems of equations, then it will be C instead of E.

In totality, it took close to 1-1.5 minutes to analyse both statements individually with another 45-60 seconds to analyse both statements together and mark E as the answer.
Remember that in GMAT Quant, you need to spend an AVERAGE of 2 minutes per question and not more. This does not mean that all questions will take you full 2 minutes. Some of the questions are bound to take less than 2 minutes while some of them will take you >2 minutes, bringing the average close to 2 minutes per question.

As this is a 'difficult' question as categorized by the GMATCLUB timer results, it is fine if you spent 2-3 minutes on this question. In GMAT, you should be able to recover this time if you know how to pick your battles and move on.

Hope this helps.


P.S.:

1. Having 2 equations for 2 variables may or may not sufficient to give you a sufficient answer.

Example, 2a+3b=6 and 4a+6b=12 are although 2 equations but they are NOT distinct and you will not get a unique value for a,b. Thus you need to check for DISTINCT equations and not just any equations while solving for variables.

2. Lets say you ended up getting 2 systems of equations as

a) 2x+3y=4 and x+y=4 ,you get x=3 and y=1

b) 3x+4y=13 and 2x+y=7, you again get x=3 and y=1

Thus in this case, you must mark C as you are getting the same unique values for x and y.

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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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New post 17 Jan 2016, 17:22
Engr2012, that makes sense and thank you for your response. However, I'm wondering how much calculation we have in this specific scenario since there are actually 3 cases:

1) 1a & 2a
2) 1a & 2b
3) 2b & 3b

Without putting out the numbers is there anyway we can pick "e" without finding the exact prices and quantities for x & y given that the total number is the only constraint and prices can be decimal quantities?

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If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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New post 17 Jan 2016, 17:37
jwamala wrote:
Engr2012, that makes sense and thank you for your response. However, I'm wondering how much calculation we have in this specific scenario since there are actually 3 cases:

1) 1a & 2a
2) 1a & 2b
3) 2b & 3b

Without putting out the numbers is there anyway we can pick "e" without finding the exact prices and quantities for x & y given that the total number is the only constraint and prices can be decimal quantities?


You are correct that we will have 3 systems of equations as Bunuel had mentioned in his post but in effect you only have 2 systems as the 2nd one mentioned below does not work as '' can only take integer values.

\(480=nx\) and \(510=(n+2)x\), meaning that \(n+2<=36\). In this case \(x=15\) and \(n=32\).

OR:
\(480=nx\) and \(510=1.5(n+2)x-18x\), meaning that \(n+1<=36\) and \(n+2>36\) (\(n=35\)). In this case n has no integer value, so this system doesn't work;

OR:
\(480=1.5nx-18x\) and \(510=1.5(n+2)x-18x\), meaning that \(n>36\). In this case \(x=10\) and \(n=44\).

But your reason for choosing E is not correct. We are marking 'E' as you will end up getting more than 1 sets of values for x and n, hence even when you combine the statements, you will not get unique values for x and n.

Hope this helps.

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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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New post 17 Jan 2016, 18:07
Engr2012, thanks for entertaining my questions. Maybe I'm dumb here, but I can't solve these three simultaneous situations as quickly as you all seemingly do. Would my thinking be incorrect to think, at a high level and through inspection:

1) We have two equations where we know x will be (510 - 480)/2 = 15. N must be 480/15 = 960/30 = 32. Ok this holds.
2) Maybe this is right, I can't tell n can't be an integer...
3) Maybe this is right, I've tapped out on my mental capacity for this question and I need to finish this exam...

E seems more likely to be correct because we only need one more solution that works and for c to be right 2 & 3 must either give the same answer a (1), not be possible bc n must be an integer, or a combination of those. I just can't see myself reasonably throwing any more firepower at a question like this so that's why I'm asking for a shortcut.

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Re: If Bob produces 36 or fewer in a week, he is paid X dollars   [#permalink] 17 Jan 2016, 18:07

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