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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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20 Dec 2009, 06:55
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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.
Edited the question and added the OA

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

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21 Dec 2009, 03:19
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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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21 Dec 2009, 05:46
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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.

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. _________________ Kudos [?]: 132984 [14], given: 12400 Math Expert Joined: 02 Aug 2009 Posts: 5223 Kudos [?]: 5868 [1], given: 118 Re: Bob's produced items last week [#permalink] Show Tags 21 Dec 2009, 06:25 1 This post received KUDOS Expert's post 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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10 Jan 2010, 09:31
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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

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

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17 May 2012, 03:06
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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17 May 2012, 05:31
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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.
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Re: Bob's produced items last week [#permalink]

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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,

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

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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,

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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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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24 Oct 2013, 01:48
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fozzzy wrote:
Its a pretty lengthy problem any other way to solve this under 2.5 mins?

Unfortunately not all question have "a silver bullet" solutions.
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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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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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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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24 May 2014, 15:47
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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.

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

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

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17 Jan 2016, 09:37
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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.

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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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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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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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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