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

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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, 17:25
jwamala wrote:
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.

You are not dumb to ask these questions. Asking questions only goes to show that you are actually thinking about this question along the right path. As for us figuring out the systems, it all comes down to practicing similar DS questions. Once you have solved 50-100 questions, you will start seeing patterns. GMAT is all about pattern recognition and time management. These 2 things come only after you have practiced a lot.

As mentioned in my post above if you see a difficult question such as this and you have already spent 2-2.5 or even 3 minutes to reach the last combined step, then yes, your high level assumptions might work. This will atleast help you to cut your losses further timewise and move on to the next question. Your explanation for (1) is correct and the same goes for (2). For (3) if you see running short on time, mark E and move on.

1 way I see between 1 and 3 is to recognise that the equations are very different in these 2 systems and your best bet will be that you will end up getting 2 different values for x and n . This in itself will be sufficient for you to mark E and move on. You dont even need to check (2) as you already have 2 different answers.

But to close the loop on this discussion, for (3) in order to look at the values, you will have to solve the equations to get x=10 and n=44. There is no other way I see to circumvent this requirement and to be absolutely sure that you will not end up getting the same numbers as those you got from (1). But this route is only recommended when you are still within the 2-2.5 minute mark.

Hope this helps.

The more straightforward way to solve this system is to substitute for 'n' in order to get x=10. After this you can plug in this value of x to get n.

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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, 18:13
Thanks Engr2012, this was very helpful. From a timing standpoint, I always take about 60 secs to digest and understand a word problem. I'm not sure I can cut that down. Building my number sense may help me push through calculations once I get to (c) in the answer choices (after eliminating A & D, and B). After this, I should have time to get through that last calculation (if I can really nail down this number sense). It just seems hard when you're 2 mins in:

(510 - 480) = 1.5(n + 2 - n)x + (18x - 18x)
30 = 3x
x = 10...plug in x

480 = 1.5(10)n - 18(10)
480 = 15n - 180
660 = 15n ... now I just need to "see" that 600/15 + 60/15 is 44.

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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, 21:50
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

When you modify the original condition and the question, you need to figure out the number of item he produced(L), the number of item he produced this week(T), and x. So there are 3 variables, which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), they become 36x+(L-36)(3x/2)=480, 36x+(L+2-36)(3x/2)=510 or Lx=480 and (L+2)x=510, which is not unique and not sufficient. Therefore, the answer is E.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink]

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05 Aug 2016, 09:10
I wonder if the GMAT will play a trap E in these type of questions and actually have one answer come out of two different equations (one is not integer while the other is) Either way, the gut answer with this question is E.

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

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15 Jul 2017, 12:06
Statement 1:
Clearly not sufficient

Statement 2:
Clearly not sufficient

1 + 2

Total paid last week = 480
Total paid this week = 510

510 - 480 = 30/2 = 15 each when assuming items are > 36

15/1.5 = 10 each when assuming items are <= 36

I believe the confusion begins when people are forgetting that statements 1 and 2 are not providing enough details about total items.
if you take 480/10 = 48 items then you have >36 items
if you take 480/15 = 32 which are < 36

The question is... do you know with certainty how many items?

because of this ambiguity of two possible answers, then statements 1 and 2 are not sufficient. Therefore, answer is E

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

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16 Sep 2017, 15:15
Bunuel wrote:
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. Hi - why are we even testing the equations in the red font ...can that step by removed all together Q2) Just confirming, we are saying its not sufficient because we are getting 2 values in the greens right ? Kudos [?]: 7 [0], given: 5 Intern Joined: 20 Jan 2014 Posts: 19 Kudos [?]: 5 [0], given: 26 Re: If Bob produces 36 or fewer in a week, he is paid X dollars [#permalink] ### Show Tags 25 Dec 2017, 05:35 Bunuel wrote: 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. Hi Bunuel, Could you please tell me whether my thinking is correct or not: After combining we can get two scenarios, 1. If items are less than 36, then per item cost would be 30/2 =$15, so x =$15 2. If items are more than 36, per item cost would be 1.5x =30 or x =$10

Since, we are getting two different values for x, we can find two different values for no of items. NS.

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Re: If Bob produces 36 or fewer in a week, he is paid X dollars   [#permalink] 25 Dec 2017, 05:35

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