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How many items did Bob produce last week?

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How many items did Bob produce last week?

by crazy4gmat » Mon Aug 31, 2009 8:22 pm
If Bob produces 36 or fewer in a week, he is paid X dollars per item. If Bob produces more than 36 items, 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 produced 2 items more than last week and was paid a total of $510 for the item that he produced this week.
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by aakaps » Mon Aug 31, 2009 8:31 pm
Both combined are insufficient as the formula is 2 way....till 36 and beyond. If I consider his objects less than 36 I will have one answer, if more then another.
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by grockit_jake » Tue Sep 01, 2009 1:39 pm
Exactly. If we knew the number sold in both weeks was over 36, the equation would be:

$ = 36x + (T-36)*(3/2)

However, since we don't know it's over 36, the equation could also be

$ = xT,

which are 2 very different things.
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by mehravikas » Tue Sep 01, 2009 9:54 pm
I may be wrong here but the answer is C.

Agree that each statement individually is insufficient. However, if you combine both the statements then

You would get X = 15 if items were fewer than 36
or X = 20 if items are more than 36

Now if X = 15

Statement 1 - Number of items produced = 480/15 = 32
Statement 2 - number of items produced = 510/15 = 34

Difference of 2 items

If X = 20

Statement 1 - Number of items produced = 480/20 = 24
Statement 2 - number of items produced = 510/20 = 25.xxx

Difference between the number of items last week and this week is not 2.

There X = 15 and we can find the number of items.
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by grockit_jake » Wed Sep 02, 2009 11:33 am
I think you are mistaken:

Together, we know that 2 items cost $30, so 1 additional item cost $15.

If below the 36 threshold, then we know X = 15.

If above the 36 threshold, we know that 3/2X = 15, so X = 10.

If x = 10, then you will have a $30 increase when adding two items, if the total is above 36. If x = 15, then adding 2 items will increase the total $30.

In this case, you don't have enough info.
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by mehravikas » Wed Sep 02, 2009 12:03 pm
But if X = 10, then total items purchased would be 48 (last week)

and the calculation of 3/2X would be for 12 items not just 2 items.

Therefore the total cost would be = 36*10 + 12*15 = 540

grockit_jake wrote:I think you are mistaken:

Together, we know that 2 items cost $30, so 1 additional item cost $15.

If below the 36 threshold, then we know X = 15.

If above the 36 threshold, we know that 3/2X = 15, so X = 10.

If x = 10, then you will have a $30 increase when adding two items, if the total is above 36. If x = 15, then adding 2 items will increase the total $30.

In this case, you don't have enough info.
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by grockit_jake » Wed Sep 02, 2009 12:10 pm
If below the 36 threshold, x = 15

Last week $480 = 15*T , so T = 32
This week $510 = 15*T , so T = 34

If above the 36 threshold, x = 10

Last week $480 = 10*36 + 15*Additional, so A = 8, so T = 36+8 = 44

This week $510 = 10*36 + 15*Additional, so A = 10, so T = 36+10= 46

Both options leave you with 2 more items and $30 more dollars.
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by mehravikas » Wed Sep 02, 2009 12:18 pm
Oh I think you are correct...

Thanks,
Vikas
grockit_jake wrote:If below the 36 threshold, x = 15

Last week $480 = 15*T , so T = 32
This week $510 = 15*T , so T = 34

If above the 36 threshold, x = 10

Last week $480 = 10*36 + 15*Additional, so A = 8, so T = 36+8 = 44

This week $510 = 10*36 + 15*Additional, so A = 10, so T = 36+10= 46

Both options leave you with 2 more items and $30 more dollars.
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by aakaps » Fri Sep 04, 2009 2:36 pm
If this is a question from OG and the answer is c, I will think this is one of the question which GMAT prep folks just want you to put formulae and equate. Wrong question and similarly flow with the answer :)
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