Data Sufficiency

This problem was touched upon before on this forum, but very briefly. Can someone please explain where my work went wrong?

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 1.5 times that amount for each additional item. How many items did Bob produce last week?

(1) Last week Bob was paid a 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.

OA: E


I chose C, and this is what I did:

Let n = number of items

From statement 1:
xn + 1.5x(n - 36) = 480 --> 2.5xn - 54x = 480

From statement 2:
I only subtracted 34, since he produced 2 more items.
xn + 1.5x(n - 34) = 510 --> 2.5xn - 51x = 510 --> xn = .4(510 + 51x)

Now combined:
2.5(.4(510 + 51x) - 54x = 480 --> solve for x. And then you can solve for n.

What did I do wrong?

student22 wrote:This problem was touched upon before on this forum, but very briefly. Can someone please explain where my work went wrong?

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 1.5 times that amount for each additional item. How many items did Bob produce last week?

(1) Last week Bob was paid a 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.

OA: E


I chose C, and this is what I did:

Let n = number of items

From statement 1:
xn + 1.5x(n - 36) = 480 --> 2.5xn - 54x = 480

From statement 2:
I only subtracted 34, since he produced 2 more items.
xn + 1.5x(n - 34) = 510 --> 2.5xn - 51x = 510 --> xn = .4(510 + 51x)

What did I do wrong?

This is where you went wrong twice in statement 1 and 2 . Do you know for sure that the items produced are more than 36 in each occasion.

Vow!! this was a good one.

First your minor errors marked in green in quoted text.

Let n = number of items

From statement 1:
36x + 1.5x(n - 36) = 480

From statement 2:
I only subtracted 34, since he produced 2 more items.
36x + 1.5x(n - 34) = 510

So these are 2 equations in 2 unknowns and hence the obvious is C. x=10, n=44
But wait.

We are asked what is the the number of items produced? And in the above quoted text we are assuming that the number is greater than 36. But he can very well produce less than 36 in which case equations would be
from 1: nx=480
from 2: (n+2)x=510
therefore 2x=30, so x=15, n=32

So even after combining 2 statements we get two valid values for n.

Therefore both statements are together INSUFFICIENT.
Hence E.

HTH

Ah, good call guys. You're right I assumed (without reason) that there would be at least 36.

But, since we can't assume that here, as iamseer pointed out, it makes sense that it's E.

Thanks!

perfect trap... fortunately I did not step it!

Unfortunately I stepped in
Nice quistion

Are the quantities of 32 and 34 respectively, the only options?

given and find the number of items produced last week, y-?
st(1) Insufficient, as we have no clue about the number of items produced last week;
st(2) Insufficient, as we have no clue about the number of items produced this week and may not deduct the number of items produced last week;
Combined st(1&2) (510-480)/(y-2)= {x or 1.5x} we cannot solve for y, as we need to define x or 1.5x? Not Sufficient.

answer E, where's the trick here?

student22 wrote:This problem was touched upon before on this forum, but very briefly. Can someone please explain where my work went wrong?

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 1.5 times that amount for each additional item. How many items did Bob produce last week?

(1) Last week Bob was paid a 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.

OA: E


I chose C, and this is what I did:

Let n = number of items

From statement 1:
xn + 1.5x(n - 36) = 480 --> 2.5xn - 54x = 480

From statement 2:
I only subtracted 34, since he produced 2 more items.
xn + 1.5x(n - 34) = 510 --> 2.5xn - 51x = 510 --> xn = .4(510 + 51x)

Now combined:
2.5(.4(510 + 51x) - 54x = 480 --> solve for x. And then you can solve for n.

What did I do wrong?

I dont know where you messed up but

we get this equation

From statement 1:
36x + 1.5x(n - 36) = 480


From statement 2:
I only subtracted 34, since he produced 2 more items.
36x + 1.5x(n - 34) = 510

There are 2 equations and 2 variables and we can find them.

But this is not the only case :

We are asked what is the the number of items produced? And in the above quoted text we are assuming that the number is greater than 36. But he can very well produce less than 36 in which case equations would be
from 1: nx=480
from 2: (n+2)x=510
therefore 2x=30, so x=15, n=32

Hence answer is E.

Hope you understand it