700+ level

[akash singhal]

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.

OE E

Please Explain How!!!

[GMATGuruNY]

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.

Statements combined:
(this week's earnings) - (last week's earnings) = 510 - 480 = $30.
Implication:
The 2 additional items produced this week each account for an additional $15 in earnings, for a total earnings increase of $30.

Case 1: x=15
In this case:
Number of items produced last week = 480/15 = 32.
Number of items produced this week = 510/15 = 34.

Case 2: (3/2)x = 15, implying that x=10
Last week:
Total earnings for the first 36 items = 36*10 = 360.
Earnings paid at $15 per item = 480-360 = 120.
Number of items paid at $15 per item = 120/15 = 8.
Total items = 36+8 = 44.

This week:
Total earnings for the first 36 items = 36*10 = 360.
Earnings paid at $15 per item = 510-360 = 150.
Number of items paid at $15 per item = 150/15 = 10.
Total items = 36+10 = 46.

Since the total number of items produced last week is 32 in Case 1 but 44 in Case 2, INSUFFICIENT.

The correct answer is E.

[Max@Math Revolution]

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 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.

This is a '2by2' question which can give a table as below:


There are 3 variables (m,n,x) and 2 equations are given by the 2 conditions, giving high chance (E) will be our answer
Even if we combine the 2 conditions, we cannot obtain unique value for m, so the answer becomes (E).

For cases where we need 3 more equation, 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.