Tough word Problem

[Uva@90]

Laura sells encyclopaedias, and her monthly income has two components, a fixed component of $1000, and a variable component of $C for each set of encyclopaedias that she sells in that month over a sales target of n sets, where n>0. How much did she earn in March?
(1) If Laura had sold three fewer sets in March, her income for that month would have been $600 lower than it was.
(2) If Laura had sold 10 sets of encyclopaedias in March, her income for that month would have been over $4000.

OA C

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Hi Uva@90

This DS question has several unknowns that we need to keep track of (and a "quirk" that you need to notice to avoid choosing one of the wrong answers).

We're asked how much money Laura earned. We're told that her pay is $1,000 + C dollars per set of encyclopedias (ABOVE her sales target of N sets). So, we need to know C and how many she sold above N.

Fact 1 tells us that 3 fewer sets sold = $600. The catch is that we don't know if she "made money" on each of the 3 sets of books. It might be that 1 or 2 of the sets were part of her "target" (so she didn't make any money on those sets).

Since her total would have been $600 less, that means that one of the 3 options occurred:
1 set "counted" and made her $600
2 sets "counted" and made her $300 each
3 sets "counted" and made her $200 each

It's possible that she only sold $600 above her target, but it's also possible that she made more than that (if all 3 sets "counted", then she could have made more money than the $600.
Fact 1 is INSUFFICIENT

Fact 2 tells us that selling 10 sets would lead to an income ABOVE $4,000 (the $1,000 + the extra money). We run into a similar problem here: we don't know how many of those sets "made her money." Since $4,000 is > $1,000, we know that she sold some number of sets above her "target" (and made some extra money), but we don't know how many. Also, we don't know how much money each set earned her.
Fact 2 is INSUFFICIENT

Combining facts, we have an interesting Number Property...
From Fact 1, we know that the extra money made above her target is either $200/set, $300/set or $600/set.
From Fact 2, we know that if she sold 10 sets, those sets made her OVER $3,000 in additional money.

If a set made her only $200 more, then she would never make OVER $3000, so this option is NOT POSSIBLE
If a set made her only $300 more, then she would never make OVER $3000, so this option is NOT POSSIBLE
So, a set MUST make her $600 more, as long as it's not part of the "target"

This means that since only 1 of the 3 sets (mentioned in Fact 1) would get her extra money, any of the sets that she sold BEFORE those sets would have been part of the "target" (and also would not have gotten her any extra money). So, she only sold 1 set above her target, at $600/set....

Her pay would have been $1000 + $600 = $1600

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[Uva@90]

Hi Uva@90

This DS question has several unknowns that we need to keep track of (and a "quirk" that you need to notice to avoid choosing one of the wrong answers).

We're asked how much money Laura earned. We're told that her pay is $1,000 + C dollars per set of encyclopedias (ABOVE her sales target of N sets). So, we need to know C and how many she sold above N.

Fact 1 tells us that 3 fewer sets sold = $600. The catch is that we don't know if she "made money" on each of the 3 sets of books. It might be that 1 or 2 of the sets were part of her "target" (so she didn't make any money on those sets).

Since her total would have been $600 less, that means that one of the 3 options occurred:
1 set "counted" and made her $600
2 sets "counted" and made her $300 each
3 sets "counted" and made her $200 each

It's possible that she only sold $600 above her target, but it's also possible that she made more than that (if all 3 sets "counted", then she could have made more money than the $600.
Fact 1 is INSUFFICIENT

Fact 2 tells us that selling 10 sets would lead to an income ABOVE $4,000 (the $1,000 + the extra money). We run into a similar problem here: we don't know how many of those sets "made her money." Since $4,000 is > $1,000, we know that she sold some number of sets above her "target" (and made some extra money), but we don't know how many. Also, we don't know how much money each set earned her.
Fact 2 is INSUFFICIENT

Combining facts, we have an interesting Number Property...
From Fact 1, we know that the extra money made above her target is either $200/set, $300/set or $600/set.
From Fact 2, we know that if she sold 10 sets, those sets made her OVER $3,000 in additional money.

If a set made her only $200 more, then she would never make OVER $3000, so this option is NOT POSSIBLE
If a set made her only $300 more, then she would never make OVER $3000, so this option is NOT POSSIBLE
So, a set MUST make her $600 more, as long as it's not part of the "target"

This means that since only 1 of the 3 sets (mentioned in Fact 1) would get her extra money, any of the sets that she sold BEFORE those sets would have been part of the "target" (and also would not have gotten her any extra money). So, she only sold 1 set above her target, at $600/set....

Her pay would have been $1000 + $600 = $1600

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Rich,
You made easy to understand.
Thanks Rich

Regards,
Uva.