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16 Mar 2023, 14:17
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msunny
Statement 1 is not sufficient -- maybe he normally gets $480 per item, and he produced one item, or maybe he gets $1 per item and made a lot of items. Statement 2 is not sufficient for essentially the same reason (knowing only the total he was paid for one week can't be sufficient).
Using both Statements, we know he earned $480 last week, and $510 this week, and he made 2 more items this week. Clearly he got $15 for each of the two additional items he made this week. We have to consider two possibilities:
- maybe the extra $15 per item he got this week is just his usual rate -- maybe he normally gets $15 per item, until he makes 36 items. We can see if that's possible: then last week, 15x = 480, and x = 32. So maybe he made 32 items last week, and 34 items this week, and got $15 per item.
- maybe the extra $15 per item he got this week is not his usual rate, because he was over the 36 item threshold, where his pay increases. When he is over that threshold, he makes 50% more per item, so that would mean his usual rate is $10 per item. In that case, he would always make $360 for the first 36 items he makes, then $15 per item after that. So when he makes $480, he is making $360 at $10 per item, and $120 at $15 per item, so he makes 120/15 = 8 additional items, or 36 + 8 = 44 items in total. He would then earn $510 by making 46 items this week.
So we can't be sure how many items he made last week, and the answer is E.
I'd add that in theory there's a third possibility -- that he made 35 items last week, and 37 this week, so only one of the two additional items was made at the higher rate. That doesn't turn out to work with the dollar totals in the question, so in this question it's impossible, and fortunately we don't have to worry about that case anyway to see that E is the answer.
05 Mar 2024, 10:55
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not a single word in two conditions indicating that bob's production in any of two given weeks is above 36 or not.
so basically, no need to calculate, and because of two different payment paterns, there's no way to calculate.
read carefully. that's the most important rule for this exam.
so basically, no need to calculate, and because of two different payment paterns, there's no way to calculate.
read carefully. that's the most important rule for this exam.
01 Jun 2026, 05:56
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Let last week's production = N.
Pay rule:
If N ≤ 36
Pay = NX
If N > 36
Pay = 36X + (3/2)X(N − 36)
Need N.
---
(1)
Total pay last week = 480
NX = 480 if N ≤ 36
or
36X + (3/2)X(N − 36) = 480 if N > 36
Many (N, X) pairs work.
Example:
N = 30, X = 16
N = 40, X = 10
Not sufficient.
---
(2)
This week:
Production = N + 2
Pay = 510
Again many possibilities.
Example:
If N = 28, then this week production = 30
30X = 510
X = 17
Works.
If N = 38, then this week production = 40
36X + 4(3/2)X = 42X = 510
X = 85/7
Works.
Different N values.
Not sufficient.
---
(1) + (2)
Pay increased from 480 to 510.
Increase = 30.
Since production increased by 2 items, check where the two weeks lie relative to 36.
Case 1: Both weeks ≤ 36
Increase = 2X
2X = 30
X = 15
Then
NX = 480
N = 32
Works.
Case 2: Last week = 36, this week = 38
Increase = 2 × (3/2)X = 3X
3X = 30
X = 10
Last week's pay = 36X = 360, not 480.
Impossible.
Case 3: Both weeks > 36
Increase = 2 × (3/2)X = 3X
3X = 30
X = 10
Last week's pay = 480
36(10) + (3/2)(10)(N − 36) = 480
360 + 15(N − 36) = 480
N − 36 = 8
N = 44
Works.
We get N = 32 or N = 44.
Both satisfy both statements.
Not sufficient.
---
Answer: E
GMAT shortcut:
From (1)+(2), pay rose by $30 when production rose by 2 items.
If both weeks are at or below 36 items:
2X = 30 ⇒ X = 15 ⇒ N = 480/15 = 32.
If both weeks are above 36 items:
3X = 30 ⇒ X = 10 ⇒ N = 44.
Two different values of N are possible.
Answer = E.
Pay rule:
If N ≤ 36
Pay = NX
If N > 36
Pay = 36X + (3/2)X(N − 36)
Need N.
---
(1)
Total pay last week = 480
NX = 480 if N ≤ 36
or
36X + (3/2)X(N − 36) = 480 if N > 36
Many (N, X) pairs work.
Example:
N = 30, X = 16
N = 40, X = 10
Not sufficient.
---
(2)
This week:
Production = N + 2
Pay = 510
Again many possibilities.
Example:
If N = 28, then this week production = 30
30X = 510
X = 17
Works.
If N = 38, then this week production = 40
36X + 4(3/2)X = 42X = 510
X = 85/7
Works.
Different N values.
Not sufficient.
---
(1) + (2)
Pay increased from 480 to 510.
Increase = 30.
Since production increased by 2 items, check where the two weeks lie relative to 36.
Case 1: Both weeks ≤ 36
Increase = 2X
2X = 30
X = 15
Then
NX = 480
N = 32
Works.
Case 2: Last week = 36, this week = 38
Increase = 2 × (3/2)X = 3X
3X = 30
X = 10
Last week's pay = 36X = 360, not 480.
Impossible.
Case 3: Both weeks > 36
Increase = 2 × (3/2)X = 3X
3X = 30
X = 10
Last week's pay = 480
36(10) + (3/2)(10)(N − 36) = 480
360 + 15(N − 36) = 480
N − 36 = 8
N = 44
Works.
We get N = 32 or N = 44.
Both satisfy both statements.
Not sufficient.
---
Answer: E
GMAT shortcut:
From (1)+(2), pay rose by $30 when production rose by 2 items.
If both weeks are at or below 36 items:
2X = 30 ⇒ X = 15 ⇒ N = 480/15 = 32.
If both weeks are above 36 items:
3X = 30 ⇒ X = 10 ⇒ N = 44.
Two different values of N are possible.
Answer = E.
