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Difficulty:
45%
(medium)
Question Stats:
64% (02:25) correct
36%
(02:28)
wrong
based on 81
sessions
History
Date
Time
Result
Not Attempted Yet
16 2/3% of 72 companies that were formed last year plan to hire workers, as do 37 1/2% of the 160 companies that were formed at least two years ago, and 15% of the companies that were formed this year. If in total 81 companies plan to hire workers, how many companies were formed this year ?
A. 40
B. 60
C. 80
D. 120
E. 160
A. 40
B. 60
C. 80
D. 120
E. 160
19 Mar 2026, 03:24
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The percentages here are designed to look messy but they're actually clean fractions in disguise. That's the concept being tested.
1. 16 2/3% = 1/6. So from the 72 companies formed last year: 72 x (1/6) = 12 companies plan to hire.
2. 37 1/2% = 3/8. From the 160 companies formed at least two years ago: 160 x (3/8) = 60 companies plan to hire.
3. 15% of the 60 companies formed this year: 60 x (15/100) = 9 companies plan to hire.
Check: 12 + 60 + 9 = 81. That matches the total given in the problem, so everything is consistent.
Now the question asks how many companies there are in total. That's just 72 + 160 + 60 = 292. Answer is E.
The trap here is thinking the problem gives 72, 160, and 60 as partial information and that you need to solve for some unknown total using the 81. But those three groups are exhaustive. The "if in total 81 companies plan to hire" line is a verification condition, not a constraint to solve. You don't need to set up an equation.
I got burned on almost this exact type of problem in practice. The messy percentages (16 2/3%, 37 1/2%) are bait to make you do ugly decimal arithmetic instead of just recognizing 1/6 and 3/8. Once you see the fractions, the arithmetic takes about 20 seconds.
1. 16 2/3% = 1/6. So from the 72 companies formed last year: 72 x (1/6) = 12 companies plan to hire.
2. 37 1/2% = 3/8. From the 160 companies formed at least two years ago: 160 x (3/8) = 60 companies plan to hire.
3. 15% of the 60 companies formed this year: 60 x (15/100) = 9 companies plan to hire.
Check: 12 + 60 + 9 = 81. That matches the total given in the problem, so everything is consistent.
Now the question asks how many companies there are in total. That's just 72 + 160 + 60 = 292. Answer is E.
The trap here is thinking the problem gives 72, 160, and 60 as partial information and that you need to solve for some unknown total using the 81. But those three groups are exhaustive. The "if in total 81 companies plan to hire" line is a verification condition, not a constraint to solve. You don't need to set up an equation.
I got burned on almost this exact type of problem in practice. The messy percentages (16 2/3%, 37 1/2%) are bait to make you do ugly decimal arithmetic instead of just recognizing 1/6 and 3/8. Once you see the fractions, the arithmetic takes about 20 seconds.
