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23 Jan 2025, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:55) correct
34%
(01:54)
wrong
based on 116
sessions
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The salesman received a quarterly bonus, equal to 20% of the total wage for October, November and December. If the salesman received 15 dollars more in December than in October, what is the amount of the bonus?
(1) The ratio of the salesman's wage in October to that in November is 9:8
(2) The ratio of wages for November and December is 6:8
(1) The ratio of the salesman's wage in October to that in November is 9:8
(2) The ratio of wages for November and December is 6:8
23 Jan 2025, 02:29
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Bunuel
Let wage of October and November be x and y, then wage in December is x + 15
Calculate => (x + y + x+15)*20/100
Statement 1 => x/y = 9/8
Can't calculate values for x and y, hence insufficient
Statement 2 => y/(x+15) = 6/8
Can't calculate values for x and y, hence insufficient
Combining both these statements should give us values of x and y as we have 2 different equations and 2 variables and hence should be sufficient.
IMO: C
PS - Wordings in statement 2 are little skewed, is it talking about salesman wage or total wages paid by a company. I am considering it as a ratio of salesman wage rather than total, otherwise answer would have been E.
23 Jan 2025, 03:35
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Given:
- Bonus = 20% of total wages for Oct (O), Nov (N), Dec (D)
- D = O + 15 (December wage is 15 more than October)
- Bonus = 0.20 * (O + N + D)
Statement (1): O/N = 9/8
- O = (9/8) * N
Statement (2): N/D = 6/8
- N = (3/4) * D
Step 1: Substitute the expressions into the total wage equation:
- O = (9/8) * N = (9/8) * (3/4) * D = (27/32) * D
- N = (3/4) * D
Step 2: Total wages = O + N + D
- Total = (27/32) * D + (3/4) * D + D
- Total = (27/32) * D + (24/32) * D + (32/32) * D
- Total = (83/32) * D
Step 3: Bonus = 20% of Total wages
- Bonus = 0.20 * (83/32) * D
- Bonus = (83/160) * D
Step 4: Solve for D using D = O + 15:
- D = (27/32) * D + 15
- 32D = 27D + 480
- 5D = 480
- D = 96
Step 5: Calculate the Bonus:
- Bonus = (83/160) * 96 = 50.16
Conclusion: Both statements (1) and (2) are necessary to determine the bonus amount.
Answer: (E) Both statements are needed.
- Bonus = 20% of total wages for Oct (O), Nov (N), Dec (D)
- D = O + 15 (December wage is 15 more than October)
- Bonus = 0.20 * (O + N + D)
Statement (1): O/N = 9/8
- O = (9/8) * N
Statement (2): N/D = 6/8
- N = (3/4) * D
Step 1: Substitute the expressions into the total wage equation:
- O = (9/8) * N = (9/8) * (3/4) * D = (27/32) * D
- N = (3/4) * D
Step 2: Total wages = O + N + D
- Total = (27/32) * D + (3/4) * D + D
- Total = (27/32) * D + (24/32) * D + (32/32) * D
- Total = (83/32) * D
Step 3: Bonus = 20% of Total wages
- Bonus = 0.20 * (83/32) * D
- Bonus = (83/160) * D
Step 4: Solve for D using D = O + 15:
- D = (27/32) * D + 15
- 32D = 27D + 480
- 5D = 480
- D = 96
Step 5: Calculate the Bonus:
- Bonus = (83/160) * 96 = 50.16
Conclusion: Both statements (1) and (2) are necessary to determine the bonus amount.
Answer: (E) Both statements are needed.
