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Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's
income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to
Quentin, Quentin's new income would be what fraction of Sam's new income?
  • a)
    11/12
  • b)
    13/17
  • c)
    13/19
  • d)
    12/19
  • e)
    11/19
Correct answer is option 'A'. Can you explain this answer?
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Paul's income is 40% less than Rex's income, Quentin's inc...
Notice that Paul’s income is expressed as a percentage of Rex’s and that the other two incomes are expressed as a percent of Paul’s. Let’s assign a value of $100 to Rex’s income. Paul’s income is 40% less than Rex's income, so (0.6)($100) = $60. Quentin’s income is 20% less than Paul's income, so (0.8)($60) = $48. Sam’s income is 40% less than Paul's income, so (0.6)($60) = $36. If Rex gives 60% of his income, or $60, to Sam, and 40% of his income, or $40, to Quentin, then: Sam would have $36 + $60 = $96 and Quentin would have $48 + $40 = $88. Quentin’s income would now be $88/$96 = 11/12 that of Sam's.
The correct answer is A.
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Paul's income is 40% less than Rex's income, Quentin's inc...
Given information:
- Paul's income is 40% less than Rex's income.
- Quentin's income is 20% less than Paul's income.
- Sam's income is 40% less than Paul's income.

Step 1: Determine the relationship between the incomes of the three individuals.
Let's assume Rex's income as "x".
- Paul's income is 40% less than Rex's income, so it is 60% of Rex's income, which is 0.6x.
- Quentin's income is 20% less than Paul's income, so it is 80% of Paul's income, which is 0.8 * 0.6x = 0.48x.
- Sam's income is 40% less than Paul's income, so it is 60% of Paul's income, which is 0.6 * 0.6x = 0.36x.

Step 2: Determine how much Rex gives to Sam and Quentin.
Rex gives 60% of his income to Sam, which is 0.6x.
Rex gives 40% of his income to Quentin, which is 0.4x.

Step 3: Determine the new income of Sam and Quentin after receiving the money.
- Sam's new income is his original income plus the amount he received from Rex, which is 0.36x + 0.6x = 0.96x.
- Quentin's new income is his original income plus the amount he received from Rex, which is 0.48x + 0.4x = 0.88x.

Step 4: Determine the ratio of Quentin's new income to Sam's new income.
The ratio is given by Quentin's new income divided by Sam's new income:
0.88x / 0.96x = 11/12.

Therefore, the answer is option A) 11/12.
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Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam'sincome is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income toQuentin, Quentin's new income would be what fraction of Sam's new income?a)11/12b)13/17c)13/19d)12/19e)11/19Correct answer is option 'A'. Can you explain this answer?
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