GMAT_Flex_Quant_Mastery_A_Expl - Quant Mastery A Answers...

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Quant Mastery A Answers and Explanations
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3 Quant Mastery A Answers and Explanations 1. D 2. D 3. C 4. D 5. B 6. E 7. B 8. B 9. B 10. C 11. D 12. C 13. D 14. E 15. D 16. B 17. E 18. E 19. A 20. B 21. C 22. C 23. E 24. A ANSWERS AND EXPLANATIONS
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4 Quant Mastery A Answers and Explanations 1. (D) Nancy works 3 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period? 3 y (7 x 1 2 xy ) 3 x 1 12 y 3 xy (7 x 1 2) 3 x (2 y 1 7) 4 x ( y 1 8) Step 1: Analyze the Question We’ve got a wordy question stem and variables in the answer choices, so we can make this question more concrete and manageable through Picking Numbers. Step 2: State the Task We need to determine Nancy’s total earnings over a seven-week period, including four regular three-day weeks and three weeks during which she worked overtime days. Step 3: Approach Strategically We need two values, so let’s set x 5 5 and y 5 2. (Note that it’s a good idea to avoid 3 and 4 when Picking Numbers for this question, since those numbers appear in the question itself and may cause confusion later when we substitute the values into the answer choices.) There are two distinct parts of the seven-week period we’re asked to consider: the first four weeks, during which she worked three days a week with no overtime, and the final three weeks, during which she worked three days a week plus overtime. Let’s start with the first four weeks. Each week she worked three days at a rate of $5 a day (her daily rate is x , which we’ve set equal to 5), for a total of $60 earned: 4 3 3 3 5 5 60. In the final three weeks, she worked three days at a rate of $5 a day, as well as two additional days (the number of overtime days she worked is y , which we’ve set equal to 2) at a rate of $10 a day (her overtime days are paid at twice her regular rate, or 2 x ), for a total of $105 earned: (3 3 3 3 5) 1 (3 3 2 3 10) 5 105. Therefore, her total earnings over this period were $165: 60 1 105 5 165. Now let’s plug our values for x and y into the answer choices to see which one equals 165: (A) 3(2)[7(5) 1 2(5)(2)] 5 6(55) 5 330. Eliminate. (B) 3(5) 1 12(2) 5 15 1 24 5 39. Eliminate. (C) 3(5)(2)[7(5) 1 2] 5 30(37) 5 1,110. Eliminate. (D) 3(5)[2(2) 1 7] 5 15(11) 5 165. Possibly correct. (E) 4(5)[2 1 8] 5 20(10) 5 200. Eliminate. Only (D) gives us 165, so we know we’ve found the right answer. Note that we can tell that (A) and (C) will be far too large even before we do the final multiplication. Thinking logically about the answer choices will help to avoid unnecessary calculations. Step 4: Confirm Your Answer Reread the question stem, making sure you didn’t miss anything about the problem. In particular, make sure that you’ve substituted your values for x and y consistently and haven’t switched them anywhere.
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5 Quant Mastery A Answers and Explanations 2. (D) If 5 8 y 1 14 = 125 4 y 2 14 , then what is the value of y ?
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  • Winter '15
  • Negative and non-negative numbers, Quant Mastery

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