Arithmetic (FDPR) Flashcards
Translate percent change from English to Math:
- 100% greater than original
- 45% less than original
- 130% of the original
- 75% of the original
- 200% of the original or 2x original
- 55% of the original
- 30% greater than the original
- 25% less than the original
What are the relative values on GMAT?
fractions, decimals, percents or ratios (proportion)
What are the concrete values on GMAT?
specific number of tickets sold, liters of water, etc
T or F: For positive numbers, if the starting faction is less than 1, the value fraction decreases - toward to 0- as you add the same number to the top and bottom
F
the fraction increase as it gets closer to 1
How does a faction value (that is greater than 1) change when you add the same number to top and bottom?
the result is smaller (getting closer to 1)
E.g: 3/2 > 4/3
List all strategies that you can approach for this problem
Which fraction is greater: 7/9 or 4/5?
1) The Double-Cross: 35/45 < 36/45
2) Percentage Exchange: 77.7% < 80%
What is the best strategy for this problem?
A TV originally priced at $700 was offered at a 12% discount. What was the sale price of the TV?
Benchmark Computation
- Amount of Reduction = 10% + 1% + 1% = 70 + 7 + 7 = 84
- Final amount = 700 - 84 = 700 - 80 - 4 = $616
Whats your approach?
65% of students have taken language classes. Of those students, 40% have studied more than one language. If there are 300 students, how many have studied more than one language?
(A) 78 (B)102. (C)120. (D) 150. (E)195
Look at the answer choices, then decide to do estimation or precise cal
- in this case, estimation is more efficient :
40% of 60% of 300 = 72 so ans must be greater but closed to choice (A)
When can you really use the estimation strategy?
1) When the problem includes “approximately” in its question
2) When the problem contains annoying/non-nice ratio number
3) When the value of answer choices vary greatly
i.e: (A) 780 (B) 2700 (C) 4320. (D) 6480. (E) 8400
When you see not nice % with decimals, what techniques to use?
When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that Leo paid was $87.50, what was the total value of the item?
1) look at the answer choices to see whether to use estimation
2) Apply Benchmark Computation:
- 7% of $1000 is $70 so the excess amount must be greater than 1,000
Simplify 60% of 45.35
3/5 x (45 +0.35) = 9x3 + 0.7x 3 = 27 +0.21= 27.21
How would only quarters and dimes add up to $2.50?
10 quarters, 0 dimes
8 quarters, 5 dimes
6 quarters, 10 dimes….
- The inverse proportion relationship is 2:5
For company A, by what percent did profit increase this over last?
1) Last year’s profit is 20% less than this year’s profit
2) Last year’s profit was 80k
Statement 1) or (A) is sufficient
- When we have the profit ratio (this/last) = 5/4, we can infer that there was 1/4 or 25% increase in profit
How do you solve the relative value of two departments within a company, when there are increase/decrease in revenue, profit, cost?
Weighted Average: Push-Pull in the increase/decrease between two apartments
What is the faster way to solve beside algebra?
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
Weighted Average
What technique you need to solve this efficiently?
If 65 percent of a certain firm’s employees are full-time and if there are 5,100 more full-time employees than part-time employees, how many employees does the firm have?
Ratio Difference and Multiplier X Ratio:
- F: P = 65% : 35%, then F-P = 30. X = 5,100
- X= 170 then Total employees = 170x100 = 17,000
What technique you need to solve this efficiently?
Karen bought a new television, originally priced at $690. However, she had a coupon that saved her $67. For what percent discount was Karen’s coupon?
Benchmark Estimation:
- 10% of $690 is 69 but since $67<69 so the discount must be smaller than 10%
what is your foremost step set-up?
If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
a. x = y
b. y = 1
c. x and y are prime integers.
Just like those problems in data sufficiency, you set up test cases in which:
- 3x/y = 3, 5, 7, 11, 13,.. -> x/y = 1, 5/3, 7/3, 11/3… From the pattern, we can eliminate a & b
- Next, since its the ratio, always do extreme cases by doubling both numerator & denominator (i.e: x/y =10/6) -> we can eliminate c as well
What is the common theme in diguise?
A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?
Weighted Average
For a recent play performance, the ticket prices were $25 per adult and $15 per child. A total of 500 tickets were sold for the performance. If the avg tix price is $21, how many of the tickets sold were for adults?
Weighted Average Ratio Line approach
What is the lesson/hidden theme for this question?
If y is greater than 110 percent of x, is y greater than 75 ? Is (2) sufficient?
(2) y - x =10
1) Distinguish btw “is greater than 110% of x” & “is 110% greater than x”
2) A better rephrase approach: Don’t plug in the variables into static equation
-1.1x -x = 10 -> x =100 (Yes) BUT
- 1.5x - x = 10 -> X = 20 (No: y is not greater than 75)
3) Always Extreme test cases for two unkown variables
Key Lesson
Was the number of books sold at Bookstore X last week greater than the number of books sold at Bookstore Y last week?
(1) Last week, more than 1,000 books were sold at Bookstore X on Saturday and fewer than 1,000 books were sold at Bookstore Y on Saturday
(2) Last week, less than 20 percent of the books sold at Bookstore X were sold on Saturday and more than 20 percent of the books sold at Bookstore Y were sold on Saturday
1) More units comprise of a smaller portion of a total indicate that the total (denominator) must be large
2) Fewer units comprise of a larger portion indicate total units must be small
What does this really test?
Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 20% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?
A. $15,840
B. $17,820
C. $18,000
D. $19,800
E. $21,780
**The Law of Large Number Estimation: **
Since 100 seats are comparatively small to 10,000 seats, we can take 20% of full 10,000, we then have:
- 2000x $1 + 8000x$2 = $18,000
- Now take into the account of 100 seats, our answer must be less than but close to $18,000
What the best approach for this problem?
During the four years that Mrs. Lopez owned her car, she found that her total car expenses were $18,000. Fuel and maintenance costs accounted for 1/3 of the total and depreciation accounted for 3/5 of the remainder. The cost of insurance was 3 times the cost of financing, and together these two costs accounted for 1/5 of the total. If the only other expenses were taxes and license fees, then the cost of financing was how much more or less than the cost of taxes and license fees?
1) Best to avoid computation for the concrete value from every fraction/ratio step
2) Combine/Subtract/ Multiply multitudes fractions so they can cancel out for the final fraction.