Arithmetic (FDPR)

Question 1

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Translate percent change from English to Math:
- 100% greater than original
- 45% less than original
- 130% of the original
- 75% of the original

Answer 1

• 200% of the original or 2x original
• 55% of the original
• 30% greater than the original
• 25% less than the original

Question 2

What are the relative values on GMAT?

Answer 2

fractions, decimals, percents or ratios (proportion)

Question 3

What are the concrete values on GMAT?

Answer 3

specific number of tickets sold, liters of water, etc

Question 4

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

Answer 4

F
the fraction increase as it gets closer to 1

Question 5

How does a faction value (that is greater than 1) change when you add the same number to top and bottom?

Answer 5

the result is smaller (getting closer to 1)
E.g: 3/2 > 4/3

Question 6

List all strategies that you can approach for this problem

Which fraction is greater: 7/9 or 4/5?

Answer 6

1) The Double-Cross: 35/45 < 36/45
2) Translate into percentage: 77.7% < 80%

Question 7

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?

Answer 7

Percentage Benchmarks:
Amount of Reduction = 10% + 1% + 1% = 70 + 7 + 7 = 84
Final amount = 700 - 84 = 700 - 80 - 4 = $616

Question 8

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

Answer 8

1) Look at the answer choices, then decide to do estimation or precise (obvious round multiplication)
2) since 0.65x0.4 = 0.26 (decent nice) we can find the ans 0.26x300=78
3) Est tech:
60% of 300 = 180 & 40% of 180= 72 so ans must be closed to A)

Question 9

When can you really use the estimation strategy?

Answer 9

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

Question 10

Trick to convert fraction into percentage, for i.e: 17/25, 4/5, 3/20 or 7/32

Answer 10

• Nice denominator, make it 100
• Not nice denominator, estimation with multiple
  i.e: 7/32 = 21/96 ~ lil bit more than 21% (since 96<100)

Question 11

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?

Answer 11

1) Benchmark Computation of percentage or ratio
2) Estimation

Question 12

Simplify 60% of 45.35

Answer 12

3/5 x (45 +0.35) = 9x3 + 0.7x 3 = 27 +0.21= 27.21

Question 13

How would only quarters and dimes add up to $2.50?

Answer 13

10 quarters, 0 dimes
8 quarters, 5 dimes
6 quarters, 10 dimes
etc.

Question 14

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

Answer 14

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

Question 15

How do you solve the relative value of two departments within a company, when there are increase/decrease in revenue, profit, cost?

Answer 15

Weighted Average: Push-Pull in the increase/decrease between two apartments

Question 16

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?

Answer 16

Weighted Average

Question 17

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?

Answer 17

Ratio Difference and Multiplier X

Question 18

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?

Answer 18

Benchmark Estimation: 10% of $690 is 69 but since $67<69 so the discount must be smaller than 10%

Question 19

Mel saved $10 by purchasing a sweater at a 15 percent discount. What does it mean for discount amount in term of revenue?

Answer 19

$10 represents the discount amount of 15% off the original price of the sweater: $10= Original - (85/100) x Original = (15/100) x Original

Question 20

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.

Answer 20

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

Question 21

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?

Answer 21

Weighted Average

Question 22

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?

Answer 22

Weighted Average Ratio Line approach

Question 23

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

Answer 23

1) Distinguish btw “is greater than 110% of x” & “is 110% greater than x”
2) You can’t just use the base case for algebra subtitution: 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.

Question 24

T or F: The percentage difference between two percentage values (i.e: 50% & 65%) is equal to the ratio of value differences to the original number

Answer 24

True

Question 25

What common sense

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

Answer 25

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

Question 26

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

Answer 26

Estimation: Since 100 seats are comparatively small to 10,000 seats, we can take 20% of full 10,000 - for the purpose of easy round calculation - 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

Question 27

What the best approach for high value total?

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?

Answer 27

1) Best to avoid computation for true value from every fraction/ratio step
2) Get the required fraction then calculate the true final value

Question 28

How do these two statement differ? (1) “Y is greater than 110 percent of x” vs (2) “Y is 110% greater than X”

Answer 28

(1) y > 1.1x (so y can be 1.15x, 1.2, 1.5x..)
(2) y = 1.1x

Question 29

For the total # of tickets X, the revenue for adult tickets (cost A/tix) and children tickets (cost B/tix) is Y, what is the range of possibility for cost A and B, given that cost A >cost B?

Answer 29

The average cost will fall in between cost A & B - i.e: B < Y/X < A

Question 30

Key lession for this problem

A certain electronic component is sold in boxes of 54 for $16.20 and in boxes of 27 for $13.20. A customer who needed only 54 components for a project had to buy 2 boxes of 27 because boxes of 54 were unavailable . Approximately how much more did the customer pay for each component due to the unavailability of the larger boxes?
(A) $0.33 (B) $0.19
(C) $0.11(D) $0.06 (E) $0.03

Answer 30

Accurate Estimation: Price diffrence for 54 units is $10 -> Pay difference/Unit = $10/54 ~ 1/5 = 0.2 so the value must be around and specifically below 0.2 (since 54 > 50)

Question 31

Translate to math expression

After paying a 10 percent tax on all income over $3,000, a person had a net income of $12,000. What was the income before taxes?

Answer 31

$12,000 = $3,000 + (X-3000)x0.9

Question 32

Set up algebraic expression & try intuitively method to solve

450 is what percent greater than 15 ?

Answer 32

1) 450 = 15 + 15X/100 -> X = 100x435/15 = 2900%
2) 450 is equal to 30 times 15 or 29 times greater than 15

Question 33

What’s your strategy?

Bottle R contains 250 capsules and costs $6.25. Bottle T contains 130 capsules and costs $2.99. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?
(A) $0.25 (B) $0.12 (C) $0.05 (D) $0.03 (E) $0.002

Answer 33

1) Look at the answer choice for the widespread range to decide estimation or precise cal
2) Make decimals into a nice number for easy calculation: $6.25 = 625 cents
3) Notice 130 caps costs $3, so $6 or 600 cents will cost around 260 caps -> Bottle R & T difference is 25cents/250 capsules ~ 0.1 cents or Answ E)

Question 34

W/o precise calculation, estimate w/ the base rate

On July 1, 1982, Ms. Fox deposited $10,000 in a new account at the annual interest rate of 12 percent compounded monthly. If no additional deposits or withdrawals were made and if interest was credited on the last day of each month, what was the amount of money in the account on September 1, 1982?
(A) $10,200 (B) $10,201

Answer 34

1) Assuming 12% rate compound annually, we will have $1200/year or $100/month. Hence, 2 months will have $10,200
2) However, because the rate compound monthly, the precise number must be greater than $10,200