Quant: FDP (01)

Last year, if Arturo spent a total of $12,000 on his mortgage payments, real estate taxes, and home insurance, how much did he spend on his real estate taxes? 1. Last year, the total amount that Arturo spent on his real estate taxes and home insurance was 33¹/₃ percent of the amount that he spent on his mortgage payments. 2. Last year, the amount that Arturo spent on his real estate taxes was 20 percent of the total amount he spent on his mortgage payments and home insurance OG360

B. 2) is sufficient. For #1: X + (M/₃-X) + M = 12,000, will only find the mortgage purchase but wouldn't know the ratio for taxes For #2: MAKE MORTGAGE & INSURANCE AS ONE VARIABLE = y Tax = 0.2y 0.2y + y = $12.000 y = $10,000 tax = 0.2($10,000) = $2,000

Bag /#marbles /% marbles are blue Bag P /37 marbles /10.8% blue Bag Q /x marbles /66.7% blue Bag R /32 marbles /50% blue If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q? (OG134)

1/3 total amount is blue, 1/3(69+x) = 20+2/3x x = 9

If n = (33)⁴³ + (43)³³, what is the units digit of n? (OG200)

10. Units digit of n^1-n^8 patterned 3, 9, 7, 1, So if (33)⁴³ + (43)³³ = 43/4 = 10+3, 3rd = 7 33/4 = 8+1, 1st = 3, 7+3 = 10

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?(OG219)

3. (10s+t)-(10t+s)=27, s-t = 3,

(0.0036)(2.8)/ (0.04)(0.1)(0.003) = ? (OG135)

840. Should transform to exponents to make it easier = (1008*10⁵)/(12*10⁴)

If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths digit in the decimal 0.02Y, where X and Y are nonzero digits, which of the following is closest to the greatest possible value of 0.1X/0.02Y?(OG139)

9. X = 9, Y = 1 if want the GREATEST

M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true? A. 1/3 < M < 1/2 B. 1/5 < M < 1/3 C. 1/7 < M < 1/5 D. 1/9 < M < 1/7 E. 1/12 < M < 1/9 OG131

A

Company X has 2 revenue streams. Consumer stream increased k% from last year, whereas machine stream decreased by k% from last year. Did Company X's overall revenue increase or decrease? 1. Last year, consumer stream generated more revenue than machine stream 2. k = 8 FDP#5

A. 1) is sufficient. Last year: Total revenue = c + m Current yr: c↑ k%, m↓ k% Same % change, just need to know which is bigger. 1) Confirms that c > m, therefore an overall increase in revenue is achieved

If n = (33)⁴³ + (43)³³, what is the units digit of n ? A. 0 B. 2 C. 4 D. 6 E. 8 OG200

A. 200 n¹, n², n³, n⁴, n⁵, n⁶, n⁷, and n⁸ = 3, 9, 7, 1, 3, 9, 7, and 1 The CYCLE is in 4 digits, So 33/4 = (8x4) + 1 →1st = 3 43/4 = (10x4) = 3 →3rd = 7 3+7 = 10

After first CD purchased, preferred customers paid $3.99 for each additional CD purchased. If the customer purchased a total of 6 compact discs and paid $15.95 for the first CD, then the dollar amount that the customer paid for the 6 CDs is equivalent to which of the following? A. 5(4.00) + 15.90 B. 5(4.00) + 19.95 C. 5(4.00 - 0.01) + 15.90 D. 5(4.00 - 0.05) + 15.95 OG D01

A. 5(4.00) + 15.90 If $4 used instead of $3.99, excess of 5(0.01) = $0.05, compensated by $15.95-0.05 = 15.90

If n is a positive integer, what is the tens digit of n ? 1) The hundreds digit of 10n is 6. 2) The tens digit of n + 1 is 7. OG403

A. Statement 1 alone is sufficient 1) If n10, each digit moves up by 1. QUESTION IS ASKING FOR TENS DIGIT! Example, n = 352, n10 = 3520, hundreds place is 5 when n10, so tens would be 5 when n normal. 2) n + 1 = 7, can be 70 or 69 - INSUFFICIENT

The harvest yield from a certain apple orchard was 350 bushels of apples. If x of the trees in the orchard each yielded 10 bushels of apples, what fraction of the harvest yield was from these x trees? A. x/35 B. 1-(x/35) C. 10x D. 35 − x E. 350 − 10x OG61

A. x/35 Since each of the x trees yielded 10 bushels, the total number of bushels yielded by these trees was 10x. Since the yield of the entire orchard was 350 bushels, 10x/350 =x/35 was the fraction of the total yield from these x trees.

OG163

E

Which of the following fractions is closest to 1/2? A. 4/7 B. 5/9 C. 6/11 D. 7/13 E. 9/16 OG82

D Find the distance b/w each fraction and 1/2 A. 4/7-1/2 = 1/14 B. 5/9 - 1/2 = 1/18 C. 6/11 - 1/2 = 1/22 D. 7/13 - 1/2 = 1/26 E. 9/16 - 1/2 = 1/16 OR Alternatively, asking which fraction is closest to 1/2 is equivalent to asking which of the fractions, when doubled, is closest to 1. The fractions after doubling are 8/7, 10/9, 12/11, 14/13, 18/16=9/8 Each of these fractions can be expressed as 1 + 1/n for some integer n. Of these fractions, the one closest to 1 is the one for which 1/n is least, or in other words, the one for which n is greatest. That fraction is 14/13

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between A. 290/12.5 & 290/11.5 B. 295/12 & 285/11.5 C. 285/12 & 295/11.5 D. 285/12.5 & 295/11.5 E. 295/12.5 & 285/11.5 (OG192)

D. min = min miles/max gal, 285/12.5 max = max miles/min gal, 295/11.5 BETWEEN not EXACT number of miles per gallon.

Each year for 4 years, a farmer increased the number of trees in a certain orchard by ¼ of the number of trees in the orchard the preceding year. If all of the trees thrived and there were 6,250 trees in the orchard at the end of the 4-year period, how many trees were in the orchard at the beginning of the 4-year period? A. 1,250 B. 1,563 C. 2,250 D. 2,560 E. 2,752 OG163

D. 2,560 1st year = 1.25n 2nd yr = 1.25(1.25n) 3rd yr = 1.25(1.25²n) 4th yr = 1.25(1.25³n) 6250 = 1.25⁴n 6250 = (⁵/₄)⁴n 6250 = ⁶²⁵/₂₅₆n ¹/₆₂₅(6250) = ¹/₆₂₅(⁶²⁵/₂₅₆n) 10 = ¹/₂₅₆n n = 2560

Will operation yield an increase, decrease/stay the same: Multiply a positive, proper fraction by 3/8

Decrease: Multiplying a positive number by a proper fraction decreases the number.

In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received? A. 0.06N + 3200 B. 0.01N + 7200 C. 0.4N + 7200 D. 0.1N + 8000 E. 0.06N + 8000 OG94

E. 0.06N + 8000 Draw a tree to make it clearer 0.1(0.6N) for the political party voters

Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich? A. (m+4)/m(m-4) B. (2m-4)/m(m-4) C. (4m-4)/m(m-4) D. (4m-8)/m(m-4) E. (4m-12)/m(m-4) OG167

E. 3 sandwiches = 1/m 4th = 1/m-4 Carol = 3/m + 1/(m-4) Carol = 3(m-4)+m/m(m-4) Carol = 4m-12/m(m-4)

if a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/4 of its revenue in November, then the store's revenue in December was how many the average of its revenue in November and January? A. 1/4 B. 1/2 C. 2/3 D. 2 E. 4 OGD08

E. 4 n = 2/5d, j = 1/4n j = 1/4(2/5d) = 1/10d Average = sum of values/number of values Average = (2/5d + 1/10d)/2 Average = 1/4d 4(average) = d Store revenue in Dec = 4 times average store revenue in Nov & Jan

Will operation yield an increase, decrease/stay the same: Add 1 to the numerator of a positive, proper fraction and subtract 1 from its denominator. (FDP p 55)

Increase: As the numerator of a positive, proper fraction increases, the value of the fraction increases. As the denominator of a positive, proper fraction decreases, the value of the fraction also increases. Both actions will work to increase the value of the fraction.

Will operation yield an increase, decrease/stay the same: Multiply the numerator of a positive, proper fraction by 3/2 (FDP p 55)

Increase: Multiplying the numerator of a positive fraction increases the numerator. As the numerator of a positive, proper fraction increases, its value increases.

If there are fewer than 8 zeros between the decimal point and the first nonzero digit in the decimal expansion of (t/1000)^4, which of the following numbers could be the value of t? 3, 5, 9, 5 & 9, or none? (OG147)

None. 8> zeros b/w decimal & nonzero digit, (t/1000)⁴ = t⁴*10¹². Didn't catch that 9^4 is only 4 = still 8 zeros. Need 4<

If d = (1)/(2³ * 5⁷) is expressed as a terminating decimal, how many nonzero digits will d have? (OG203)

Two non-zero digits. 1/(2³)*(5⁷) = (1/2×5)³ x (1/5)⁴ 0.00001~ x 0.2⁴ --> 16 r non-0 digits

Are √3/2 and 2√3/3 reciprocal? (FDP p 55)

YES, test by multiplying = 1

OG220

D

List T consists of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E − S? I. -16 II. 6 III. 10 A. I only B. I & II only C. I & III only D. II, III only E. All (OG225)

B. I & II only (-16 & 6) Even round up, odd round down. Find difference when round up or down 1.2 = 0.8 x 10 = 8 0.1 = 0.1 x 20 = -2 1.4 = 0.6 x 10 = 6 0.3 = 0.3 x 20 = -6 1.6 = 0.4 x 10 = 4 0.5 = 0.5 x 20 = -10 1.8 = 0.2 x 10 = 2 0.7 = 0.7 x 20 = -14, 0.9 = -18 2-18 = -16, 8-2 = 6, Cant result to 10

If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r = A. 1/3 B. 4/3 C. 3 D. 4 E. 12 OG72

C

At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket? A. $60 B. $80 C. $90 D. $120 OG30

C. $90 2/30 = $6 30/30 = $90