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A worker carries jugs of liquid soap from a production line to a packing area, carrying 4 jugs per trip. If the jugs are packed into cartons that hold 7 jugs each, how many jugs are needed to fill the last partially filled carton after the worker has made 17 trips? A. 1 B. 2 C. 4 D. 5 E. 6

After 17 trips, the worker has carried 17 x 4 = 68 jugs.From those 68 jugs, 68/7 = 9 cartons have been filled, with 5 extra jugs remaining. So, the worker needs one more trip to carry 2 more jugs to fill the partially filled carton with those 2 jugs. Answer: B

In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of r^2 + s^2? (1) The circle has radius 2 (2) The point (2‾√, −2‾√)(2, −2) lies on the circle

D If the circle is centered at the origin (0, 0), then the equation simplifies to: x^2+y^2=r^2.

If x and y are positive, is 4x > 3y? (1) x > y - x (2) x/y < 1

Question: is 4x>3yOr is (x/y)>(3/4)? Stmt1 -- Given x>y-xHence, 2x>y or (x/y)>(1/2) --INSUFF Stmt 2 -- Given (x/y)<1 --INSUFF Together 1/2<x/y<1 INSUFF answer would be E

In a certain fraction, the denominator is 16 greater than the numerator. If the fraction is equivalent to 80 percent, what is the denominator of the fraction?A. 32B. 64C. 72D. 80E. 120

xx+16xx+16 = 8010080100 = 4/5Cross Multiply to Get:4x + 64 = 5x ---> x = 64Denominator = x + 16 = 64 + 16 = 80Answer: D

A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount? A. 20% B. 40% C. 50% D. 60% E. 75%

(1+M/100)*(1-D/100)=(1+P/100) D=20, P=20 (1+M/100)*4/5=6/5 m=1.5 50%

0.0015*10^m/0.03*10^k=5*10^7, then m - k =

0.0015∗10m0.03∗10k=5∗1070.0015∗10m0.03∗10k=5∗107;15∗10−4∗10m3∗10−2∗10k=5∗10715∗10−4∗10m3∗10−2∗10k=5∗107;5∗10m−410k−2=5∗1075∗10m−410k−2=5∗107;10(m−4)−(k−2)=10710(m−4)−(k−2)=107;(m−4)−(k−2)=7(m−4)−(k−2)=7;m−k=9m−k=9.Answer: A.

A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes? A. 1/12 B. 1/6 C. 1/5 D. 1/3 E. ½

2*1*2*1/4*3*2*1= 1/6 B

The price of gasoline at a service station increased from $1.65 per gallon last week to $1.82 per gallon this week. Sally paid $26.40 for gasoline last week at the station. How much more will Sally pay this week at the station for the same amount of gasoline? A. $1.70 B. $2.55 C. $2.64 D. $2.72 E. $2.90

Answer is D. Gasoline = 26.40/1.65 = 16 galloons Price difference = (1.82-1.65) = $0.17 per gallon Price difference for 16 gallons = (0.17*16) = 2.72

Each of the 4 students in a certain class read several books during the past month. What was the standard deviation of the numbers of books read by the 4 students during the past month?(1) The range of the number of books read by the 4 students during the past month was 0.(2) One of the 4 students read 5 books during the past month.

CONCEPT: Standard deviation depends on the following inputs1) The number of terms in the set. (Which is given in this question as 4)2) The gaps between the terms when arranged in increasing orderQuestion: FInd the standard deviation of number of books read by the 4 students?Statement 1: The range of the number of books read by the 4 students during the past month was 0Range = Highest - Lowest = 0 (Given)i.e Highest = Lowesti.e. Highest number of books read by any student = Lowest number of books read by any studentSince the gaps between the terms is ZERO, therefore Standard Deviation of the set = 0SUFFICIENTStatement 2:One of the 4 students read 5 books during the past month.The statemebnt doesn't give any information about the gaps between the terms. The value of one term in set can NOT lead us to any conclusion about the standard deviation of teh set henceNOT SUFFICIENTAnswer: Option A

In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females? A. 3/5 B. 2/3 C. 3/4 D. 4/5 E. 5/6

D 0.5m + 0.4f = 0.42(m+f) 0.5m + 0.4f = 0.42m + 0.42f 0.08m = 0.02f4m = f This means that if m = 1 (or 1 male) then f = 4. so there are 4 f's for every 1 m. or 4/5.

If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2k2k is a factor of n? A. 10 B. 12 C. 15 D. 18 E. 20

D. 18 n=20! 20/2+20/4+20/8+20/16=18

If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits? A) 2/11 B) 1/3 C) 41/99 D) 2/3 E) 23/37

E After reading of the problem I pick E by intuition: I thought that:1. nominators do not influence on length of sequence. (for right fraction)2.the largest prime in denominator lead to the largest sequence).

Does the line with equation ax+by = c, where a,b and c are real constants, cross the x-axis?(1) b not equal to 0(2) ab>0

Hi,ONLY line that will not cross x axis is the line parallel to x axis...THe equation of line parallel to x axis is y=b..so if ax+by = c has to be parallel to x- axis, a should be 0.. lets see the statements.. (1) b not equal to 0This tells us that the line is not parallel to y-axisInsuff(2) ab>0this tells us that neither of a or b is 0..so the line crosses the x-axisSuffB

In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4/5. After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?(A) 100(B) 300(C) 400(D) 1,000(E) 2,500

Old ratio: republicansdemocrats=3x5xrepublicansdemocrats=3x5x.New ratio: 3x+6005x+500=453x+6005x+500=45 --> x=200x=200.Current difference is (5x+500)−(3x+600)=2x−100=300(5x+500)−(3x+600)=2x−100=300.Answer: B.

If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 26, 19, 33 and 35 ? A) 33B) 28C) 27D) 24E) 23

The median of {19, 22, 24, 26, 30, 33, 35, 42} is 28.The numbers less than the median are {19, 22, 24, 26}. The median of this list is 23.Answer: E.

Departments A, B, and C have 10 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible? A. 19,000B. 40,000C. 100,000D. 190,000E. 400,000

The number of ways to select 1 employee from each of departments A, B, and C and 2 employees from department D is10C1 x 10C1 x 10C1 x 20C2 = 10 x 10 x 10 x (20 x 19)/2 = 10 x 10 x 10 x 10 x 19 = 190,000Answer: D

If the volume of a box is 1,463,000 cubic millimeters, what is the volume of the box in cubic meters? (1 millimeter = 0.001 meter) A) 14.63B) 1.463C) 0.1463D) 0.01463E) 0.001463

The trick here maybe to just drop the ugly numbers and transform 1,463,000 cubic mm into 1,000,000 cubic mm just to understand the logic behind.If volume of a cube equals 106106 cubic mm and the formula is side * side * side, we can infer that the side measures 102102 mm, or 100 mm.And 100 mm = 0.1 mt. Therefore the side measures 0.1 mt.In volume, this would be represented as 0.1 mt * 0.1 mt * 0.1 mt, which yields 0.001 cubic mt.The answer choice should have 2 zeroes between the point and the first decimal different to zero.

Solution X is 15% salt and solution Y is 50% salt. If the two solutions are combined to form 7 gallons of a 30% solution, how many gallons of solution X must be used? (A) 2 (B) 2.5 (C) 3 (D) 4 (E) 4.2

We can let the number of gallons of solution in solution X = x and the number of gallons of solution in solution Y = y. Thus:0.15x + 0.5y = 0.3(x + y)15x + 50y = 30x + 30y20y = 15x4y = 3xWe also know that x + y = 7, or y = 7 - x, and thus:4(7 - x) = 3x28 - 4x = 3x28 = 7xx = 4Answer: D

A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly? A. 3 B. 4 C. 15 D. 18 E. 20

We have that 3.5*x-1*y=63.5, where x and y are the # of correct and incorrect answers. Notice that x must be odd number in order the sum (63.5) to have 5 as the tenths digit (if x=even then 3.5*x-1*y=integer). So, y=22-x=22-odd=odd. There are only two odd choices 3 and 15. y cannot be 15 since in this case the total score would be less than 63.5, so y=3.Answer: A.

A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x? (1) x = 3y/4 (2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

a+b=60000 a*x*year b*x*year ax+by=4080 1.x=3y/4 ins no info on a or b 2. a:b= 3:2 ins no info on x or y 3. suf, info on x,y,a,b C

In a sequence 1, 2, 4, 8, 16, 32, ... each term after the first is twice the previous term. What is the sum of the 16th, 17th and 18th terms in the sequence ? A. 2^18 B. 3(2^17) C. 7(2^16) D. 3(2^16) E. 7(2^15)

an= a1*r^n-1 2^15,2^16,2^17 notice how 2^1+2^2+2^3=7*2^1 so 2^15+2^16+2&17= 7*2^15

For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 100 terms?(a) 1(b) 0(c) 25(d) 99/100(e) 100/101

notice the pattern... 1-1/101=100/101