GRE Math

A class consists of 24 students. Which of the following CANNOT be the ratio of the number of girls to the number of boys?

(B) 3:5 --> 24 is divisible by 3+5 = 8 (9 girls and 15 boys) (C) 1:1 --> 24 is divisible by 1+1= 2 (12 girls and 12 boys) (D) 4:3 --> 24 is NOT divisible by 4+3 = 7 (E) 7:5 --> 24 is divisible by 7+5 = 12 (14 girls and 10 boys) Answer: (D)

Which of the following inequalities is equivalent to 12 - 3x < -18

-3<-30 The symbol then gets reverse x > 10

If 10^a x 10^b x 10^c = 1,000,000, and a, b, and c are different positive integers, then 10^a + 10^b + 10^c =

10^a * 10^b * 10^c=1,000,000 10^a+b+c=10⁶ 10^a+10^b+10^c=10¹+10²+10³ =10+100+1000 =1110

If 16x = 8, what is the value of x?

16^X=8→(2^4)^x=2^3→2^4X 4/3=.75 ​​

Which of the following is a root of the equation 2x^2 - 20x = 48?

2x^2 - 20x - 48 = 0 We can factor out a 2, which leaves us with 2(x^2 - 10x - 24) = 0. Now we need to factor the part in parentheses the way we would any quadratic equation, giving us: 2(x - 12)(x + 2) = 0 Now we can conclude that either x - 12 = 0, or x + 2 = 0. This leaves us with the following when we solve: x = 12 x = -2 12 is one of our answer choices, so we choose (E).

Sue planted 4 times as many apple seeds as she planted orange seeds. 15 percent of the apple seeds grew into trees, and 10 percent of the orange seeds grew into trees. If a total of 420 apple trees and orange trees grew from the seeds, how many orange seeds did Sue plant? a. 540 b. 600 c. 660 d. 720 e. 760

600 Set A = number of apple seeds, and O = number of orange seeds. We know: A = 4*O number of apple trees = 0.15*A number of orange trees = 0.1*O 0.15*A + 0.1*O = 420 --> 15*A + 10*O = 42000 Substitute A = 4*O: 15*(4*O) + 10*0 = 42000 60*O + 10*O = 42000 70*O = 42000 O = 600

From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls? a. 16 b. 24 c. 60 d. 120 e. 240

Boys: A,B,C,D,E Girls: F,G,H,I ₅C₂/select 2 boys ₄C₂/select 2 girls Formula: nCr= (n/r)=n!/r!(n-r)! ₅C₂ X ₄C₂=5!/2!3! X 4!/2!2! =10X6 = 60

In 2006, the ratio of the number of widgets sold by Company C, Company E (not shown) and Company D was 5 to 8 to 2, respectively. How many widgets did Company E sell in 2006?

C:E:D=5:8:2 E.D=8:2 E:D=4:1 Company E/Company D: x/1.2=4/1 x= (1.2)(4)=4.8

While driving from A-ville to B-town, Harriet drove at a constant speed of 115 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 135 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town? a. 138 b. 148 c. 150 d.162 e. 168

D = 115 km/hr * T D = 135 km/hr * (5 - T) Since the distances are equal, we can set those two equations equal to each other and work from there: 115T = 135(5 - T) 115T = 675 - 135T 250T = 675 T = 675/250 T = 27/10 hours Since the problem wants the answer in minutes, we need to convert: 27/10 hours * 60 minutes / hour = 27 * 6 minutes = 162 minutes

If x > 21/40, then x could be which of the following? Indicate all possible values of x.

First of all, 1/2 is not a valid answer, because it has to be bigger than 1/2 plus anything positive. 11/20=1/2+1/20>1/2+1/40 because 1/20>1/40

In a group of 100 adults, 75 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?

For this question, it's very convenient to convert the percent to a fraction. We know that 25% as a fraction is 3/4 We don't know how many women there are: let's say that number is W. We know that 3/4 W are left handed, so this must mean that 1/4 W are right handed. 1/4W =12 (12*4=48) W=48 100-48=52 ​If there are 48 women, then there must be 100 - 48 = 52 men,

If a pie graph were drawn to scale to represent the animal distribution at the zoo, what would be the measure (in degrees) of the central angle of the sector representing bobcats? Animal distribution at the zoo animal Percent Lions 32% Leopards 16% Ocelots 20% Tigers 8% Bobcats 24%

In the first ratio, the angle of the slice, what we are trying to find, is the "part" and the angle of the whole circle, 360°, is the "whole." Call the angle we are seeking A. In the second, the percentage for bobcats, 24%, is the "part" and 100% is the "whole." Here are the two Part-to-Whole ratios set equal to each other because they're proportional. A/360=24/100 Multiply both sides by 360 A=360*24/100 we get 86.4 degrees ​​

How many multiples of 5 are there between 81 and 358? a. 54 b. 55 c. 56 d. 57 e. 58

Now, let's go ahead and write 85 as a multiple of 5. 85 = 5 * 17 What are the next multiples of 5? 90 = 5 * 18 95 = 5 * 19 100 = 5 * 20 And so-on-and-so-forth until we find the multiple of 5 that is closest to 358. That would be 355. :) Now, let's go ahead and write 355 as a multiple of 5. 355 = 5 * 71 Let's say x = 17 and y = 71 and plug them into the equation. y - x + 1 = 71 - 17 + 1 = 55 There are 55 multiples of 5 between 81 and 358.

Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

Pump A: 1/3 Pump B: 1/2 1/3+1/2=5/6 6/5*60=72

A certain taxi charges $0.85 for the first ½ mile and $0.25 for every ½ mile after that. The total cost of a trip was $8.85 Column A Column B The trip's distance in miles 16

Text Explanation $0.25 for 0.5 miles = $0.50 for 1 mile Cost for a 16 mile trip: $0.85 + $0.5*15.5 = $8.60 This is less than $8.85, which means that the trip must have been longer than 16 miles. So Column A is greater. Answer: (A)

If (2^-n/3)(3^-n/2)=1/36 what is the value of n?

Text Explanation If (2^-n/3)(3^-n/2)=1/36 Formula a^n b^n=(ab)^n 6^-n/6=1/36 6^-n/6^1=6^2 6^-n-1=6^-2 -n-1=-2 -n=-1 n=1

In triangle FGH, the base has a length of FH = 126.3, and the altitude from G to FH is constructed and has a length of h. What could be the value of h if we know that the area of the triangle is an integer?

The base is 126.3, which could be thought of as an improper fraction, 1263/10 **This has a 10 in the denominator that will have to be canceled in order to have an integer product. Recall that, for a triangle A=1/2 bh in order to get an integer area, we must cancel both of these factors in the denominator. We need to cancel 10*2 = 20, so the height must be a multiple of 20. The correct answers are the multiples of 20: 40, 80, and 100.

1/3 + 2/5 = N, and, in lowest terms, N = p/q, where p and q are positive integers. Column A Column B q 10

The quantity in Column A is greater Basically, this question is asking us to add two fractions. Of course, we add fractions by finding a common denominator. A reminder: of course, we are allowed to multiply by fractions like 3/3 and 5/5 because those fractions equal 1, and multiplying by 1 doesn't change the value of a number. Multiplying by a fraction equal to one is a way to change the appearance of a number without changing its actual mathematical value. 1/3+2/5=1/3*5/5+2/5*3/3=5/15+6/15= 11/15 The numbers 11 and 15 have no common factors greater than 1, so that final fraction is already in lowest terms. This means q = 15, which is greater than 10.

Column A Column B Sum of integers from 1 to 40 inclusive 800

The sum of a series of integers is [n(n+1)] / 2: 40(40+1)/2 -divide 40/2 20(41)=820

A bag contains x blue chips and y red chips. If the probability of selecting a red chip at random is 3/7, then x/y =

Thus we know there are 3 red chips, and 7 chips in total. Therefore there are 4 blue chips. x=blue chips =4 y=red chips= 3 x/y=4/3 ​​

A retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 80 percent greater than the wholesale price. If the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent?

W = wholesale price R = original retail price. The multiplier for an 80% increase, or 80% higher, is (1 + 0.80) = 1.8. We are told that, originally, R = (1.8)W. The discounted price is 30% lower than R. The multiplier for a 30% decrease, or 30% lower, is (1 - 0.30) = 0.70. Thus, discounted price = (0.7)R = (0.7)(1.8)W = (1.26)W The number 1.26 is the multiplier for a 26% increase, or 26% higher. This tells us that the discounted price is 26% higher than the wholesale price.

If Michael can shovel all the snow off a standard driveway in 12 minutes, and Eamon can shovel all the snow off a standard driveway in 36 minutes, then working together, how many minutes would it take for them both to shovel all the snow off a standard driveway?

We can't add or subtract times to complete the driveway M=1/12 E=1/36 1/12+1/36 (find common denominator) 1/12*3= 3/36 3/36+1/36=4/36 =1/9 9 min. is the answer

Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent?

When dealing with percents when we're not given specific numbers, 100 is a good number to use. If we set the original price at 100, increasing it by 25% makes it 125. Increasing 125 by 25% adds 31.25, making the final number 156.25. That's an increase of 56.25% from the original. The correct answer is (E)

An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee? a. 10 b. 12 c. 15 d. 24 e. 30

ere are 3 seats on the committee. We know that 1 seat must be filled by the male employee. That leaves us with 2 seats to deal with. We have 5 female employees and 2 seats to fill. Order doesn't matter here — this is a combinations problem. 5C2 = 10.

For which values of x is 3x/x^2 + 2x - 1/5 < 0 Indicate all possible values of x.

move 1/5 to the other side 3x/x^2 +2x < 1/5 now cross multiply 15x < X^2 + 2x now subtract 2x on both side 13x < X^2 Therefore, any number bigger than 13 is the answer...14, 15 & 16