GMAT Math Problems
factor x^2 + 5x -24
(x+8)(x-3)
simplify (x-y)/(y-x)
-1
If (2/3)^n = (3/2)^2, what is n?
-2
A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?
.1x + .15(300-x) = 38 .1x + 45 - .15x = 38 -.05x = -7 x = 140
Meredith jogged to the top of a steep hill at an average pace of 6 miles per hour. She took the same trail back down. To her relief, the descent was much faster; her average speed rose to 14 miles per hour. If the entire run took Meredith exactly one hour to complete and she did not make any stops, how many miles, approximately, is the trail one way?
1 = D/14 + D/6 1 = 6D+14D/14*6 1*14*6 = 20D D = 14*6/20 D = 4.2 one way
To get a 30% decrease, what is the multiplier?
1-.3 = 0.7 * X
1/(1+(1/2+1/3)
1/ 1+ 1/7/3 = 1/1+3/7 = 1/10/7 = 7/10
1/(2-.25)
1/(8/4 - ¼) = 1/(7/4) = 4/7
A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
1/2 chance the combination where the sum can be odd is like this: odd, odd. odd = 1/2 * 1/2 * 1/2 = 1/8 odd, even, even = 1/8 even, odd, even = 1/8 even, even, odd = 1/8
Perry can paint a standard room in 3 hours, Maria can paint a standard room in 2 hours, and Lorna can paint a standard room in 2 hours 30 minutes. Perry, Maria, and Lorna have decided that, to speed up the work, 2 of them will paint a standard room together. What is the fastest time and longest time a pair of 2 can do?
1/2.5 is the same as 2/5 Fastest: 1/2x + 2/5x = 1 9/10x = 10/9(60) = 1 hour and 7 minutes Longest: 1/3 + 2/5x = 15/11(60) = 1 hour and 22 minutes
3^(-2)
1/3^2 = 1/9
A theater company has 10 scripts for fall, winter, and spring. How many possible seasons are there?
10 * 9 * 8 = 720
Lady Edith bought several necklaces at the jewelry store, and each necklace cost 16 dollars. Lady Mary also purchased several necklaces, at a cost of $20 each. If the ratio of the number of necklaces Lady Edith purchased to the number of necklaces Lady Mary purchased is 3 to 2, what is the average cost of the necklaces purchased by Lady Edith and Lady Mary?
16(3) + 20(2) = 88 88/5 = 17.6
is an integer. What is the smallest value of y? (1) is negative. (2) |y| < 10
2 is sufficient because you know that -9 is the lowest value of y. #1 has negative infinity choices
2^18(5^m) = 20^n
20^n = 2^2n(5^m) Therefore 18 = 2n and m = n
0.0027 x 10^x/0.09 x 10^y = 3x10^8 what is the value of y less than x
27x10^x-4/9x10^y-2 = 3x10^8 3x10^x-4/10^y-2 = 3x10^8 10^x-4/10^y-2 = 10^8 when you divide exponents with the same base, you can subtract the exponents x-4 - (y-2) = 8 x-4 -y +2 = 8 x- y = 10
(4^w)^3 = 32^w-1
2^6w = 2^5(w-1) 6w = 5w-5 w = -5
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average rate of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
2pi is the circumference, so 2pi roughly equal 6.3. 6.3/3 = 2 2 < t < 2.5
3 x ? = 11
3 x 11/3 = 11
A circle is cut into 8 congruent pieces. What is the angle of each one?
360/8 = 45 degrees
cuberoot(64)
4
Average speed over a trip. 60 mph for 240 miles and 40 mph for 240 miles
4 hours + 6 hours = total trip time. 480/10 = 48mph
If x = 4^20 + 4^21 + 4^22, what is the largest prime factor of x?
4^20(1+4^1+4^2) = 4^20(21) 7*3 = 21 so 7 is the largest prime factor
University reading list consists of 1 play, 2 short stories, and one novel. There are 5 of each option, so how many reading lists can be created?
5 x 5c2 x 5 = 5 x 10 x 5 = 250 reading lists
If Susan spends 53 seconds folding y napkins, how many seconds will it take her to fold x napkins at the same rate?
53/y * x = 53x/y
How many integers can be squared to get an integer less than 10?
6 integers +/- 1, 2, 3
if you win a prize and get to select two items out of a total 6, how many combinations of the six prizes are there?
6! / 2!*(6-2)! = 15
(2*sqrt(3))^3
8*sqrt(3)^2*sqrt(3) = 24*sqrt(3)
1/(A/B) = ?
= 1/1 x B/A = B/A
What is the smallest possible integer that is not a factor of 20!?
All of 20 x 19 x 18 etc. are factors by very definition 21 is a multiple of 7 and 3, so it doesn't count Same with 22 23 is a prime number and is the answer
What was the approximate percent increase from 2001 to 2002 in the cost of a Sleeping Pod Time Unit (SPTU)? (1) The average SPTU is 5 minutes long, and costed 65 cents in 2001. (2) In 2002 the average cost of a SPTU was 2.5 times as much as a 2001 SPTU.
All you need is #2. Always use the percent increase formula: 250-100/100 * (100) = 150% increase
'Crazy Matt's Electronics' earned 90% more than did 'Sane Dan Plumbing' last year. Is Matt's earnings this year higher than Dan's last year's earnings? (1) Dan earned 735,123 dollars last year. (2) Matt earned 50% less than he did last year.
Always use the percent change formula when you see this problems: 190-100/100 = 90% 190 x 50% = 95. Therefore he made less than Dan's last year earnings. Only statement 2 is sufficient
36/b = b-5
Beware of hidden quadratics 36 = b^2 -5b 0 = b^2-5b -36 (b-9)(b+4) b= 9 , -4
Circle P is inside Circle Q, and the two circles share the same center X. If the circumference of Q is four times the circumference of P, and the radius of Circle P is three, what is the difference between Circle Q's diameter and Circle P's diameter?
Circle P circumference = 6pi Circle Q circumference = 24pi Difference in diameter = 24-6 = 18
How many employees does a company have? i. If 3 additional employees are hired by the company and all of the present employees remain, there will be at least 20 employees in the company ii. If no additional employees are hired by the company and 3 of the present employees resign, there will be fewer than 15 employees in the company.
Create the inequalities x +3 >=20 becomes x >= 17 x-3 < 15 becomes x <18 x = 17. Both together are sufficient
T/F: sqrt(10) > cuberoot(29)
Cube both sides, then square both sides. At this point, it will be obvious that the left side is larger
Does integer k have a factor p that 1 < p < k? i. k > 4! ii. 13! +2 <= k <= 13! + 13
Don't forget about prime numbers. If k is a prime number, i. is not sufficient. Between the range of 2-11 for statement ii, you have primes as well but they are all factors of 13!. Statement b is sufficient
The sum of the integers in list S is the same as the sum of the integers in list T. Does S contain more integers than T ? 1. The average (arithmetic mean) of the integers in S is less than the average of the integers in T. 2. The median of the integers in S is greater than the median of the integers in T.
Don't forget that the integers could be negative or 0. With this in mind, you can make rearrangements to the mean and median that make neither statement true. Therefore, E
Percent change for double? Triple?
Double: increases by 100% Triple: increases by 200%
A circle has its center at the origin and passes through the point (7,2). What is its area?
Draw it out! Use pythagorean theorem to find the missing side (which is the r^2). 7^ + 2^2 = r^2 Use area formula pi*r^2. 53pi
A codebreaking device is made up of a rectangular box filled with x cylinders of ball bearings placed together such that the diameter of the bearings and the cylinders are equal, and the cylinders line up evenly, touching, with no extra room inside the device. If the cylinders are the same height as the box, and the box is 18 inches long and 10 inches wide, what's the value of x? (1) 9 cylinders can line up along the length of the box. (2) Each ball bearing has a radius of 1.
Each alone is sufficient For statement 1, 18 length/9 = 2 diameter For statement 2, radius 1 = 2 diameter
If N > K, and if N is divisible by every prime factor of K, then N is divisible by K
False (75 and 45 is a counter example)
T/F: If A > B, and if A & B are multiples of p, then A/B is a multiple of p
False - (35, 21, with p being 7 is a counter example)
T/F: 1/(a-b) = 1/a - 1/b
False. You can't make this separation in the denominator for subtraction or addition
What is the value of the square root of the square root of .00000256?
First, write this in scientific notation: 256 x 10^-8 square root of 256 = 16 x 10^-4 square root = 4 x 10^-2 0.04
What is the value of n? (1) n^2 + 16 = 25 (2) (6 + n)^2 = n^2
For statement 1, n could be 3 or -3, so that is insufficient For statement 2, if you foil and then cancel out the n^2, you only get 1 answer. Statement 2 is sufficient
For integers w, x, y, and z, is wxyz = -1? (1) wx / yz = -1 (2) w = -1/x and y = 1/z
For statement 1, this may work for 1 and -1, but it doesn't work for 2, -2 etc. For statement 2, plug in the new values: -1/x(x)1/z(z), the x's and z's cancel out and you are left with -1*1 = 1. Statement 2 is sufficient
If x and y are integers and -50 < x < 0, what is the greatest possible value of xy ? (1) y ≥ 1 (2) y = -x
For statement 1, y could be infinite values for the denominator. Not sufficient. Statement 2, y only has 1 value. It is sufficient
Esther is giving Christmas presents to her family members. Each family member gets the same number of presents and no presents were leftover. If each family member gets at least one present, did each family member receive more than one present? (1) Esther has forty Christmas presents to give out. (2) If the number of family members were doubled, it would not be possible for each family member to get at least one present.
For statement 2, you can rewrite it as: number of presents/number of family members*2 < 1 Therefore number of presents/number of family members < 2 Each family member did not get at least one present (answer is NO), meaning statement 2 is sufficient
At a medical research lab, nine doctors are conducting multiple clinical trials. Six of the doctors are working on a clinical trial with exactly one other doctor and three doctors are working on a clinical trial with exactly two other doctors. If two doctors are selected at random from the lab, what is the probability that those two doctors are NOT working together on a clinical trial?
For the first person, you can have 6/9*1/8 = 1/12 For the second person, you can have 3/9*2/8 = 1/12 Since either option works, then you add them together: 2/12 The probability of something not happening is 1 - [event happening] answer is 5/6
If x and y are non-negative integers, is 11 a factor of x + y? (1) 22 is a factor of x (2) x - y is divisible by 11
For the first, it's not sufficient because you can do 22 + anything For the second, 17-6 is divisible by 11 but 17+6 is not a factor of 11 Together, they are sufficient
How many girls are members of both the Diving Team and the Swim Team? (1) At a joint meeting of the Diving and Swim Teams, no members were absent and 18 girls were present. (2) The Diving Team has 27 members, one-third of whom are girls, and the Swim Team has 24 members, half of whom are girls.
From the first statement, 18 is the total number of girls From the second statement, 9 girls from the diving and 12 from the swim team makes 21 girls. 21-18 = 3, which are the number of girls from both teams
x is positive, is it a prime number? i. x <8 ii. x is odd
If both statements are true, then 1,3,5,7 seems like it would be true. BUT 1 is not a prime number
A right triangle has sides that are consecutive even integers. The longest side is z. Which of the following equations could be used to find z?
If we know all three sides are consecutive even integers, then we can write the Pythagorean theorem as: (z-2)^2 + (z-4)^2 = z^2
Tom drives from town A to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between A and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour? 1. 12 2. 20 3. 24 4. 30 5. 36
If we plug in numbers, and we assume from A to B is 60 miles, then B to C is 30 miles. If we plug in 20, then it will take 30/20 or 1.5 hours. 60+30/1+1.5 = 90/2.5 = 36
Rectangle LMNO is inscribed in a circle with center P. If the area of the rectangle is 8 times its width, and the distance from P to side LM is 3, what is the circle's approximate circumference?
If you draw it out, you can see that 8 is the length of the rectangle, and you can draw a line between the center and the corner of the rectangle. The line is the hypotenuse of a right triangle, 3:4:5. So the radius is 5. Circumference formula is 5*2*Pi = roughly 31
J and K are positive numbers. Is J/K > 1? (1) JK < 1 (2) J-K > 0
J*K < 1means that one of them is a fraction 1/1/2 >1 but 1/2/1 is not. Insufficient J-K>0 must mean that J/K > 1. Statement 2 alone.
If N is a multiple of p, what is the LCM of N and p?
N
If both x and y are nonzero numbers, what is the value of y/x? i. x = 6 ii. y^2 = x^2
Neither are sufficient If y = negative number, then statement 2 would still be true but we wouldn't know y/x
Six people selected at random had an average (arithmetic mean) weight of 125 pounds. How many of the people weighed more than 125 pounds? (1) Three of the people weighed exactly 100 pounds. (2) None of the people weighed exactly 125 pounds.
Neither is sufficient because there could be one value that totally throws off the amounts
If the price of each apple and the price of each pear both remain constant no matter how many apples or pears are purchased, what is the price of five apples and five pears? (1) Two apples and ten pears cost $6.10. (2) Two apples and two pears cost $1.50.
Normally, you would need both equations to get the amount. However, since 2A and 2P cost 6.10, you can factor out a 2 for the variables. Then you can just multiply that equation by 5. So only statement 2 is necessary
What is the value of m? (1) |m| = −36/m (2) 2m+2|m| = 0
Only #1 is sufficient. m = -6 and the other answer is a root of a negative, which is not a real number #2 simplifies to |m| = -m which always has no solution
Does 2m -3n = 0 i. m <> 0 ii. 6m = 9n
Only statement 2 is sufficient, but not statement 1 If 6m = 9n, then you can do 3(2m) = 3(3n), which means 2m = 3n which is the original statement
If q is divisible by 2, 6, 9, 12, 15, and 30, is q divisible by 8?
Possibly. Prime factorize, then find the LCM. If there aren't three 2s, then it is not necessarily. It could be, but not sufficient
If x < y, and we do x/y, what is the quotient and the remainder?
Quotient is 0 and the remainder is x
Triangle side lengths: side 1 is 35, side 2 is 84, what is side 3?
Recognize that this the 5,12,13 triplet multiplied by 7. The answer will be 7*13
(2+√7)=?
Since root(7) is kind of like a square, you can use the difference of squares pattern: 2+root7) * root7-2/root7-2 | you can do this since it equals 1 -4 +7/root7-2 = 3/root7-2
If each term in the sum a1 + a2 + . . . + an is either 7 or 77 and the sum equals 350, which of the following could be equal to n? 38 39 40 41 42
Since the units digit of 350 is 0, you know that the answer choice must be a multiple of 10. Therefore 40 is the only choice
Marge has two square baking pans. One pan has a 12-inch diagonal and the other has a 16-inch diagonal. The area of the larger pan is how many square inches greater than the area of the smaller pan?
Since they are squares, 12 is the hypotenuse of an isoselces triangle. 12^2 = s^2 + s^2 144 = 2s^2 s^2 = 72 And 16^ = 2s^2 256 = 2s^2 = 128 128-72 = 56 which is the answer
The ratio of toddlers to infants at a day care center is 7 to 3. If twelve more infants join the day care to change the ratio to 7 to 5, how many toddlers are there at this day care center?
Since you know that 2 of the ratio is worth 12, then 1 is worth 6. 7*6 = 42
In the xy-plane, at what two points does the graph of y = (x + a)(x + b) intersect the x-axis? 1. a + b = -1 2. The graph intersects the y-axis at: (0,-6)
Statement 1 gives you a+b and statement 2 gives you a*b, which are enough for your to solve the quadratic equation: x^2 + (a+b)x + ab Both together are sufficient
If x > y, is zx > yx? (1) z > 0 (2) y < 0
Taken together they are still insufficient. It's important here to take a positive number, a negative number and 0 as tests to quickly see if they hold up or not.
In a party with more than three children, the average age (arithmetic mean) was 6. What is the average age of the remaining children in the party after three of the children have left? (1) Each of the three children who left was of age 6. (2) The average age of the three children who left was 6.
Test with some real numbers. Basically, you can remove numbers from the mean, and it won't disturb the mean. For both 1 and 2, the mean will still be 6
Fractional exponents
The denominator is the square root and the numerator is the exponent. You can do either order, so choose the easiest first.
A sum of $200,000 from a certain estate was divided among a spouse and three children. How much of the estate did the youngest child receive? i. The spouse received 1/2 of the sum from the estate, and the oldest child received 1/4 of the remainder. ii. Each of the two younger children received $12,500 more than the oldest child and $62,500 less than the spouse.
The first statement gives you the amount of the spouse and the oldest child, but not the division between the two younger ones. The second statement can be written out as: 200,000 = x + x + (x - 12500) + (x +62500)
5x-8y/4-7y = 3x+10/12
The first step is to cross multiply (5x-8y)*12 = (3x+10)*(4-7y) 60x-96y = 12x-21xy-70y+40 Combine like terms 48x+21xy = 26y+40 x(48+21y) = 26y+40 x = 26 y+40/21y+48
If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side? i. 8 ii. 5 iii. 11
The length of the longest side must be smaller than the sum of the lengths of the other two sides 8 can work 5 cannot (3+5=8) 11 cannot (3+8=11)
Each cell of Type X divides into a certain number of X-cells every hour. Each Type Y cell also divides into a constant number of Y-cells every hour, but not necessarily at the same rate as X. At a certain time, container A contained 10,000 X-cells and container B contained 10,000 Y-cells. After one hour, there were 30,000 more X-cells in container A than Y-cells in container B. After another hour, there were 330,000 more X-cells than Y-cells. What is the division rate per hour for the X-cells? 4, 5, 6, 7, 8
The trick here is ignore a lot of the busy info and focus on the key. Try the options out. 7*10,000 = 70000 - the 30000 of Y, = 40000. So X has a rate of 7 and Y of 4. Then after another hour 490,000 - 160,000 = 330,000 so the answer is 7
What is the total value of Company H's stock? 1. Investor P owns 1/4 of the shares of company H's stock 2. The total value of Investor Q's share of stock is $16,000
This is a trick question! You think both together would be sufficient, but you have to read carefully. Investor P owns 1/4 and investor Q's stock is worth $16,000. There is no cross-over. Neither is sufficient
For which of the following functions g is g(z) = g(1 - z) for all z? 1. g(z) = 1 - z 2. g(z) = 1 - z^2 3. g(z) = z^2(1 - z)^2
This is a very difficult problem, but what you need to do is plug in a number to the original equation. Take 4 g(1-4) = g(4) = g(-3) = g(4) This means that for each of these options, you have to plug in 4 and -3, and whichever one is equal, satisfies the condition
Which of the following is NOT a possible value of 1/4-x 1. -4 2. 4/17 3. 0 4. 4 5. 17/4
This is an easy answer, but the trick is that it is what this is equal to (y) as opposed to what values for x. 1 divided by anything will never equal 0
Helena invested $8000 in the Tallahassee City Bank at z% simple annual interest for one year with a yield of $450. How much should she invest at s% simple annual interest for one year to yield the same amount? (1) s/100 = 3/4 (2) s = .4z
This is an example of, you don't have to solve the problem but just need to know if it can be solved. 450 = 1*8000*z For both #1 and #2, you need to know how much to invest, so if you plugged in z for either one, you would get that answer. No need to do so actually (both alone are sufficient)
There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?
This is just 1/2(n-1)n 8*15 = 120
the slope of a line is 3/4. Does it pass through point (-2/3, 1/2) 1. The line passes through (4,4) 2. The line passes through (-4, -2)
This problem doesn't actually need to be solved. To check each point, you would find the slope of the first and second points through the point-slope formula. However, if the slope is the same or is different from 3/4, you already know whether it passes or not. Therefore, the question in themselves are both sufficient. D)
True/False: if x^3 > 0 , then x > 0
True
What is the probability that out of 8 kids, B will end up to the right of A in any order?
Use symmetry. There is a mirror version of each option, so it is 50%. Although I don't think this would be the case if the total was odd(?)
Sean and George collect two kinds of kernels: apricot kernels and mango kernels. If George has 4 apricot kernels, and together they have a total of 40 kernels (of both kinds,) then how many of these 40 kernels are mango kernels? (1) The number of apricot kernels that Sean has is half the total number of mango kernels they have together. (2) Sean has three times as many kernels as George has.
When you have multiple items for multiple people, use the double matrix solution. Draw out Sean, George and total and Apricots, Mango and total. It's relatively easy to figure out that #1 is sufficient
Are at least 10 percent of the people in Country X who are 65 years old or older employed? 1. In Country X, 11.3 percent of the population is 65 years old or older. 2. In Country X, of the population 65 years old or older, 20 percent of the men and 10 percent of the women are employed.
While statement 1 just tells you the total population breakdown, statement 2 gives you the percent of people 65+ who are employed, which is all you need. Statement 2 is sufficient
If the ratio of the price of 1 kilogram Camembert cheese to the price of 1 kilogram Brie cheese is 5:8, then the price of a kilogram of Toma cheese is how much higher (in dollars) than the price of a kilogram of Camembert cheese? (1) The price of 1 kilogram of Brie cheese is 25% higher than the price of 1 kilogram of Toma cheese. (2) The price of 1 kilogram of Toma cheese is 28% higher than the price of 1 kilogram of Camembert cheese.
While you can find relative ratios and percent changes, since you don't have any dollar amounts, you can't find the actual dollar difference. Therefore neither is sufficient
A designer purchased 20 mannequins that each cost an equal amount and then sold each one at a constant price. What was the designer's gross profit on the sale of the 20 mannequins? (1) If the selling price per mannequin had been double what it was, the gross profit on the total would have been $2400. (2) If the selling price per mannequin had been $2 more, the store's gross profit on the total would have been $440.
Write out the equations: Statement 1: (20(2s-c) = 2400. Insufficient data Statement 2: 20(s+2-c) = 440 20s +40 -20c = 440 20(s-c) = 400. It's only asking us for the gross profit, which is s-c
A shopping center increased its revenues by 10% between 2010 and 2011. The shopping center's costs increased by 8% during the same period. What is the firm's percent increase in profits over this period, if profits are defined as revenues minus costs? (1) The firm's initial profit is $200,000. (2) The firm's initial revenues are 1.5 times its initial costs.
Write out the equations: Statement 1: R-C = 200000 (initial) 1.1R-1.08C (new) (1.1R-1.08C) - R-C / R-C*100 (0.1R-0.08C/2000 *100. Too many variables Statement 2: R = 1.5C (1.1R-1.08C) - R-C/R-C*100 (0.1R-0.08C/2000 *100 0.1(1.5C) -.08C/1.5C-C *100 .07C/0.5C *100 = 14% Statement 2 is sufficient
The difference between John's and Paul's heights is twice the difference between John's and Thom's heights. If John is the tallest, what is the average (arithmetic mean) height of the three? (1) Paul is 163 centimeters tall. (2) Thom is 173 centimeters tall.
Write out the formulas: J-P = 2(J-T) J-P = 2J - 2T 2T = J + P So if you know T, and you know J+P, then you know the mean, which is just (T+P+J)/3 #2 is sufficient but not #1
Circle B's diameter was multiplied by 1.8. By what percent, approximately, was the area increased?
You can plug in values to test. If the radius increases by 1.8, then a radius of 10 would have an area of 100pi and and a radius of 18 would have an area of 324. 324-100/100 = 224% increase
42% of $80000
You can solve by taking 10% *4 Then 10% of that to get 4%, then divide by 2% and then add those up
4^a + 4^a+1 = 4^a+2 - 176
You can't add or subtract exponents because you aren't multiplying. Move the 4^a+2 to the other side -176 = 4^a +4^a+1 - 4^a+2 -176 = 4^a(1+4^1 - 4^2) -176=4^a(-11) 16=4^a a = 2
sqrt(-¼) = x
You can't solve this because you can't square root a negative
Store X sells every hat for the same price, and store X sells every tablecloth for the same price. What is the total cost of 5 hats and 7 tablecloths at store X? (1) The cost of 4 hats and 12 tablecloths at store X is $184. (2) The cost of 1 hat and 3 tablecloths at store X is $46.
Your first instinct is to say both together are sufficient in order to solve the problem. But, if you test it out, combining the equations cancels out both variables, so there is no solution. Neither is sufficient.
Is 0 even, odd, or neither?
even
216^(1/3)
find the prime factors 3*3*3*2*2*2 = 6^3 = 6
If r and s are positive integers, is r/s an integer i. every factor of s is also a factor of r ii. every prime factor of s is also a prime factor of r
for statement 1, if every factor of s, including s itself is a factor of r, then it is obviously an integer for statement 2, take 18 and 8. The prime factor of 8 is 2, and this is in 18 as well, but 8 is not a factor of 18
If n is the product of 2, 3 and a two-digit prime number, how many of its factors are greater than 6
four 2*two digit prime 3*two digit prime two digit prime The number itself
Is the triangle above equilateral (x,y,z are angles) i. x = y ii. z = 60.
if x = y, then it could just be an isosceles if z = 60, then x could be 80 and y could be 50 If both are true, then you can write it as: 2x + 60 = 180
If y > 1 and y = 2x-3/3x+4, then which of the following gives x in terms of y?
multiply both sides by 3x+4 3xy + 4y = 2x-3 3xy - 2x = -4y-3 x(3y-2) = -4y-3 x = -4y-3/3y-2 x = 4y+3/2-3y
sqrt(20a) x sqrt(5a)
sqrt(100a^2) = 10a
sqrt(50) x sqrt(18)
sqrt(25*2*9*2) = 5*2*3 = 30
sqrt(150) - sqrt(96)
sqrt(25*6) - sqrt(16*6) 5root6 - 4root6 = root6
Sqrt(p/q)
sqrt(p) / sqrt(q)
sqrt(p x q)
sqrt(p) x sqrt(q)
sqrt(x^2) = ?
sqrt(x^2) = |x|
sqrt(x^2y^3 + 3x^2y^3)
sqrt(y^3(x^2+3x^2) sqrt(y^3(4x^2) 2x(sqrt(y^3)) = 2xy(rooty) - you can pull out an y^2 and then square root it
If m=√x, and m is an integer, x CANNOT be which of the following? 1. 25+39 2. (.3)(30) 3. 147/3 4. sqrt(25) 5. 0
the answer is square root 25, because this would be 5. and root(5) is not an integer 0 is an integer.
3w^2 = 6w
this is a quadratic equation! w(3w-6) = 0 w = 0 or 2
xy + x
x(y) + x(1) = x(y+1)
