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If a and b are positive integers, and a× 105 = b × 10n what is the value of n ?
(1)a = 100b
(2) a+b =5050
Mrs. Smith stores her homemade applesauce in glass jars of only two sizes: large and small. If a certain quantity of applesauce will fill either 2 large jars and 12 small jars, or 4 large jars and 4 small jars, how many ounces of applesauce does each small jar hold?
(1) Each large jar holds 4 times as much as each small jar.
(2) Two large jars together hold 24 ounces.
A certain number of people wait in line at a bank until served. How many people are presently in line?
(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.
(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.
The ratio of men to women to children at an assembly is 2:3:4 . If 720 children are present, how many men and women are there?
Working alone, Allen can paint a room in 12 hours. Working alone, Charles can paint this room in 6 hours. How many hours would it take Allen and Charles to paint the room if they work together?
Is a − b > 0?
(1) a > 2b
(2) b > a + 3
If Tom's age is 5 years less than the combined ages of Dick and Harry, what is the sum of the ages of Tom, Dick, and Harry?
(1) Two of the people are the same age.
(2) Dick is 2 years older than Harry.
If a and b are greater than 0, a is what percent greater than b?
(1) 4a =5b
What is the value of n?
(1) n2 + 16 = 25
(2) (6 + n)2 = n2
Bill’s street address is wxyz Oak Street where w, x, y, and z each represent a unique nonzero digit. What is Bill’s street address?
(1) w = 2x = 4y = 8z
(2) w = y3 and x = y2.
The only contents in a container are green disks, blue disks, and orange disks. If one disk is selected at random from the container, what is the probability that the disk is orange?
(1) The ratio of the number of orange disks to the number of disks that are not orange is 7 to 36.
(2) The ratio of the number of green disks to the number of blue disks is 7 to 3, and the ratio of the number of green disks to the number of orange disks is 18 to 5.
D. Either alone is sufficient
This Value question asks us for the probability of drawing an orange disk from a container which contains orange, blue, and green disks. The probability formula is:
Probability = desired outcome/total outcome
While we do not need to calculate the exact values to answer the question, the least common multiple of 7 and 18 is 126. If there are 126 green disks, there are 54 blue disks, and 35 orange disks. So, the total number of disks in this case would be 126 + 54 + 35 = 215, so the probability of selecting an orange disk is: 35/215 or 7/43
If x and y are positive, does (x – 2)(y – 3) = 6?
(1) 3x = y(x – 2)
(2) (x – 8)(y2 + 5) = 0
If 2^y=4^(5x+3) and 3^(x-7) = 9^y, what is the value of x + y?37
In the sequence r, s, t, if each term after the first is x more than the previous term, what is the average of r, s, and t in terms of r and x?
If xy ≠ 0, does 5/x = y/4 ?
(1) 100x – 35y = 0
(2) x > 7
There are 35 students in a college lecture theater. What is the ratio of male students to female students in the lecture theater?
(1) There are 10 male students in the lecture theater.
(2) If the number of male students in the lecture theater was doubled, the ratio of male students to female students in the lecture theater would be 4 to 5.
A particular chainsaw requires a premixed combination of gasoline and oil in a 4 to 1 ratio. The chainsaw’s default mixing recipe produces enough mix for two chainsaws. If the default mixing recipe were changed to yield enough mix for three chainsaws, how many quarts of oil would be needed?
(1) 12 quarts of gas would be needed if the mixing recipe was changed to yield enough mix for four chainsaws.
(2) 6 quarts of gas are used in the default mixing recipe.
What is the value of z if 27/5 + 2 = 3z/4?
Advertisement: Today's consumer expects a level of personalized customer care that was undreamt of only recently. Every advance in personalized care increases customer expectations. The company that is satisfied with its present level of customer care will soon find that its customers no longer are. At Courtier Services, our goal is to meet or exceed our customers' expectations.
Based on the statements in the advertisement above, which of the following must be true?1. Courtier Services's goal can only be met if continuing improvements in personalized customer care are possible.
When the nineteenth-century German bacteriologist Robert Koch identified a particular bacterium as responsible for cholera, Max von Pettenkoffer, a physician, expressed his skepticism by voluntarily drinking an entire bottle of the allegedly responsible bacteria. Although von Pettenkoffer took his failure to come down with the disease as a refutation of Koch's hypothesis that cholera was caused by bacteria, Koch argued that von Pettenkoffer had been protected by his own stomach acid. The acid secreted by the stomach, Koch explained, kills most ingested bacteria.
Which of the following, if true, provides the most evidence to support Koch's counterargument?
1. Peptic ulcers, often associated with excessive secretions of stomach acid, are common in certain areas characterized by low rates of cholera.
2.Cholera bacteria ingested with bicarbonate of soda, a neutralizer of stomach acid, is more likely to result in cholera than if the bacteria is ingested alone.
Gamma Insurance Company is contemplating offering a new type of life insurance policy to people who engage in high-risk sports such as skydiving. The cost of the new policy must be low enough to entice people to buy it. Therefore, Gamma Company is concerned that revenues from sales of the policy would be insufficient to cover the costs of claims by policyholders.
Which of the following strategies would be most likely to minimize Gamma Insurance Company's losses on the new policy?
A. Appealing to people who engage only occasionally in high-risk sports.
B. Marketing the policy to high-risk sports enthusiasts who have been rejected by other life insurance companies.
Until the Federal government began providing low-cost flood insurance to coastal property owners, construction along beaches was limited by owners’ fears that their property would be washed away. Since the insurance was made available, however, beachfront construction has boomed and therefore land erosion has increased at a dangerous rate.
Which of the following, if feasible, offers the best prospects for the Federal government to put a stop to the problem of land erosion along beaches?
A. Compensating beachfront property owners for moving to a new location off the coast while canceling flood insurance benefits for any new or remaining beachfront construction.
The Nordlingen WE luxury sports car uses a special imported rosewood in the extensive wood trimming of its interior. Unfortunately, trade sanctions imposed on the nation that is the primary supplier of that type of rosewood has resulted in a considerable increase in price of the now extremely rare commodity. Purchasers of new models of the Nordlingen WE can expect to see that increase reflected in an increase in the Norlingen's ticket price.
The conclusion above is based on which of the following assumptions?
A. The price of rosewood is a major contributing factor to the Nordlingen WE's ticket price.
B. The imported rosewood will continue to be used for the wood trim in new models of the Nordlingen WE.
A play was performed as part of a benefit for a charity. Nobody who wanted to buy tickets to the benefit had ever seen the play performed before. Because of the high demand, only people who had never seen the play performed before were allowed to buy tickets for the benefit. Therefore, everyone who wanted to buy a ticket to the benefit was able to do so.
In order for this argument to be logically correct, it must also be true that...
A.there was no limit to the number of tickets available
B. everyone who was unable to buy a ticket did not want to buy one
Additional to being source of Vitamin C and Vitamin A, a tomato contain a carotenoid called lycopene that is thought to help protect against diseases such as cancer and heart disease.
A.Tomatoes not only are a source of Vitamin C and Vitamin A, but also contain
B. A tomato not only is a source of Vitamin C and Vitamin A, it also contains
A lawyer defending a doctor from malpractice charges will find it easy to avoid damages if there is a lack of some other doctor to testify about proper medical procedures.
A. if there is a lack of some other doctor to testify
B. unless there will be another doctor to testify
C. without another doctor's testimony
If a candy manufacturer makes a new candy consisting of a core composed of 10% chocolate by weight, and an outer layer composed of 40% chocolate by weight, what percent of the entire candy, by weight, consists of chocolate?
(1)The entire candy weighs 250 grams.
(2)The ratio of the weight of the core to the weight of the outer layer is 4:1.
A supermarket purchased 60 identically priced tubes of toothpaste for a total of k dollars. If each tube of toothpaste was sold for 40% more than the price paid by the supermarket per tube, then at what price was each tube of toothpaste sold?
(1)The toothpaste was sold for a total of 48 dollars more than the supermarket paid for it.
(2)Each tube of toothpaste was sold for 80 cents more than it cost the supermarket.
Is the positive integer y a multiple of 12?
(1) y3 is a multiple of 48.
(2) y2 is a multiple of 30.
Is xy < 0?
(1) x2y < 0
(2) x3y < 0
A grocer purchased 50 identical cans of soup for a total cost of x dollars. If the grocer then sells each can at 10% above its original cost, then in terms of x, for how many dollars would each can sell?
Is a > b?
(1) 6b + a = 50
(2) 6b + a > 40
A class of n students, where n > 2, has an average (arithmetic mean) grade of G, where G > 0. A student, whose grade is only half the average, drops the class. What is the new class average?
A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 5 feet and a height of 10 feet, how far did the oil level drop in the stationary tank?
Suppose that the length is CD, which is 8, the width is BC, which is 6, and the space diagonal AD is 26. We need the length of AB, which is the height. Let's look at right triangle BCD. Triangle BCD is a 3-4-5 right triangle, with each member of the 3 to 4 to 5 ratio multiplied by 2. The question stem gives us that BC=6=2x3 and CD=8 =2x4. Therefore, BD=2x5=10.
Now let's look at right triangle ABD. Triangle ABD is a 5-12-13 right triangle, with each member of the 5 to 12 to 13 ratio multiplied by 2. We just solved for the fact that BD = 10=2x5, and the question stem gives us that AD =26 =2x13. Therefore, AB = 2x12=24.. Since h=24 , Answer Choice (D) is correct.
In a certain museum gift shop, did sales of calendars account for 15 percent of the shop's $40,000 revenue for the month of December?
(1) In December, sales of calendars brought in 1/7 as much revenue as sales of all other items.
(2) In December, the shop sold a total of 625 calendars for $8 each.
At store W, in June of year X, the price of a cabinet was 20 percent less than it was in July of year X, and at store W, in June of year X, the price of a lamp was 15 percent greater than it was in July of year X. What was the price of the lamp in store W, in June of year X?
(1) In July of year X, the price of the cabinet was $260 greater than the price of the lamp.
(2) The ratio of the price of the cabinet in June of year X to the price of the cabinet in July of year X was 4 to 5.
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