Data Sufficiency

What is the value of |x| ? (1) x = - |x| (2) x^2 = 4

A certain 4-liter solution of vinegar and water consists of x liters of vinegar and y liters of water. How many liters of vinegar does the solution contain? (1) x/4 = 3/8 (2) y/4 = 5/8 Show Spoiler My concern

In a school election, if each of the 900 voters voted for either Edith or Jose (but not both), what percent of the female voters in this election voted for Jose? (1) Eighty percent of the female voters voted for Edith. (2) Sixty percent of the male voters voted for Jose.

Last year 4/5 of the applicants for a job on a police force passed the physical examination. If 3/4 of the applicants who passed the physical examination also passed the written examination, how many of the applicants passed both examinations ? (1) The number of applicants who did not pass either examination was equal to the number who passed the written examination only. (2) There was a total of 100 applicants.

If x > y, is cx > cy ? (1) c > 0 (2) xy > 0 DS21218

A swim club that sold only individual and family memberships charged $300foranindividualmembership.Iftheclub\hat{a}€™stotalrevenuefrommembershipswas$480,000, what was the charge for a family membership ? (1) The revenue from individual memberships was 1/4 of the total revenue from memberships. (2) The club sold 1.5 times as many family member- ships as individual memberships.

If Pat saved $600 of his earnings last month, how much did Pat earn last month? (1) Pat spent 1/2 of his earnings last month for living expenses and saved 1/3 of the remainder. (2) Of his earnings last month, Pat paid twice as much in taxes as he saved.

Was the amount of John's heating bill for February greater than it was for January? (1) The ratio of the amount of John's heating bill for February to that for January was 26/25. (2) The sum of the amounts of John's heating bills for January and February was $183.60.

Was 70 the average (arithmetic mean) grade on a class test? (1) On the test, half of the class had grades below 70 and half of the class had grades above 70. (2) The lowest grade on the test was 45 and the highest grade on the test was 95.

Claire paid a total of $1.60forstamps,someofwhichcost$0.20 each, and the rest of which cost $0.15 each. How many 20-cent stamps did Claire buy? (1) Claire bought exactly 9 stamps. (2) The number of 20-cent stamps Claire bought was 1 more than the number of 15-cent stamps she bought.

What is the value of z in the triangle above? (1) x + y = 139 (2) y + z = 108 Show Spoiler

Is x > 0? (1) -2x > 0 (2) x^3 < 0

During week W, how much did it cost, per mile, for the gasoline used by car X? (1) During week W, car X used gasoline that cost $1.24 per gallon. (2) During week W, car X was driven 270 miles.

Is the integer n even ? (1) n^2 - 1 is odd. (2) n √ 𝑛 is an integer.

Terry and Pat collected cans for recycling. What was the ratio of the number of cans Terry collected to the number of cans Pat collected? (1) Pat collected 50 percent of the cans that they collected. (2) Terry collected 140 cans. This is a DS Butler Question Check the links to other Butler Projects: Problem Solving Butler Critical Reasoning Butler Sentence Correction Butler Reading Comprehension Butler Integrated Reasoning Butler

If x, y, and z are positive numbers, is x > y > z ? (1) xz > yz (2) yx > yz

The purchase price of Beth's new car, including the sales tax, is $8,000.Ifshefinancesthecar,makingadownpaymentof$2,000 and paying off the rest in equal monthly installments, what will be the total cost of the car, including the sales tax and financing ? (1) The installments are to be $200 per month. (2) The installments will extend over a period of exactly 3 years

What is the length of Train A if it crosses Bridge X in 30 seconds from the moment it enters the bridge to the moment its final carriage exits the bridge? (1) Train B, which is 200 meters long, traveling at a constant speed of 20 meters per second, crosses Bridge X in 40 seconds. (2) The end of Train A, which is traveling at a constant speed, passes a pole in 10 seconds from the moment the train meets the pole.

If Ruth began a job and worked continuously until she finished, at what time of day did she finish the job? (1) She started the job at 8:15 a.m. and at noon of the same day she had worked exactly half of the time that it took her to do the whole job. (2) She was finished exactly 7.5 hours after she had started.

A certain bakery sells rye bread in 16-ounce loaves and 24-ounce loaves, and all loaves of the same size sell for the same price per loaf regardless of the number of loaves purchased. What is the price of a 24-ounce loaf of rye bread in this bakery? (1) The total price of a 16-ounce loaf and a 24-ounce loaf of this bread is $2.40. (2) The total price of two 16-ounce loaves and one 24-ounce loaf of this bread is $3.40.