Data Sufficiency

A rectangular garden that is 10 feet long and 5 feet wide is to be covered with a layer of mulch 0.5 foot deep. At which store, K or L, will the cost of the necessary amount of mulch be less? (1) Store K sells mulch only in bags, each of which costs $7 and contains 6.25 cubic feet of mulch. (2) Store L sells mulch only in bags, each of which costs $40 and contains 25 cubic feet of mulch.

A thoroughly blended biscuit mix includes only flour and baking powder. What is the ratio of the number of grams of baking powder to the number of grams of flour in the mix? (1) Exactly 9.9 grams of flour is contained in 10 grams of the mix. (2) Exactly 0.3 gram of baking powder is contained in 30 grams of the mix

If r and s are integers, is r+s divisible by 3? (1) s is divisible by 3 (2) r is not divisible by 3

If x and y are integers, what is the value of y ? (1) xy = 27 (2) x = y^2

If x + 2y = 6, what is the value of x ? (1) 2x + y = 9 (2) 3x + 2y = 14

What are the populations of Cities Y and Z ? (1) The population of City Z is 275,000 more than the population of City Y. (2) The ratio of the population of City Z to the population of City Y is 76 to 21. 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

Is the number x between 0.2 and 0.7? (1) 560x < 280 (2) 700x > 280

How many numbers do the sets S and T have in common? (1) S is a set of 10 numbers. (2) T is a set of 100 numbers.

Mohit went cycling on 10 consecutive days. Every day he started from Point X, cycled a certain distance in an easterly direction, and then returned to Point X. What is the total distance he covered in those 10 days? (1) From the second day onward, Mohit covered twice the distance he covered the previous day. On the fifth day, he covered 3.2 km from Point X east, and then back to Point X. (2) On the first day, Mohit cycled less than 0.3 km.

In parallelogram ABCD above, what is the measure of ∠ADC? (1) The measure of ∠ABC is greater than 90°. (2) The measure of ∠BCD is 70°. Show Spoiler

If S = {2, 3, x, y}, what is the value of x + y? (1) x and y are prime numbers. (2) 3, x, and y are consecutive odd integers in ascending order.

If a real estate agent received a commission of 6 percent of the selling price of a certain house, what was the selling price of the house? (1) The selling price minus the real estate agent’s commission was $84,600. (2) The selling price was 250 percent of the original purchase price of $36,000.

What is the radius of the circle above with center O? (1) The ratio of OP to PQ is 1 to 2. (2) P is the midpoint of chord AB. Show Spoiler

In the figure above, segments PR and QR are each parallel to one of the rectangular coordinate axes. Is the ratio of the length of QR to the length of PR equal to 1? (1) c = 3 and d = 4. (2) a = -2 and b = -1. Show Spoiler

If n is an integer, is n odd ? (1) The tens digit of n is odd. (2) n^2 is odd.

Is x an integer? (1) x/2 is an integer (2) 2x is an integer Show Spoiler

In the figure above, if line l1 is parallel to line l2, what is the value of x ? (1) y = 50 (2) z = 130 Show Spoiler

Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year? (1) The company's total revenue from the sale of product X last year was greater than $110,000. (2) For each unit of product X sold last year, the company's revenue was $5.

Is x^2 equal to xy? (1) x^2 – y^2 = (x + 5)(y - 5) (2) x = y PS21275

In △ △ HGM , what is the length of side HM? (1) HG = 5 (2) GM = 8