Data Sufficiency

The top surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made? (1) After the changes were made, the surface area was 70 square inches. (2) There was a 25 percent increase in one of the dimensions. DS58302.01

If b is an integer, is a 2 + b 2 − − − − − − √ 𝑎 2 + 𝑏 2 an integer? (1) a^2 + b^2 is an integer. (2) a^2 – 3b^2 = 0 DS46402.01

If n is an integer, is n/15 an integer? (1) 3n/15 is an integer. (2) 8n/15 is an integer DS37602.01

A total of 774 doctorates in mathematics were granted to United States citizens by American universities in the 1972-1973 school year, and W of these doctorates were granted to women. The total of such doctorates in the 1986-1987 school year was 362, and w of these were granted to women. If the number of doctorates in mathematics granted to female citizens of the United States by American universities decreased from the 1972-1973 school year to the 1986-1987 school year, was the decrease less than 10 percent? (1) 1/10 < W/774 < 1/9 (2) W = w + 5

If x = 0.rstu, where r, s, t, and u each represent a nonzero digit of x, what is the value of x ? (1) r = 3s = 2t = 6u (2) The product of r and u is equal to the product of sand t.

If x is a positive number, what is the value of x ? (1) |x – 2| = 1 (2) x^2 = 4x -3 DS20559

What is the greatest common divisor of positive integers m and n? (1) m is a prime number. (2) m and n are consecutive integers.

Is 7< n √ <8 7 < 𝑛 < 8 ? (1) n > 50 (2) n < 60

The price of a television set was reduced by 25 percent. What was its original price? (1) The reduced price was $187.50. (2) The original price exceeded the reduced price by more than $60.00.

Last year, if Arturo spent a total of $12,000 on his mortgage payments, real estate taxes, and home insurance, how much did he spend on his real estate taxes? (1) Last year, the total amount that Arturo spent on his real estate taxes and home insurance was 33 1/3 percent of the amount that he spent on his mortgage payments. (2) Last year, the amount that Arturo spent on his real estate taxes was 20 percent of the total amount he spent on his mortgage payments and home insurance.

If x > 0, is x/y > x ? (1) 0 < y < 1 (2) x > 1

Who types at a faster rate, John or Bob? (1) The difference between their typing rates is 1 word per minute (2) Bob types at a rate of 80 words per minute

If x and y are positive what is the value of x? (1) x = 3.927y (2) y = 2.279

Committee member W wants to schedule a one-hour meeting on Thursday for himself and three other committee members, X, Y, and Z. Is there a one-hour period on Thursday that is open for all four members? (1) On Thursday W and X have an open period from 9:00 a.m. to 12:00 noon. (2) On Thursday Y has an open period from 10:00 a.m. to 1:00 p.m. and Z has an open period from 8:00 a.m. to 11:00 a.m.

If Hans purchased a pair of skis and a ski jacket, what was the cost of the skis? (1) The ratio of the cost of the skis to the cost of the jacket was 5 to 1. (2) The total cost of the skis and the jacket was $360.

What is the total number of employees in the personnel and data processing divisions of Company S ? (1) The number of employees in the data processing division is 3 more than twice the number of employees in the personnel division. (2) The number of employees in the data processing division is 15.

Is 1 < x < 2? (1) 0 < x (2) x < 3

If a total of 84 students are enrolled in two sections of a calculus course, how many of the 84 students are female? (1) 2/3 of the students in Section 1 are female. (2) 1/2 of the students in Section 2 are male.

What is the remainder when the positive integer n is divided by 6? (1) n is multiple of 5 (2) n is a multiple of 12

In planning for a car trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hours of the actual time that the trip took? (1) Joan’s estimate for the distance was within 5 miles of the actual distance. (2) Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed.