Data Sufficiency

If p and q are positive integers and pq = 24, what is the value of p ? (1) q/6 is an integer. (2) p/2 is an integer.

If the total price of n equally priced shares of a certain stock was $12,000, what was the price per share of the stock? (1) If the price per share of the stock had been $1more,thetotalpriceofthenshareswouldhavebeen$300 more. (2) If the price per share of the stock had been $2 less, the total price of the n shares would have been 5 percent less.­ ID: 700113

Did the population of Country S increase by less than 20 percent from 1965 to 1975 ? (1) The population of Country S in 1965 was 180 million. (2) The population of Country S in 1975 was 1.17 times what it was in 1965.

Larry saves x dollars per month. Will Larry’s total savings one year from now exceed his present savings by at least $500 ? (1) In 6 months Larry's total savings will be $900. (2) In 3 months Larry's total savings will exceed his present savings by $150. ID: 700138 DS21223­

Quadrilateral RSTU shown above is a site plan for a parking lot in which side RU is parallel to side ST and RU is longer than ST. What is the area of the parking lot? (1) RU = 80 meters (2) TU = 20 10 − − √ 20 10 meters Show Spoiler

What digit does t represent in the decimal 0.t73 ? (1) t<5 𝑡 < 5 (2) 0.t73< 1 t 0. 𝑡 73 < 1 𝑡

A school administrator will assign each student in a group of N students to one of M classrooms. If 3<M<13<N, is it possible to assign each of the N students to one of the M classrooms so that each classroom has the same number of students assigned to it? (1) It is possible to assign each of 3N students to one of M classrooms so that each classroom has the same number of students assigned to it. (2) It is possible to assign each of 13N students to one of M classrooms so that each classroom has the same number of students assigned to it.

What is 5 percent of x ? (1) x = 200 (2) 10 percent of x is 20.

Is x - y > r - s ? (1) x > r and y < s (2) y = 2, s = 3, r = 5, and x = 6 PS21276

If x and y are integers, is xy + 1 divisible by 3 ? (1) When x is divided by 3, the remainder is 1. (2) When y is divided by 9, the remainder is 8. DS06402.01

3.2XY6 If X and Y each represent single digits in the decimal above, what digit does X represent? (1) When the decimal is rounded to the nearest tenth, 3.2 is the result. (2) When the decimal is rounded to the nearest hundredth, 3.24 is the result.

If x≠0 , what is the value of ( x p x q ) 4 ? (1) p = q (2) x = 3

What is the ratio of x:y:z? (1) z = 1 and xy =32 (2) x/y = 2 and z/y = 1/4

If a and b are positive integers, is a/b = 2/3 ? (1) 3a = 2b (2) For integers m and n, a = 2m and b = 3n

Is |x – 3| < 7 ? (1) x > 0 (2) x < 10

If xy = - 6, what is the value of xy(x + y)? (1) x−y=5 𝑥 − 𝑦 = 5 (2) x y 2 =18 𝑥 𝑦 2 = 18

On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers? (1) q + s =24 (2) The average (arithmetic mean) of q and r is 11. Show Spoiler

Three dice, each of which has its 6 sides numbered 1 through 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5? (1) None of the 3 numbers that are facing up is divisible by 3 (2) Of the numbers that are facing up, 2, but not all 3, are equal

On a certain day it took Bill three times as long to drive from home to work as it took Sue to drive from home to work. How many kilometers did Bill drive from home to work? (1) Sue drove 10 kilometers from home to work, and the ratio of (distance driven from home to work) (time to drive from home to work) ( 𝑑 𝑖 𝑠 𝑡 𝑎 𝑛 𝑐 𝑒   𝑑 𝑟 𝑖 𝑣 𝑒 𝑛   𝑓 𝑟 𝑜 𝑚   ℎ 𝑜 𝑚 𝑒   𝑡 𝑜   𝑤 𝑜 𝑟 𝑘 ) ( 𝑡 𝑖 𝑚 𝑒   𝑡 𝑜   𝑑 𝑟 𝑖 𝑣 𝑒   𝑓 𝑟 𝑜 𝑚   ℎ 𝑜 𝑚 𝑒   𝑡 𝑜   𝑤 𝑜 𝑟 𝑘 ) was the same for Bill and Sue that day. (2) The ratio of (distance driven from home to work) (time to drive from home to work) ( 𝑑 𝑖 𝑠 𝑡 𝑎 𝑛 𝑐 𝑒   𝑑 𝑟 𝑖 𝑣 𝑒 𝑛   𝑓 𝑟 𝑜 𝑚   ℎ 𝑜 𝑚 𝑒   𝑡 𝑜   𝑤 𝑜 𝑟 𝑘 ) ( 𝑡 𝑖 𝑚 𝑒   𝑡 𝑜   𝑑 𝑟 𝑖 𝑣 𝑒   𝑓 𝑟 𝑜 𝑚   ℎ 𝑜 𝑚 𝑒   𝑡 𝑜   𝑤 𝑜 𝑟 𝑘 ) for Sue that day was 64 kilometers per hour.

If x ≠ 0, is |x| < 1 ? (1) x^2 < 1 (2) |x| < 1/x