Data Sufficiency

If a and b are positive integers, what is the value of a + b? (1) a b = 5 8 𝑎 𝑏 = 5 8 (2) The greatest common divisor of a and b is 1.

If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K? (1) N is divisible by 3. (2) N is divisible by 7. DS38302.01

If $representsadigitinthe7-digitnumber3,62$,215, what is the value of $? (1) The sum of the 7 digits is equal to 4 times an integer. (2) The missing digit is different from any of the other digits in the number Show Spoiler

What is the circumference of the circle above? (1) The length of arc XYZ is 18. (2) r = s Show Spoiler

What was Janet’s score on the fourth physics test she took? (1) Her score on the fourth test was 12 points higher than her average (arithmetic mean) score on the first three tests she took. (2) Her score on the fourth test raised her average (arithmetic mean) test score from 87 to 90

A Town T has 20,000 residents, 60 percent of whom are female. What percent of the residents were born in Town T? (1) The number of female residents who were born in Town T is twice the number of male residents who were not born in Town T. (2) The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T.

If x and y are positive. is y< 2 ? (1) x > 2y (2) x < y + 2 DS20555

A small factory that produces only upholstered chairs and sofas uses 1 cushion for each chair and 4 cushions for each sofa. If the factory used a total of 300 cushions on the furniture it produced last week, how many sofas did it produce last week ? (1) Last week the factory produced more chairs than sofas. (2) Last week the factory produced a total of 150 chairs and sofas. ID: 700117 DS20349­

If a certain grove consists of 36 pecan trees, what was the yield per tree last year? (1) The yield per tree for the 18 trees in the northern half of the grove was 60 kilograms last year. (2) The yield per tree for the 18 trees in the eastern half of the grove was 55 kilograms last year.

Are all of the numbers in a certain list of 15 numbers equal? (1) The sum of all the numbers in the list is 60. (2) The sum of any 3 numbers in the list is 12.

At a bakery, all donuts are priced equally and all bagels are priced equally. What is the total price of 5 donuts and 3 bagels at the bakery? (1) At the bakery, the total price of 10 donuts and 6 bagels is $12.90. (2) At the bakery, the price of a donut is $0.15 less than the price of a bagel.

In a serving of a breakfast cereal that contains only oats, raisins, and nuts, the ratio of oats to raisins to nuts by weight is 3 to 2 to 1, respectively. How many ounces of raisins are in the serving ? (1) The serving weighs 4 ounces. (2) The serving contains 2 ounces of oats.

A jewelry dealer initially offered a bracelet for sale at an asking price that would give a profit to the dealer of 40 percent of the original cost. What was the original cost of the bracelet? (1) After reducing this asking price by 10 percent, the jewelry dealer sold the bracelet at a profit of $403. (2) The jewelry dealer sold the bracelet for $1,953.

Last Tuesday a trucker paid $155.76, including 10 percent state and federal taxes, for diesel fuel. What was the price per gallon for the fuel if the taxes are excluded? (1) The trucker paid $0.118 per gallon in state and federal taxes on the fuel last Tuesday. (2) The trucker purchased 120 gallons of the fuel last Tuesday.

If p, q, r, and s are nonzero numbers, is (p – 1)(q - 2)^2(r – 3)^3(s – 4)^4 >= 0? (1) (q - (2) ^2(r – 3)^3(s – 4)^4 >= 0? (1) q > 2 and s > 4 (2) p > 1 and r > 3

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

Can the positive integer n be written as the sum of two different positive prime numbers? (1) n is greater than 3. (2) n is odd. DS38602.01

If n is a positive integer, is n divisible by at least six positive integers? (1) n is the product of three different prime numbers (2) n = 30 DS20556

If integer p is a factor of 42, is p a prime number? (1) p > 6 (2) p < 21 DS21228

What was the percent increase in the value of a certain antique from January 1, 1981, to December 31, 1981? (1) The value of the antique on January 1, 1981, was $3,000. (2) The value of the antique on December 31, 1981, was double the value of the antique on January 1,1981.