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If x, y, P, and Q are positive integers such that x + y = P and \(x^2=\dfrac{Q^2}{Y^2},\) then

E-GMAT

If x, y, P, and Q are positive integers such that x + y = P and \(x^2=\dfrac{Q^2}{Y^2},\) then (x-3y)(y+3x)=

A. \(3P^2-8Q\)
B. \(3PQ-8Q\)
C. \(3Q^2-8Q\)
D. \(3P(\sqrt{P^2-4Q})-8Q\)
E. \(3P(\sqrt{P-2Q})-8Q\)

OA D


Starting from the same point, a sparrow and a hawk flew in opposite directions. Each traveled at a constant speed until

Princeton Review Starting from the same point, a sparrow and a hawk flew in opposite directions. Each traveled at a constant speed until they were 200 feet apart. How far did the sparrow travel? 1) The ratio of the sparrow's speed to the hawk's speed was 3 to 2 2) The average speed of the sparrow w...


A wildlife preserve is being planned for 3,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of water

GMAT Paper Tests A wildlife preserve is being planned for 3,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should ...


The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?

GMAT Paper Tests

The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?

A. 10 and 20
B. 12 and 18
C. 24 and 32
D. 21 and 63
E. 22 and 88

OA C


The 9 participants in a race were divided into 3 teams with 3 runners on each team. A team was awarded 6 – n points if

Official Guide The 9 participants in a race were divided into 3 teams with 3 runners on each team. A team was awarded 6 – n points if one of its runners finished in nth place, where 1 ≤ n ≤ 5. If all the runners finished the race and if there were no ties, was each team awarded at least 1 point? 1)...


Line A is represented by the line y = 3x - 4. Which of the following represents the equation of a line that is

Veritas Prep

Line A is represented by the line y = 3x - 4. Which of the following represents the equation of a line that is perpendicular to Line A and that travels through point (1,2)?

A. y = -3x + 4
B. y = -x/3 + 4/3
C. y = -3x + 3/4
D. y = -x/3 + 7/3
E. y = -x/3 − 4

OA D


If you are drawing one card from a regular deck of cards (52 cards, with 13 sets of four), what is the probability that

Veritas Prep

If you are drawing one card from a regular deck of cards (52 cards with 13 sets of four), what is the probability that you draw a 4 or a spade?

A. 4/13
B. 5/13
C. 7/13
D. 9/13
E. 11/13

OA A


If the positive integer n is greater than 6, what is the remainder when n is divided by 6?

Manhattan Prep

If the positive integer n is greater than 6, what is the remainder when n is divided by 6?

1) When n is divided by 9, the remainder is 2
2) When n is divided by 4, the remainder is 1

OA C


At Perry High School, the ratio of students who participate in either the band program or the choral program to students

Princeton Review At Perry High School, the ratio of students who participate in either the band program or the choral program to students who participate in neither program is 3 to 8. If 220 students attend Perry High School, how many of them do NOT participate in either program? A. 40 B. 60 C. 100...


A certain game requires players to collect both blue tokens, which are worth b points each, and red tokens...

Princeton Review A certain game requires players to collect both blue tokens, which are worth b points each, and red tokens, which are worth r points each. If p percent of player A's points are from blue tokens and q percent of player A's token are red, which of the following is an expression for t...


Trains A and B travel at the same constant rate in opposite directions along the same route between Town G and Town H.

Manhattan Prep Trains A and B travel at the same constant rate in opposite directions along the same route between Town G and Town H. If, after traveling 2 hours, Train A passes Train B, how long does it take Train B to travel the entire distance between Town G and Town H? 1) Train B started travel...


Cheryl purchased 5 identical hollow pine doors and 6 identical solid oak doors for the house she is building. The

Official Guide Cheryl purchased 5 identical hollow pine doors and 6 identical solid oak doors for the house she is building. The regular price of each solid oak door was twice the regular price of each hollow pine door. However, Cheryl was given a discount of 25% off the regular price of each solid...


Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the

Official Guide AMOUNT OF BACTERIA PRESENT Time Amount 1:00 P.M. 10.0 grams 4:00 P.M. x grams 7:00 P.M. 14.4 grams Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how man...