Quant Questions Flashcards
If 60! is written out as an integer, with how many consecutive 0’s will that integer end? 6 12 14
- 14 2’s and 5s make ten. 5 is the constraining factor. Keep in mind there’re extra 5’s in 25 and 50.
If the square root of p^2 is an integer greater than 1, which of the following must be true? I. p^2 has an odd number of positive factors II. p^2 can be expressed as the product of an even number of positive prime factors III. p has an even number of positive factors Which one(s) are true?
I and II I - For any perfect square, the number of factors will always be odd. II - A perfect square will always be able to be expressed as the product of an even number of prime factors because a perfect square is formed by taking some integer and squaring it.
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210? 14 30 42
- 16 = 2 x 2 x 2 x 2 45 = 3 x 3 x 5 210 = 2 x 3 x 5 x 7 n MUST HAVE a factor of 2, 2, and 3. maybe a 7 def not a 5.
If x is a prime number, what is the value of x? (1) 2 x + 2 is the cube of a positive integer. (2) The average of any x consecutive integers is an integer.
E - (1): x can equal to 3 or 31 which yields 8 and 64 - (2): simply tells us x is an odd integer
How many factors does 36^2 have?
25 -use the prime box and determine that 36^2 = 2x2x2x2x3x3x3x3 -You have 5 independent choices for 2 AND 5 independent choices for 3: 5*5 = 25
If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a? 13 18 50
13 a/b = 286/100 = 143/50 –> 50a = 143b 5x5x2xa = 11x13xb, a must be divisible by 11 or 13.
Guests at a recent party ate a total of fifteen hamburgers. Each guest who was neither a student nor a vegetarian ate exactly one hamburger; no other guests ate hamburgers. If half of the guests were vegetarians, how many guests attended the party? (1) The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians. (2) 30% of the guests were vegetarian non-students.
A. - double the rate -> double the first number of the ratio - you should be able to find that there are 70 attendee in total. CAT 5 - “Party Burgers (2)”
Bill has a set of 6 black cards and a set of 6 red cards. Each card has a number from 1 through 6, such that each of the numbers 1 through 6 appears on 1 black card and 1 red card. Bill likes to play a game in which he shuffles all 12 cards, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
17/33 P(1 - no pairs) find P(no pair from first draw) = 1 P(no pair from second draw) = 10/11 P(no pair from third draw) = 8/10 P(no pair from fourth draw) = 6/9 multiply them all = 16/33 1 - 16/33 = 17/33
The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in four colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?
32 - number of ways to select first car = 8 - number of ways to select second car = 6 (can’t have same color) - number of ways to select third car = 4 - divide by factorial of number of choices to eliminate over-counting = 3!
It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?
z(y-x)/(x+y) - try smart numbers or - use RTD chart and find out that t = xy/(x+y), then plug t back into the equation for delta(Distance).
30 people in total attended an office party for a colleague’s birthday. The birthday cake was sliced into exactly 32 pieces, all of which were eaten. Did everyone who attended eat at least one slice of cake? (1) One person ate exactly 2 slices of cake. (2) One person ate exactly 3 slices of cake.
(1) INSUFFICIENT: Since one person ate exactly 2 slices of cake, there are 30 slices for the remaining 29 people. It is possible, though not certain, that each of the remaining people ate at least one slice of cake. (2) INSUFFICIENT: Similar to (1), there are 29 slices of cake remaining for the other 29 people. It is possible, but not certain, that everyone else had exactly one slice of cake. (1) AND (2) SUFFICIENT: Combined we know that 2 of the people ate a combined 5 slices of cake. Thus there are only 27 slices remaining for the other 28 people, which is not enough for everyone to have his or her own slice of cake.
If a and b are positive integers such that a/b = 2.86, which of the following must be a divisor of a? 10 13 18 26 50
13 -> 50a = 143b -> 5x5x2xa = 11x13xb -> we know that a must be divisble by 11, 13 or b
If 6xy = x2y + 9y, what is the value of xy? (1) x = –2 (2) x < 0
D x = 3 or y = 0 1 -> y = 0 –> xy = 0 2-> x<0 -> y = 0 –> xy = 0 Retarded.
nCr define. 5C2
n!/(r!(n-r)!) 5!/(2!3!) = 10
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
3/7 - total = 8C4 = 70 - ways to choose two women = 5C2 = 10 - ways to choose two men = 3C2 = 3 3x10/70 = 3/7
