List of top Quantitative Aptitude Questions

If \( m \) and \( n \) are positive integers, is \( \sqrt{m} \times \sqrt{n} \) an integer?
(1) \( \sqrt{m} \) is an integer.
(2) \( \sqrt{n} \) is an integer.

If \( \frac{x + y}{z}>0 \), is \( x<0 \)?
(1) \( x = y + 2 \)
(2) \( z<0 \)

If 5,000 invested for one year at p percent simple annual interest yields $500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars?
(1) k = 0.8p
(2) k = 8

In the \( xy \)-plane, if line \( k \) has negative slope and passes through the point \((-5, r)\), is the \( x \)-intercept of line \( k \) positive?
(1) The slope of line \( k \) is \( -5 \).
(2) \( r>0 \)

Is \( x>y \)? (1) \( x = y + 2 \) (2) \( \frac{x}{2} = y - 1 \)

What is the value of \( w + q \)?
(1) \( 3w = 3q - 3 \)
(2) \( 5w + 5q = 5 \)

Is \( \frac{5x^2 + 2}{25}<1 \)?
(1) \( 5x^2<1 \)
(2) \( x<0 \)

Is the standard deviation of the set of measurements \( x_1, x_2, x_3, x_4, \dots, x_{20} \) less than 3?
(1) The variance for the set of measurements is 4.
(2) For each measurement, the difference between the mean and that measurement is 2.

If \( k \) is an integer and \( 2<k<7 \), for how many different values of \( k \) is there a triangle with sides of lengths 2, 7, and \( k \)?

If \( n = \sqrt{\frac{16}{81}} \), what is the value of \( \sqrt{n} \)?

If \( \sqrt{3 - 2x} = \sqrt{2x + 1} \), then \( 4x^2 = \)?

The sequence \( a_1, a_2, a_3, \dots \) is such that \[ a_n = \frac{a_{n-1} + a_{n+1}}{2} \text{ for all } n \geq 3, \text{ if } a_4 = 4 \text{ and } a_5 = 20, \text{ what is the value of } a_2? \]

Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid 3.99 for each additional compact disc purchased. If a preferred customer purchased a total of 6 compact discs and paid $15.95 for the first compact disc, then the dollar amount that the customer paid for the 6 compact discs is equivalent to which of the following?

If \( p \) is the perimeter of rectangle \( Q \), what is the value of \( p \)?
(1) Each diagonal of rectangle \( Q \) has length 10.
(2) The area of rectangle \( Q \) is 48.

Does the integer \( k \) have at least three different positive prime factors?
(1) \( \frac{k}{15} \) is an integer.
(2) \( \frac{k}{10} \) is an integer.

In City X last April, was the average (arithmetic mean) daily high temperature greater than the median daily high temperature?
(1) In City X last April, the sum of the 30 daily high temperatures was 2,160°.
(2) In City X last April, 60 percent of the daily high temperatures were less than the average daily high temperature.

Of the 66 people in a certain auditorium, at most 6 people have their birthdays in any given month. Does at least one person in the auditorium have a birthday in January?
(1) More of the people in the auditorium have their birthday in February than in March.
(2) Five of the people in the auditorium have their birthday in March.

In a certain classroom, there are 80 books, of which 24 are fiction and 23 are written in Spanish. How many of the fiction books are written in Spanish?
(1) Of the fiction books, there are 6 more that are not written in Spanish than are written in Spanish.
(2) Of the books written in Spanish, there are 5 more nonfiction books than fiction books.

If Paula drove the distance from her home to her college at an average speed that was greater than 70 kilometers per hour, did it take her less than 3 hours to drive this distance? (1) The distance that Paula drove from her home to her college was greater than 200 kilometers. (2) The distance that Paula drove from her home to her college was less than 205 kilometers.

If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?
(1) The length of line segment XY is 3.
(2) The length of line segment OY is 1.5.

Is the range of the integers 6, 3, \( y \), 4, 5, and \( x \) greater than 9?
(1) \( y>3x \)
(2) \( y>x>3 \)

The only gift certificates that a certain store sold yesterday were worth either 100 each or 10 each. If the store sold a total of 20 gift certificates yesterday, how many gift certificates worth \$10 each did the store sell yesterday?
(1) The gift certificates sold by the store yesterday were worth a total of between 1,650 and 1,800.
(2) Yesterday the store sold more than 15 gift certificates worth 100 each.

Of the companies surveyed about the skills they required in prospective employees, 20 percent required both computer skills and writing skills. What percent of the companies surveyed required neither computer skills nor writing skills?
(1) Of those companies surveyed that required computer skills, half required writing skills.
(2) 45 percent of the companies surveyed required writing skills but not computer skills.

If the units digit of integer \( n \) is greater than 2, what is the units digit of \( n \)?
(1) The units digit of \( n \) is the same as the units digit of \( n^2 \).
(2) The units digit of \( n \) is the same as the units digit of \( n^3 \).