Graduate Online Recruitment Test [grt4582]

A student’s average (arithmetic mean) test score on 4 tests is 78.  What must be the student’s score on a 5th test for the student’s average score on the 5 tests to be 80?

• 80

• 82

• 84

• 86

• 88

On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains.  If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?  

• 0.008

• 0.128

• 0.488

• 0.512

• 0.640

Theater M has 25 rows with 27 seats in each row.  How many of the seats were occupied during a certain show? (1)   During the show, there was an average (arithmetic mean) of 10 unoccupied seats per row for the front 20 rows.   (2)   During the show, there was an average (arithmetic mean) of 20 unoccupied seats per row for the back 15 rows.  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

 In the xy-plane, line l and line k intersect at the point .  What is the slope of line l? (1)  The product of the slopes of line l and line k is –1.   (2)    Line k passes through the origin.  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

A certain candy manufacturer reduced the weight of candy bar M by 20 percent but left the price unchanged. What was the resulting percent increase in the price per ounce of the candy bar M?

• 5%

• 10%

• 15%

• 20%

• 25%

The tortoise and the hare are racing. The faster hare gives the tortoise a 1-hour head start. The tortoise runs the race at a constant speed of 2 kilometers per hour. The hare runs the race at a constant speed of 10 kilometers per hour. If the hare and the tortoise start from the same point and follow the same route, how long will it take the hare to overtake the tortoise ?  

• 10 minutes

• 12 minutes

• 15 minutes

• 30 minutes

• 1 hour

What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?   (1)   The average height of the students in class X is 120 centimeters.   (2)   The average height of the students in class X and class Y combined is 126 centimeters.  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

Yesterday each of the 35 members of a certain task force spent some time working on project P.  The graph shows the number of hours and the number of members who spent that number of hours working on project P yesterday.  What was the median number of hours that the members of the task force spent working on project P yesterday?  

• 2

• 3

• 4

• 5

• 6

The mass of 1 cubic meter of a substance is 800 kilograms under certain conditions. What is the volume, in cubic centimeters of 1 gram of this substance under these condition (1 kilogram= 1000 grams and 1 cubic meter = 1,000,000 cubic centimeters. 

• 0.80

• 1.25

• 8.00

• 12.50

• 80.00

In how many different ways can a chairperson and a secretary be selected from a committee of 9 people?  

• 24

• 36

• 72

• 80

• 120

  For the cube shown above, what is the degree measure of PQR?  

• 30

• 45

• 60

• 75

• 90

If , and , which of the following is NOT a possible value of ?

• -2

• -1

• 0

• 1

• 2

If f is the function defined for all k by = , what is f(2k) in terms of f(k)?

In the xy-plane, line k passes through the point (1,1) and line m passes through the point (1,-1).Are the lines k and m perpendicular to each other? (1)   Lines k and m intersect at the point (1,-1).   (2)   Line k intersects the x axis at the point (1,0).  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

There are 6 pairs of balls with each pair in a different color. If we select 2 from the 12 balls without replacement, what’s the probability of selecting 2 balls with the same color?  

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2ⁱ3^k5^m7^p, then i + k + m + p =

• 4

• 7

• 8

• 11

• 12

In the figure above, O is the center of the circle.  If the area of the shaded region is 2π, what is the value of x?  

  In the figure shown, the length of line segment QS is  . What is the perimeter of equilateral triangle PQR ?

On a map Town G is 10 centimeters due east of Town H and 8 centimeters due south of Town J.  Which of the following is closest to the straight-line distance, in centimeters, between Town H and Town J on the map?

• 6

• 13

• 18

• 20

• 24

Pierre is driving 50 miles per hour for the first 20 miles of a 40-mile trip. What must be his average speed in the remaining 20 miles in order for his total average speed to be 60 miles per hour?  

• 60

• 65

• 70

• 75

• 80

If an automobile averaged 22.5 miles per gallon of gasoline, approximately how many kilometers per liter of gasoline did the automobile average?  (1 mile = 1.6 kilometers and 1 gallon = 3.8 liters, both rounded to the nearest tenth.)  

• 3.7

• 9.5

• 31.4

• 53.4

• 136.8

Joshua and Jose work at an auto repair center with 4 other workers. For a survey on healthcare insurance, 2 of the 6 workers will be randomly chosen to be interviewd. What is the probability that Joshua and Jose both will be chosen? 

If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?  

• 600

• 700

• 900

• 2,100

• 4,900

The points R, T, and U lie on a circle that has radius 4.  If the length of arc RTU is , what is the length of line segment RU?  

Which of the following fractions has a decimal equivalent that is a terminating decimal?

At a garage sale, all of the prices of the items sold were different.  If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?

• 33

• 34

• 35

• 36

• 37

When flipped, a certain coin has an equal chance of landing on either side.  If the coin is flipped 6 times, what is the probability that it will land heads up on the first 3 flips,  and not on the last 3 ?  

What is the value of the integer n? (1)   n(n + 2) = 15   (2)   (n + 2)ⁿ = 125  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively.  If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?     I.               3 II.              7 III.            12

• I only

• II only

• III only

• I and III only

• I, II, and III

The number of books read by 7 students is 10,5, , 29 and 20. what was the range of books read by 7 students? (1)      (2)    

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

If 5^x – 5^{x - 3} = (124)(5^y), what is y in terms of x?

• X

• X - 6

• X - 3

• 2x + 3

• 2x + 6

  Lines m and n intersect, as shown in the figure above.  What is the value of u - w? (1)   u = 90   (2)   Lines m and n are perpendicular.  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

Is x² + y² > 6? (1)   (x + y)² > 6 (2)    xy = 2  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

If s⁴v³x⁷ < 0, is svx < 0? (1)   v < 0 (2)   x > 0  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

If the length of a certain rectangle is 2 greater than the width of the rectangle, what is the perimeter of the rectangle?   (1)   The length of each diagonal of the rectangle is 10.   (2)   The area of the rectangular region is 48.  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

Of 500 people surveyed, 78 percent said they use their laptop computers at home, 65 percent said they use them in cafes, and 52 percent said they use them both at home and in cafes. How many of the people surveyed said they do NOT use their laptop computers either at home or in cafes?

• 60

• 48

• 45

• 40

• 9

What is the total value of Company H’s stock?     (1)   Investor P owns  of the shares of Company H’s total stock.   (2)   The total value of Investor Q’s shares of Company H’s stock is $16,000.  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

Of the families in City X in 1994, 40 percent owned a personal computer.  The number of families in City X owning a computer in 1998 was 30 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994.  What percent of the families in City X owned a personal computer in 1998?

• 50%

• 52%

• 56%

• 70%

• 74%

One day Hotel Merinda rented 75 percent of its rooms, including  of its luxury rooms. If 60 percent of Hotel Merinda’s rooms are luxury rooms, what percent of the rooms that were NOT rented are luxury rooms?  

• 80%

• 40%

• 30%

• 33.33%

• 10%

2x + y = 12                                      ≤ 12 For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?  

• 7

• 10

• 12

• 13

• 14

Three thousand families live in a certain town. How many families who live in the town own neither a car nor a television set? (1)   Of the families who live in the town, 2,980 own a car.   (2)   Of the families who live in the town, 2,970 own both a car and a television set.   

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

If x is equal to the sum of the even integers from 40 to 60, inclusive, and y is the number of even integers from 40 to 60, inclusive, what is the value of x+y ?

• 550

• 551

• 560

• 561

• 572

The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers.  If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will be an English teacher and a Mathematics teacher?  

Two different pipes fill the same pool. Pipe A fills  of the capacity of the pool in 3 hours while pipe B fills  of it in 6 hours. If the two pipes fill the pool simultaneously with their respective rates, how long will it take for the pool to be filled to capacity?  

• 3 hours

• 3 hours 20 minutes

• 3 hours 36 minutes

• 4 hours 20 minutes

• 4 hours 30 minutes

In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?  

What is the sum of a certain pair of consecutive odd integers? (1)   At least one of the integers is negative.   (2)   At least one of the integers is positive.  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.

Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours.  S and T, working together at their respective constant rates, can do the same job in 5 hours.  How many hours would it take R, working alone at its constant rate, to do the same job?

• 8

• 10

• 12

• 15

• 20

A certain list consist of several different integers. Is the product of all integers in the list positive? (1)   The product of the greatest and smallest of the integers in the list is positive.   (2)   There is an even number of integers in the list.  

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

• EACH statement ALONE is sufficient.

• Statements (1) and (2) TOGETHER are NOT sufficient.