# Graduate Online Recruitment Test [grt4582]

37 Questions  Settings  This is a GMAT quantitative diagnostic test: Exam 1.

• 1.
When tossed, a certain coin has an equal chance of landing on either side.  If the coin is tossed 4 times, what is the probability that it will land on the same side each time?
• A.
• B.
• C.
• D.
• E.

• 2.
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 ?
• A.
• B.
• C.
• D.
• E.
• 3.
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?
• A.
• B.
• C.
• D.
• E.
• 4.
Plane A leaves San Francisco International Airport for New York’s John F. Kennedy International Airport, a distance of 2500 miles. At the same time, Plane B, taking the same route in the opposite direction, leaves New York’s John F. Kennedy International Airport for San Francisco International Airport. How long will it take Plane A and Plane B to cross, assuming the average speed of Plane A was 475 miles per hour and the average speed of Plane B was 525 miles per hour at the time the two planes passed?
• A.

5 hours

• B.

4 hours 30 minutes

• C.

3 hours 30 minutes

• D.

3 hours

• E.

2 hours 30 minutes

• 5.
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 ?
• A.

10 minutes

• B.

12 minutes

• C.

15 minutes

• D.

30 minutes

• E.

1 hour

• 6.
A glass was filled with 10 ounces of water, and 0.01 ounce of the water evaporated each day during a twenty-day period.  What percent of the original amount of water evaporated during this period?
• A.

0.002%

• B.

0.02%

• C.

0.2%

• D.

2%

• E.

20%

• 7.
(n-x) + (n-y) + (n-c) + (n-k) What is the value of the expression above? (1)   The average (arithmetic mean) of x, y, c, and k is n. (2)   x, y, c, and k are consecutive integers.
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 8.
If f is the function defined for all k by = , what is f(2k) in terms of f(k)?
• A.
• B.
• C.
• D.
• E.
• 9.
If x and y are integers and x > 0, is y > 0?   (1)   7x – 2y > 0   (2)   -y < x
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 10.
Each week a certain salesman is made a fixed amount equal to \$300 plus a commission equal to 5 percent of the amount of these sales that week over \$1,000.  What is the total amount the salesman was paid last week?   (1)   The total amount the salesman was paid last week is equal to 10 percent of the amount of these sales last week.   (2)   The salesman’s sales last week total \$5,000.
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 11.
If S is a set of ten consecutive integers, is the integer 5 in S? (1)   The integer –3 is in S. (2)   The integer 4 is in S.
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 12.
If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?   (1)   k is parallel to the line with equation y = (1-m)x + b +1.   (2)   k intersects the line with equation y = 2x + 3 at the point (2, 7).
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 13.
In June 1989, what was the ratio of the number of sales transactions made by Salesperson X to the number of sales transactions made by Salesperson Y? (1)   In June 1989, Salesperson X made 50 percent more sales transactions than Salesperson Y did in May 1989. (2)   In June 1989, Salesperson Y made 25 percent more sales transactions than in May 1989.
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 14.
Is xy > x2y2? (1)   14x2 = 3 (2)    y2 = 1
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 15.
Is x2 + y2 > 6? (1)   (x + y)2 > 6 (2)    xy = 2
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 16.
If s4v3x7 < 0, is svx < 0? (1)   v < 0 (2)   x > 0
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 17.
Is += 1 ? (1)   x  0 (2)   x  1
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 18.
Is , is  > 0 ? (1)   (2)
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 19.
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K.  What is the median weight of the 89 boxes on these shelves? (1)   The heaviest box on shelf J weighs 15 pounds. (2)    The lightest box on shelf K weighs 20 pounds.
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 20.
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.
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 21.
If ,  what is the value of ?   (1)       (2)
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 22.
If r is a constant and an = r·n for all positive integers n, for how many values of n is an < 100?   (1)   a50 = 500     (2)   a100 + a105 = 2,050
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 23.
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.
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 24.
If n and k are positive integers, is  an even integer?   (1)   n is divisible by 8.   (2)   k is divisible by 4.
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 25.
If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?
• A.

600

• B.

700

• C.

900

• D.

2,100

• E.

4,900

• 26.
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?
• A.
• B.
• C.
• D.
• E.
• 27.
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?
• A.

60

• B.

48

• C.

45

• D.

40

• E.

9

• 28.
• A.

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

• B.

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

• C.

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

• D.

EACH statement ALONE is sufficient.

• E.

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

• 29.
In a poll involving two yes- or no-questions, all the people who were asked the two questions answered “yes” or “no”. If 75 percent of these people answered “yes” to the first question, 55 percent of the people answered “yes” to the second question, and 20 percent of the people answered “no” to both questions, what percentage of the people answered “yes” to both questions?
• A.

70%

• B.

50%

• C.

25%

• D.

20%

• E.

10%

• 30.
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?
• A.

80%

• B.

40%

• C.

30%

• D.

33.33%

• E.

10%

• 31.
2x + y = 12                                      ≤ 12 For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
• A.

7

• B.

10

• C.

12

• D.

13

• E.

14

• 32.
Mary walked from home to work in the morning at an average speed of 3 miles per hour. She returned in the evening taking the same route running an average speed of 6 miles per hour. What was her average speed, in miles per hour, for the whole journey to and from work?
• A.

3.5

• B.

4

• C.

4.5

• D.

5

• E.

5.5

• 33.
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?
• A.

60

• B.

65

• C.

70

• D.

75

• E.

80

• 34.
In how many different ways can a chairperson and a secretary be selected from a committee of 9 people?
• A.

24

• B.

36

• C.

72

• D.

80

• E.

120

• 35.
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?
• A.

0.008

• B.

0.128

• C.

0.488

• D.

0.512

• E.

0.640

• 36.
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?
• A.
• B.
• C.
• D.
• E.
• 37.
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?
• A.

3 hours

• B.

3 hours 20 minutes

• C.

3 hours 36 minutes

• D.

4 hours 20 minutes

• E.

4 hours 30 minutes