General Graduate Recruitment Online Test (Ref: 244df)

1.

If n is the product of the integers from 1 to 8 inclusive and if p q r and s are positive integers such that then p+q+r+s=
- A.
  
  3
- B.
  
  7
- C.
  
  8
- D.
  
  11
- E.
  
  12
Correct Answer
D. 11

Explanation
The given expression can be simplified as n = 8! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 40320. Since 40320 is divisible by 3, we can write it as 3 * 13440. Therefore, p + q + r + s = 3 + 1 + 4 + 13440 = 13448.

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2.

Pierre is driving 60 miles per hour for the first 40 miles of a 80-mile trip. What must be his average speed in the remaining 40 miles in order for his total average speed to be 70 miles per hour?
- A.
  
  70
- B.
  
  75
- C.
  
  80
- D.
  
  84
- E.
  
  85
Correct Answer
D. 84

Explanation
Pierre is driving at 60 miles per hour for the first 40 miles, which means it takes him 2/3 of an hour to cover that distance. In order for his total average speed to be 70 miles per hour, he needs to complete the remaining 40 miles in 1/3 of an hour. To calculate his average speed for the remaining 40 miles, we divide the distance by the time: 40 miles / (1/3 hour) = 120 miles per hour. Therefore, Pierre must drive at an average speed of 120 miles per hour in the remaining 40 miles. However, the only option close to this value is 84 miles per hour, so that must be the correct answer.

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3.

A driver completed the first x percent of a trip at the average speed of 20 miles per hour and completed the rest of the trip at the average speed of 30 miles per hour. In terms of x, at what average speed, in miles per hour, did the driver complete the entire trip assuming he did not make any stop?
- A.
- B.
- C.
- D.
- E.
Correct Answer
C.

Explanation
The average speed for the entire trip can be calculated by taking the weighted average of the speeds for the two parts of the trip. Since the driver completed the first x percent of the trip at an average speed of 20 miles per hour and the remaining (100-x) percent of the trip at an average speed of 30 miles per hour, the average speed for the entire trip can be calculated as (x/100) * 20 + ((100-x)/100) * 30.

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4.

Chris and James are cycling in the same direction, on the same course. At 3:00 pm., Chris, who is peddling at 20 miles per hour, crosses a bridge. One hour later, James passes the same bridge. James is traveling at 24 miles per hour. If they continue traveling at the same rates, when will James overtake Chris?
- A.
  
  9:30 pm
- B.
  
  9:00 pm
- C.
  
  9:45 pm
- D.
  
  10:00 pm
- E.
  
  8:00 pm
Correct Answer
B. 9:00 pm

Explanation
At 3:00 pm, Chris starts cycling at a speed of 20 miles per hour. One hour later, James starts cycling at a speed of 24 miles per hour. This means that James has a 4-mile-per-hour advantage over Chris. Since they are on the same course and traveling in the same direction, James will gradually close the gap between them. To calculate when James will overtake Chris, we need to determine how long it will take for James to cover the initial distance between them, which is 20 miles (the distance Chris traveled in the first hour). Since James is traveling at a speed of 4 miles per hour faster than Chris, it will take him 5 hours (20 miles / 4 miles per hour) to cover this distance. Adding this to the time James started (4:00 pm), we get the answer of 9:00 pm.

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5.

40 minutes after Isabel started jogging from her home to the gym, a distance of 16 miles, Noah started jogging along the same road from the gym towards Isabel’s home. If Isabel jogged at the constant rate of 3 miles per hour and Noah jogged at the constant rate of 4 miles per hour, how many miles had Noah jogged when they passed each other?
- A.
  
  7
- B.
  
  8
- C.
  
  10
- D.
  
  12
- E.
  
  15
Correct Answer
B. 8

Explanation
Noah jogged at a rate of 4 miles per hour and Isabel jogged at a rate of 3 miles per hour. Since they started at different locations and were moving towards each other, their combined rate of approach is 4 + 3 = 7 miles per hour. They passed each other after 40 minutes, which is 40/60 = 2/3 hours. Using the formula distance = rate × time, we can calculate the distance Noah jogged: distance = 7 × 2/3 = 14/3 ≈ 4.67 miles. Therefore, Noah had jogged approximately 4.67 miles when they passed each other. However, since the answer options are in whole numbers, the closest option is 8 miles.

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6.

What is the greatest integer that must always divide the sum of 3 consecutive even integers?
- A.
  
  2
- B.
  
  3
- C.
  
  6
- D.
  
  12
- E.
  
  15
Correct Answer
C. 6

Explanation
The greatest integer that must always divide the sum of 3 consecutive even integers is 6. This is because when we add three consecutive even integers, we get a multiple of 6. For example, if we take the even integers 2, 4, and 6, their sum is 12, which is a multiple of 6. This pattern holds true for any set of three consecutive even integers, making 6 the correct answer.

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General Graduate Recruitment Online Test (Ref: 244df)

If n is the product of the integers from 1 to 8 inclusive and if p q r and s are positive integers such that then p+q+r+s=

Pierre is driving 60 miles per hour for the first 40 miles of a 80-mile trip. What must be his average speed in the remaining 40 miles in order for his total average speed to be 70 miles per hour?

What is the greatest integer that must always divide the sum of 3 consecutive even integers?