TCS: Can You Pass The Numerical Aptitude Test?

1) A train travels 240 miles at a speed of 80 miles/hour. On the way back the train slows down to 40 miles/hour.
What is the overall time the train traveled?

7

9

10

12

4

The overall time the train traveled can be calculated by dividing the total distance traveled (240 miles) by the average speed of the train. The average speed can be found by taking the harmonic mean of the two speeds (80 miles/hour and 40 miles/hour). The harmonic mean is calculated by dividing the number of values by the sum of their reciprocals. In this case, the harmonic mean is 2(1/80 + 1/40) = 2(1/80 + 2/80) = 2/120 = 1/60. Therefore, the overall time the train traveled is 240 miles / (1/60 hour/mile) = 240 * 60 = 14400 minutes = 9 hours.

Explanation

The overall time the train traveled can be calculated by dividing the total distance traveled (240 miles) by the average speed of the train. The average speed can be found by taking the harmonic mean of the two speeds (80 miles/hour and 40 miles/hour). The harmonic mean is calculated by dividing the number of values by the sum of their reciprocals. In this case, the harmonic mean is 2(1/80 + 1/40) = 2(1/80 + 2/80) = 2/120 = 1/60. Therefore, the overall time the train traveled is 240 miles / (1/60 hour/mile) = 240 * 60 = 14400 minutes = 9 hours.

2) Nick returned from the market with a bag full of fruits and vegetables: 4 tomatoes, 10 onions, and 16 blueberries. Approximately, what is the percentage of tomatoes out of all the fruits and vegetables?

12.5%

13.3%

11.6%

10%

20%

To find the percentage of tomatoes out of all the fruits and vegetables, we need to calculate the ratio of the number of tomatoes to the total number of fruits and vegetables. The total number of fruits and vegetables is 4 (tomatoes) + 10 (onions) + 16 (blueberries) = 30. The ratio of tomatoes to the total is 4/30. To find the percentage, we multiply this ratio by 100: (4/30) * 100 = 13.3%. Therefore, the correct answer is 13.3%.

Explanation

To find the percentage of tomatoes out of all the fruits and vegetables, we need to calculate the ratio of the number of tomatoes to the total number of fruits and vegetables. The total number of fruits and vegetables is 4 (tomatoes) + 10 (onions) + 16 (blueberries) = 30. The ratio of tomatoes to the total is 4/30. To find the percentage, we multiply this ratio by 100: (4/30) * 100 = 13.3%. Therefore, the correct answer is 13.3%.

3)

Six lawyers are summoned to individual meetings at the firm's Chief Executive Office. Due to a rough financial quarter, 3 lawyers are to be laid off. David has just recently signed a long term contract that ensures his place for the next three years, and James was already notified yesterday that he is about to be promoted. How many dismissal combinations are currently possible?

24

20

4

5

6

The question states that 3 lawyers need to be laid off. However, David has a long term contract that ensures his place for the next three years, and James was already notified that he is about to be promoted. Therefore, David and James cannot be laid off. This means that out of the remaining 4 lawyers, only 3 can be laid off. So, the number of dismissal combinations is 4.

Explanation

The question states that 3 lawyers need to be laid off. However, David has a long term contract that ensures his place for the next three years, and James was already notified that he is about to be promoted. Therefore, David and James cannot be laid off. This means that out of the remaining 4 lawyers, only 3 can be laid off. So, the number of dismissal combinations is 4.

4) In the horse market, five Arabian horses can be bought for the price of two Mongolian horses and one Australian horse. How many Mongolian horses can be bought for the value of three Australian horses? A. A Mongolian horse costs 60,000 pounds.

B. Two Mongolian horses can be bought for the price of three Arabian horses. Which combinations of the statements can answer the above question?

A and not B (only A)

B and not A (only B)

A and B together

A or B (alone)

Not A, not B

Statement B states that two Mongolian horses can be bought for the price of three Arabian horses. This information allows us to determine the relative value of Mongolian horses compared to Arabian horses. Since we know that five Arabian horses can be bought for the price of two Mongolian horses and one Australian horse, we can conclude that the value of two Mongolian horses is equal to the value of five Arabian horses. Therefore, the value of three Australian horses can be determined by multiplying the value of two Mongolian horses by 1.5. So, the answer is B and not A (only B).

Explanation

Statement B states that two Mongolian horses can be bought for the price of three Arabian horses. This information allows us to determine the relative value of Mongolian horses compared to Arabian horses. Since we know that five Arabian horses can be bought for the price of two Mongolian horses and one Australian horse, we can conclude that the value of two Mongolian horses is equal to the value of five Arabian horses. Therefore, the value of three Australian horses can be determined by multiplying the value of two Mongolian horses by 1.5. So, the answer is B and not A (only B).

5)

Hannah and her parents are walking in the street. Her parents walk at a rate of 80 steps per minute. The father precedes the mother by 12 steps. Hannah walks behind her parents at a rate of 90 steps per minute. The average length of a step is equal among all family members. How many seconds would pass since the moment she passes her mother until the moment she passes her father?

8

12

1.2

72

80

Since Hannah walks at a faster rate than her parents, she will catch up to her mother first. The time it takes for her to catch up to her mother is equal to the number of steps her mother is ahead divided by the rate at which Hannah walks faster than her mother. In this case, her mother is 12 steps ahead and Hannah walks 10 steps per minute faster, so it would take her 1.2 minutes (72 seconds) to catch up to her mother.

Explanation

Since Hannah walks at a faster rate than her parents, she will catch up to her mother first. The time it takes for her to catch up to her mother is equal to the number of steps her mother is ahead divided by the rate at which Hannah walks faster than her mother. In this case, her mother is 12 steps ahead and Hannah walks 10 steps per minute faster, so it would take her 1.2 minutes (72 seconds) to catch up to her mother.

6)

A mobile company offers insurance that covers cases of theft and accidental water damage. According to their policy, the insurance pays 60% and 50%, respectively and with a £30 deductible. This means the client pays the first £30, after which the insurance pays 60% in the case of a theft and 50% in the case of accidental water damage. How much will a client pay if her cell phone worth £1,080 was stolen?

£420

£450

£464

£660

678

If the client's cell phone worth £1,080 was stolen, the insurance policy states that the client will have to pay the first £30 as a deductible. After that, the insurance will pay 60% of the remaining amount.

So, the remaining amount after the deductible is £1,080 - £30 = £1,050.

60% of £1,050 is £630.

Therefore, the client will have to pay £30 + £630 = £660.

Therefore, the correct answer is £660.

Explanation

If the client's cell phone worth £1,080 was stolen, the insurance policy states that the client will have to pay the first £30 as a deductible. After that, the insurance will pay 60% of the remaining amount.

So, the remaining amount after the deductible is £1,080 - £30 = £1,050.

60% of £1,050 is £630.

Therefore, the client will have to pay £30 + £630 = £660.

Therefore, the correct answer is £660.

7) A sphere-shaped moon completes a rotation around its axis every 80 hours. Within 20% of that time it also completes a rotation around a sphere-shaped planet.

Between December 4th 6AM and December 7th 10PM, how many degrees of rotation around the planet did any point on the moon complete?

1980

882

396

196

2376

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Explanation

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8) Each container includes 6 electrical appliances. Each shipment contains the same number of microwave containers.
A. The number of appliances in a shipment containing 3 more than twice as many TV-set containers than microwave containers. B. The number of appliances in a shipment containing 2 fewer than 3 times as many TV-set containers than microwave containers.

A is greater than B

B is greater than A

A and B are equal.

Insufficient Data

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Explanation

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