CCAT Mathematical Reasoning: Unitary Method

Note the meanings of the symbols being used here and later:

• * (or asterisk / star) = X (the multiplication sign): Example: 5 * 3 = 15
• / (or slash) = the division sign: Example: 10 / 2 = 5

Unitary Method

The basic theory here is that we find the value (could be price, or weight, or time etc) for 1 (one), then find the value for many.

Q1: If a factory produces 15 cars per hour, how many cars can it produce in eight hours?

Answer: This is the simplest type of Unitary Method question. The value of 1 (in this case, the number of cars produced in 1 hour) is given, and we need to find the value of many (in this case, cars produced in 8 hours).

Number of cars produced in 1 hour = 15

Therefore, number of cars produced in 8 hours = 8 * 15 = 120 cars

Q2: A man can chop 24 logs in 3 hours. How long will it take him to chop 56 logs?

Answer: Here we have been given the time taken to chop 24 logs. Using this, we must first find the time taken to chop 1 log. Then we can find the time taken to chop 56 logs.

Time taken to chop 24 logs = 3 hours

So, time taken to chop 1 log = 3 / 24 hours

And, time needed to chop 56 logs = (3 / 24) * 56 = (⅛) * 56 = 56 / 8 = 7 hours.

Now, there are simple variations on the above theme. For instance:

Q3: A magazine sells for 75 cents. How much will it cost to buy seven magazines?

Answer: The method of solving this is the same, a slight conversion from cents to dollars and cents is required at the end:

Cost of 1 magazine = 75 cents

Hence, cost of 7 magazines = 7 * 75 = 525 cents = $5.25

Q4: It takes a machine 45 minutes to make a part. How long will it take to make 9 parts?

Answer: Time taken to make 1 part = 45 minutes

Hence, time taken to make 9 parts = 9 * 45 = 405 minutes = 405 / 60 hours = 6 hours 45 minutes

Q5: An electrician requires 2.5 metres of wire to electrify a room. How much wire will he need to electrify 30 rooms?

Answer: Length of wire needed for 1 room = 2.5 metres

Hence, length of wire needed for 30 rooms = 30 *2.5

= 3 * 25

= 75 metres

Q6: A juicemaker uses 3.5 ounces of concentrate to make a gallon of juice. How much concentrate is needed to make 200 gallons of juice?

Answer: Amount of concentrate needed to make 1 gallon = 3.5 ounces

Hence, amount of concentrate needed to make 200 gallons = 200 * 3.5

= 20 * 35

= 700 ounces

Q7: A customer service rep handles 7.5 calls in one hours, while hercolleague handles 8 calls per hour. If both the reps start working at the same time, and each spends 60 hours handling calls over a two week period, how many calls will they handle in total?

Answer: Number of calls handled per hour by 1st rep = 7.5

Number of calls handled per hour by 2nd rep = 8

Hence, number of calls handled per hour by both of them = 7.5 + 8 = 15.5

And number of calls handled in 60 hours = 60 * 15.5 = 6 * 155 = 930

(Note: 60 * 15.5 = (60 *15) + (60 * 0.5) = 900 + 30 = 930)

Now try these on your own (solutions are provided below). Note the CCAT trick of sometimes making things harder by using words instead of numbers, for example, “seven” instead of “7”:

Q-1: If a factory produces 16 lawn mowers per hour, how many lawn mowers can it produce in seven hours?

Q-2: If a student completes 12 courses in one year, how many courses does he complete in six years?

Q-3: An artist can draw 18 sketches in 2 hours. How long will it take her to draw 63 sketches?

Q-4: Mrs. Brown can milk 24 cows in 2 hours. How many cows can she milk in 9 hours?

Solutions:

Q-1: If a factory produces 16 lawn mowers per hour, how many lawn mowers can it produce in seven hours?

Answer: Number of lawn mowers produced in one hour = 16

Hence, number of lawn mowers produced in seven hours = 7 * 16 = 112

Q-2: If a student completes 12 courses in one year, how many courses does he complete in six years?

Answer: Number of courses produced in one year = 12

Hence, number of courses produced in six years = 6 * 12 = 72

Q-3: An artist can draw 18 sketches in 2 hours. How long will it take her to draw 63 sketches?

Answer: Time taken to draw 18 sketches = 2 hours

Hence, time taken to draw 1 sketch = 2 / 18 hours

And, time taken to draw 63 sketches = (2 / 18) * 63

= (2 / 2) * 7

= 7 hours

Q-4: Mrs. Brown can milk 24 cows in 2 hours. How many cows can she milk in 9 hours?

Answer: In 2 hours, the number of cows which can be milked = 24

Hence, in 1 hour, the number of cows which can be milked = 24 / 2 = 12

And, in 9 hours, the number of cows which can be milked = 9 * 12

= 108 cows

Coming next: Mathematical Reasoning Percentages: https://av-krishnan.medium.com/ccat-mathematical-reasoning-percentages-bd561711ced9

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