# FREE PSEE Arithmetic Reasoning Question and Answers

#### There are 28 blue pencils and 7 black pencils in a box.

How many black pens are there compared to blue pens?

Explanation:

Black and blue pens are 7 to 28 or 7:28 in ratio. Divide both sides by 7 to get the lowest terms (1:4)

#### What percentage of the page can Kate type if she can type a page in p minutes?

Explanation:

This is a straightforward direct proportion issue.

x pages can be typed by Kate in 5 minutes if she can type 1 page in p minutes.

Cross multiplication is what we do. x * p = 5 * 1

So, x = 5/p.

#### A automobile is being sold for $12,590, which is a 20% discount from the original cost.

What was the initial cost?

Explanation:

Original price = x,

80/100 = 12590/X,

80X = 1259000,

X = 15,737.50

#### How long will it take for both Sarah and John to paint a house if Sarah takes four hours and Johnny takes six?

Explanation:

This is an inverse ratio problem.

1/x = 1/a + 1/b where a is the time Sarah can paint a house, b is the time Johnny can paint a house, x is the time Sarah and Johnny can together paint a house.

So,

1/x = 1/4 + 1/6 … We use the least common multiple in the denominator which is 24:

1/x = 6/24 + 4/24

1/x = 10/24

x = 24/10

x = 2.4 hours.

In other words; 2 hours + 0.4 hours = 2 hours + 0.4‣60 minutes

= 2 hours 24 minutes

#### According to the manager of a weaving mill, ten machines could create 1450 meters of cloth if they operated at 100% efficiency for eight hours. Four machines operate at a 95% efficiency due to technical issues, while the remaining six operate at a 90% efficiency. In an eight-hour period, how many meters of cloth can these machines produce?

Explanation:

One machine can generate 1450/10 = 145 meters of cloth with 100% efficiency.

4 machines generate 4 * 145 * 95/100 = 551 m of cloth while operating at 95% efficiency.

Six machines can create 6 * 145 * 90/100 = 783 m of cloth with a 90% efficiency.

All 10 machines produced a total of 551 + 783 = 1334 m of cloth.

We didn't need to use the time to arrive at the solution because the information is given and the question are based on 8 hours.

#### Employees of a discount appliance retailer get an extra 20% off the item's lowest price.

How much will an employee pay if he buys a dishwasher during a 15% off sale when the dishwasher originally cost $450?

Explanation:

The dishwasher is $450 in price.

15% off the total payment equals 450‣15/100 = $67.5

The reduced cost is $382.5 (450 - 67.5).

20% more off the lowest price, or 382.5 ‣ 20/100, or $76.5.

The final discounted cost is therefore = 382.5 - 76.5 = $306.0049.

#### A worker put in 11 hours a day. Her typical workday is 7.5 hours, with the additional time being overtime for which she was compensated at 1.5 times her standard hourly rate.

What was her standard hourly rate for that day if she was paid $112 for the day?

Explanation:

The employee is paid in normal time for 7.5 hours and 1.5 times the regular rate for the remaining hours (3.5 hours). 12.75 hours are compensated in total (7.5 + 1.5 x 3.5). You may calculate her hourly rate, $8.78, by dividing the amount she received for the day ($112) by the number of hours she was paid ($12.75).