Word Problems

[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_column_text]There is a video for this lesson:

[/vc_column_text][/vc_column_inner][/vc_row_inner][vc_tta_accordion active_section=”0″ collapsible_all=”true”][vc_tta_section title=”Answer to last question in the video” tab_id=”1608978420089-6716cf25-26c2″][vc_column_text]This question mechanism is often used in the real test. It measures your ability to move between different fraction forms (decimals, fractions, percentages) and find the whole/parts of the whole. It may appear in simple versions, and in slightly more complex versions, as is the one below, where more time may be needed for calculations.

Mary purchased a box of marbles. Of all the marbles in the box, 80% were red, 1/8 were green, and the remaining nine were blue. How many green marbles were in the box?

Solution:

All marble proportions should sum up to 1, or 100%:

Red: 80%

Green: 1/8 = 12.5%

Blue: 1- (80+12.5)=1-92.5=7.5%

We were told that 9 marbles were blue. i.e. 9 marbles are 7.5% of all marbles. These two data points allow us to find the number of green marbles, using a simple ratio equation:

7.5% = 9 blue marbles

75%=90 marbles, i.e. 3/4 of a number is 90

3/4*x= 90

3x=360

x=120

Total number of marbles is 120.

12.5%, or 1/8 of the whole are green marbles

120*(1/8) = 120/8 =  15 green marbles[/vc_column_text][/vc_tta_section][/vc_tta_accordion][vc_separator][/vc_column][/vc_row][vc_row][vc_column][vc_column_text]Word problems are one of the most challenging topics included in the PI cognitive assessment. In the absence of a calculator, you need to respond quickly and utilize a handful of shortcuts to save your time on lengthy calculations. [/vc_column_text][/vc_column][/vc_row][vc_row][vc_column][vc_message icon_fontawesome=”fa fa-gratipay”]

Tip: Pick your fights wisely

This is the most important rule of thumb when approaching a word problem in a cognitive ability test. If it’s too long or too hard then it might not be worth the hassle. There’s no point in crunching on a lengthy and difficult word problem. Instead, focus on the low-hanging fruit and move on to the next question.

But how can you tell if a word problem is too difficult? Simply start reading it, and ask yourself whether the information in the question is straight forward or not. Does it take a long time to read and understand it? Is there a lot of data (e.g. a table) that is packed with extra information which you find confusing? If that’s the case, then just mark an educated guess and move on. If you have an option to flag the question, flag it, just in case you’ll have time to get back to it. But remember to always mark an answer choice before moving on![/vc_message][vc_column_text]

Practice, Practice, Practice

There are a few calculation shortcuts that can really save your time on the test. Below is a tab list of word problem topics which give you some starter tips. Below the tabs, you’ll find untimed, instructional practice sessions which go through those word problem topics. Each question was hand-picked and is followed by an explanation with solving tips. I highly recommend taking all the quizzes and paying attention to the explanations. [/vc_column_text][/vc_column][/vc_row][vc_row][vc_column][vc_tta_accordion active_section=”89″ collapsible_all=”true”][vc_tta_section title=”Percentages” tab_id=”1608982677394-22edbf14-f931″][vc_row_inner][vc_column_inner][vc_column_text]Percent means per 100 (value/100). Before you start the quiz, remember the following rules:

1. Finding 10% and 1%: those two values can really help cut down on calculations. To find 10% of a certain number, simply shift the decimal point one place to the left. To find 1% shift it two places to the left.
2. Quick trick 1: remove the zeros
   20% of 30 is 2×3=6
   25% of 40 is 2.5×4=10!
3. Quick trick 2: 35% of 20  is same as 20% of 35

[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_tta_section][vc_tta_section title=”Ratios” tab_id=”1608982677433-9b550ecc-7ef8″][vc_column_text]Ratios are everywhere! Work rates;  speed, distance, time; these are all ratio questions. Here a few quick reminders:

1. Ratios are basically fractions, and are based on multiplication and division, NOT on addition and subtraction: x to y is [x:y] or [x/y]
   
2. Ratio units only describe proportions, not real values. You multiply those proportions by values given in the question to arrive at actual numbers.

[/vc_column_text][/vc_tta_section][vc_tta_section title=”Averages” tab_id=”1608982900724-10efd840-10f0″][vc_column_text]Quick reminder on how to find the average, also known as the mean:

1. Average = sum/count
2. Add up all the numbers in the group, then divide by how many numbers there are. 

[/vc_column_text][/vc_tta_section][vc_tta_section title=”Speed & distance” tab_id=”1608982860329-ea88a2cd-4554″][vc_column_text]Distance, speed time problems are ratio problems as well!

1. Here’s a formula to speed things up: Distance = Speed × Time
2. The Speed is: [distance crossed] / [time unit] e.g. 60 miles per hour.

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