Data Insights

Question 1

DI notes

Answer 1

> goal of Data Insights section is to test your ability to MAKE SENSE OF COMPLICATED DATA efficiently —-> which data you need to answer the question

READ WORDING CAREFULLY

> even though you will have an on-screen calculator, ESTIMATION is an important skills to master for DI questions that use the words “approximately”, “nearest to” or “closest to” —-> before resorting to the calculator, see if you can solve the problem in a smarter way

> in fact, it IS a SOUND STRATEGY to attempt to estimate your way through correct answers whenever possible in data insights

> not all DI questions require calculations (even in quant ones) –> some answers will be answerable through simply interpreting the information provided to us

> be comfortable with interacting with DI questions displayed on the computer screen
e.g., multiple tabs for Multi-Source reasoning; sort function for Table analysis

> Develop a smart timing strategy (e.g., spending 1 min to Graphics Qs and saving more time for complex questions)

> still better to FINISH all questions with some guesses than leave answers blank

> keep in mind may of the DI questions involve multiple parts –> ALL parts need to be answered correctly (no partial credit)

> watch out for EXTRANEOUS INFO in DI questions that won’t be needed to answer the questions —-> USE THE ANSWER CHOICES as a guide

Question 2

Graphics Interpretation

Answer 2

What: select correct answer from a DROP-DOWN LIST based on information presented in a GRAPH or CHART
> typically TWO questions / statements
> “From each drop-down menu, select the option that creates the most accurate statement based on the information provided”

Types of charts:
> bar charts
> scatterplots **
> column charts / pareto charts
> cluster charts
> stacked column charts ***
> bubble diagrams
> Venn diagram
> Other DIAGRAMS with symbols
> Flow charts
> Frequency table and Histograms
> line graphs **
> Concept maps
> Pie charts
> hybrid charts with double axis
etc.

Most often, graphics interpretation questions are QUANTITATIVE
> ask about probability, slope of a line, direct and indirect variation, averages, ratios, standard deviation, mean, median, mode, range, percent of and percent change

Strategy for Solving:
(1) Summarize the high level message of the graph + textual information (“this graph shows the number of mangos sold during each ten-year period from 1980 to 2020.”) – “simple story”
> no need to get caught up in the details yet

(2) Go to the sentences — BEFORE DETAILS (might not need all the info)

(3) Pay attention to DETAILS of the graphic and its components (title, units of measurement, axes, axis titles, axis GRIDLINES, legend, colours, SYMBOLS patterns)
> READ the labels
> Symbols might be used to represent numbers
> be careful of y axis scales that DON’T start at 0 and can be misleading in terms of relative size (avoid using visual comparisons to make conclusions about values); use actual values instead
> Some visual estimation requires precision of reading values from the chart –> add imaginary gridlines if you must! And compare relative to other values in the chart (e.g., max value for Range calcs)

Notes:
> when you see estimation markers like “approximately”, “nearest to”, “closest to” —> solve question using savvy and disciplined estimation
> another trigger for estimation is when the ANSWER OPTIONS are SPREAD RELATIVELY FAR apart
> when a chart has NO numerical scales on its y axis –> can only perform RELATIVE comparisons across categories (e.g., one value is greater than or less than another value) ——> cannot say anything related to absolute value differences or ratios of values

ESTIMATION STRATEGIES:
> Division —> round to easy DECIMALS (NOT always nearest integer), then set fraction = x so you can cross multiply

e.g., 6.25/0.62 = x —-> ~6.2/0.62 = x —–> 6.2 = 0.62x —-> x = 10

> can also write down necessary info from charts in a TABLE (helpful to calculate percent change)

Question 3

Graphics interpretation: Column and pareto charts

Answer 3

Category on x axis, and frequency or relative frequency on y axis

Questions focus on comparing RELATIVE heights of vertical bars

See word doc

Watch out for:
> y axis that don’t start at 0 –> cannot rely on visual aid
> y axis with no numerical values at all –> cannot determine actual values or ratios of values; just know if something is bigger/biggest vs smaller/smallest

e.g., 1, 2, 3 increments OR 101, 102, 103 increments

> HOWEVER, if we are given: axis starts at 0 and the increments are CONSTANT (difference) —> then we can determine RATIO VALUES on the chart

Try: One line’s value / lower line’s value —> see if this ratio is constant when you vary values

Question 4

Graphics interpretation: Stacked column chart **

Answer 4

Allows us to compare relative frequencies of a single column (% split) and nicely illustrates the SUM of the series of numbers

Be careful when calculating the PARTS
e.g., if A + B = total

Then A = Total - B

Also don’t get overwhelmed by too many information in the CHART AND text —> keep track of what you need to solve

Other tips:
> can shorten the list of potential answers asking about proportion of a series using VISUAL APPROACH –> does the series represent over or less 50% of the bar?

Question 5

Graphics Interpretation: Histograms and frequency tables

Answer 5

Represent FREQUENCY (count) of certain INDIVIDUAL VALUES or RANGES OF VALUES

Cumulative Frequency => helpful for “at least” or “at most” questions (sum of multiple categories)

e.g., How many attorneys at at least 4 pieces of fruit per day? = number of attorneys who ate 4 pieces + number who ate 5 pieces + number who ate 6 pieces

e.g., How many attorneys at at most 3 pieces of fruit per day? = number of attorneys who at 0 pieces + 1 pieces + 2 pieces + 3 pieces

Or total number of attorneys - number of attorneys who at at least 4 pieces per day

Frequency of certain RANGES of values e.g., 3 ppl aged 40-49

Histograms are similar to column chart except the x axis has NUMBER RANGES

Question 6

Graphical Interpretation: Hybrid and double axis

Answer 6

Usually a bar and line chart with 2Y axis

> PAY ATTENTION to which axis to use (especially pernicious when the units are the SAME on both sides, like $)

Question 7

Graphical Interpretation: Scatter plots

Answer 7

Allows us to analyze any RELATIONSHIPS between TWO VARIABLES (represented by the x and y axis)
> positive relationship
> negative relationship
> no relationship (almost horizontal line)

Trend lines make it very easy to identify relationship between two variables
(you can add a trend line to see relationships more clearly)

Scatterplots can aid us in making predictions
> e.g., temperature (x axis) vs number of customers (y axis). When temperature is 70 F, we find the region in the scatterplot WHERE MOST OF THE DOTS ARE. Then find the respective y axis (can also determine the max and min prediction based on actual data points near it)

HOWEVER: when working with scatterplots, do NOT make predictions about data OUTSIDE of the data that was measured, UNLESS language in the question states that we can extend the relationship (“extrapolation)

> extrapolation can be dangerous unless the QUESTION makes an explicit assumption that the trend will continue (who knows whether the opposite trend or unexpected trend could happen!)

Question 8

Graphics Interpretation: Correlation

Answer 8

Line charts and scatter plots can depict relationships:
> positive relationship (as x increases, y increases; as x decreases, y decreases)
> negative relationship (as x increases, y decreases; as x decreases, y increases)
> no relationship (almost horizontal trend line)
Remember: Correlation =/ causation

Graphics Interpretation Question also will often present us with a LINE GRAPH(s) and ask us what type of correlation exists between the data sets (groups) represented by the line(s)

Detecting correlation among two or more lines?
> see if the lines MOVE TOGETHER from left to right (don’t need to move perfectly by the same amount every time, just IN THE SAME DIRECTION)
> Always TRACK INTERVALS along the X axis for EACH LINE (which denote a CHANGE IN DIRECTION for that line) –> observe whether those intervals line up and what happens to each line

KEEP TRACK OF TWO CORRELATIONS:
> 1) X variable and Y variable (generally, applies to both groups of data)
> 2) Group A vs Group B (moving together or moving in opposite directions over same interval)
—-> test by: as x increases, A (increases/decreases/stable) and B (increases/decreases/stable)

What happens if there are a few cases where data does NOT follow a trend?
> COULD still be a correlation between the two variables –> look at the GENERAL TREND
> sometimes though there could just be NO GENERAL

Question 9

Bivariate data

Answer 9

Data point representing TWO VALUES (x, y)

> scatter plots
line charts

Question 10

Graphics Interpretation: Scatter plots with double axis and PAIR of symbols

Answer 10

Keep careful track of which symbols tie to which axis AND GRIDLINES

Pair of points aligned vertically, and SHARE the same x axis
> Careful to ALIGN CORRECTLY

Question 11

Graphics Interpretation: Bubble chart

Answer 11

Center of the circle = data point

Represents 3 variables –> x, y and size of the bubble

Question 12

Graphics Interpretation: Pie charts

Answer 12

Be careful of complex pie chart questions involving:
> Pie chart
> Plus column or bar chart
> Plus tables

You need to expertly decide which data to use (you may not need to use them all!)

Supplemental data could be a double click into one slice of the pie chart or be something completed unrelated

Tips:
> might not need to calculate actual Total count to know actual count of a slice —> can creatively use other slices and their % (proportions of actual counts)

e.g., A = 12% * T
Looking for B = 36%*T

B/A = 3

So if A = 240, B = 3*240 = 720

Question 13

Graphics Interpretation: Venn Diagrams

Answer 13

Venn Diagram Qs are similar to what we learned in PS
> often accompanied by probability questions —> be careful which region you are taking the values from

Be careful:
> AND vs OR
e.g., ketchup AND mayonnaise =/ ketchup only + mayonnaise only + overlap

Tip:
> use the sub-part view (4 or 8) to understand which sub-parts must be included or excluded
> for counting symbols:
» Go top to bottom (3 sets)
» Go left to right (2 sets)

Question 14

Fractions (for estimating probability)

7/8

Answer 14

87.5%

Question 15

Graphics Interpretation: Flowcharts

Answer 15

Describes a process using shapes, arrows, and text
e.g., decision process

Tip:
> read the accompanying description of how the flow chart works and LOOK AT THE CHART each time the text mentions a part of the chart
> Before reading the questions, develop a GENERAL UNDERSTANDING of how the chart works, but don’t seek to understand every detail of the chart

Question 16

Table Insights

Answer 16

What: Data is provided in a table with COLUMNS that CAN BE SORTED (least to greatest)
> generally quantitative info stored in tables accompanied by an explanatory text (but can also be text in cells e.g., “High / Low”, “Yes / No”, “Name 1”)
> followed by 3 True or False statements
> “For each of the following statements, select True if the statement can be verified to be true based on the information provided. Otherwise select False” —–> does the data SUPPORT / validate the statement?
> True = data supports the statement
> False = data does not support the statement (incorrect or not enough data)
—> ADD a QUESTION MARK to evaluate the statement

Specially worded Qs: still two options per statement, but just need to read carefully
> “Less than the median” vs “Greater than or equal to the median”

Content:
> change
> percent difference
> average, median, range, standard deviation
> ratios (of values or counts) and proportions (part to whole involving values or counts)
> probability (often will be = criteria within subgroup / subgroup count)
> Correlation
> comparative ranking (highest, lowest, higher, lower)
> DS variations (does the table have enough info to support a conclusion?)
> nonstandard table analysis Qs (incl. verbal data)

How to solve:
(1) Read explanatory text to understand the table and come up with a single sentence that captures your understanding of the info in the tab

(2) Focus on high level understanding and look for most obvious patterns, relationships and trends
> don’t get into the details yet

(3) Go to questions and determine EXACTLY what data you need (without getting distracted by all the other info in the table)

Tips:
>Skillful sorting: not all Table Analysis qs will require using info from multiple sorting screens
> Estimation is key for qs that don’t need high level of accuracy for SAVING TIME (e.g., if N is the same in average calculations, just compare numerators, eyeballing data that is always greater to determine highest average, using fractions to compare sizes of ratios)
> Double check that you are using the right column (labels)
> sometimes the table with provide TOTALS at the BOTTOM of the columns –> can be useful when calculating average
> be careful NOT to count the total or mean rows as part of datasets
> COUNT CAREFULLY
> be careful when doing “mental filter” –> sorting using function, THEN mentally or manually sorting again (don’t expect sub-group of values to be sorted)

e.g., first sort for all chocolate chip cookies, then need to arrange manually prices from least to greatest

Question 17

Table Analysis: Values that fit a specified criterion in a table

Answer 17

Often to answer a Table Analysis question, we must determine something about a SUBSET of data that fits a specified criterion
> e.g., sort by Country first, then find the median value of a specific country
(kind of like creating a “mental filter” using Sort –> helps GROUP relevant values together, then you have to manually sort again to find median)

Sorting can help GROUP relevant values together and focus our attention to the right subgroups

Question 18

Table Analysis: Calculating mean

Answer 18

Tips
> sometimes the table will come with TOTAL ROW –> useful for calculating average (sum)
> you can sometimes also skip the actual calculation and EYEBALL the data (e.g., if you notice ALL the data in one average calculation is smaller than the data in another average calculation –> can conclude average is smaller)

** eyeball complicated additions first (lots of decimal sums) to see if you can find a short cut

Question 19

Table Analysis: Calculating median

Answer 19

To calculate mean of criterion (‘mentally filtered’ via sorting –> we can use the sort functionality to shortlist our values

BUT THEN we have to MANUALLY sort the next level of values to calculate median (because we cannot apply more than 1 sort)

Question 20

Table Analysis: Standard Deviation

Answer 20

You won’t have to calculate standard deviation, but instead be asked to make judgements about Standard Deviation

Recall: Standard deviation = HOW FAR values in a set are FROM THE MEAN

Can compare standard deviations of sets by:
> considering the SPACING of values in sets (range)
> considering how FAR THE VALUES in the sets are FROM the set’s MEAN

Dealing with EQUAL NUMBER OF TERMS in sets
> look at the MAX and MIN values and how far they are from the mean —> Range is a good proxy here (smaller range, smaller SD)
e.g., mean is 205 and max value is 220 while min value is 190. Each is within 15 units from the mean

> sum of ABSOLUTE DIFFERENCES | value - mean | is a good proxy (if it’s really hard to make a judgement about dispersion of values)

Also may be asked about CHANGES TO STANDARD DEVIATION IF values are changed
> depends on how far the value being removed or added is FROM the MEAN
> the MORE values CLOSE to or AT the mean in a data set ADDED to the set, the SMALLER the SD of the set
> the more values close to or at the mean REMOVED from a set, the LARGER the SD of the set

e.g., let’s say mean goals scored is 61 in a set containing {14, 54, 55, 61, 61, 62, 76, 79, 87}. If we remove 61, 61 and 62 from the set (values equal to or very close to the mean), the standard deviation would INCREASE (mean might stay around the same)

Note:
> EVEN BETTER if the table gives us the MEAN so we don’t even have to calculate it!

Question 21

Table Analysis: Percents

Answer 21

1) Asked to calculate percent change or percent of based on VALUES in the table
> Time saving tactic estimation of % change –> if a value doubles, we know it is >20% –> don’t need to calculate % change
e.g., 300 to 1240

2) Asked to work with percentage information presented in the table
> be ware of statements that make conclusions about an ABSOLUTE NUMBER rather than a percentage (might not be supported)

e.g., just because one percentage value is greater than another percentage value, this does NOT necessarily mean the absolute count is greater

Question 22

Table Analysis: Correlation

Answer 22

Very easy to check for correlation between variables by SORTING ONE column and seeing if any trends emerge on the OTHER COLUMN
> move in same direction, opposite direction or no correlation

Note:
> it’s okay if a FEW VALUES are not correlating in perfect unison with another variable
e.g., despite the # of beachgoers decreasing when the Average Temperature increases from 56 to 62, 45 to 52, and 40 to 44, there is STILL a strong positive correlation between Average Temperature and # of Beachgoers

Question 23

Two Part Analysis

Answer 23

Asks you two select TWO CORRECT ANSWERS about scenarios or mathematical expression, with answers presented in a table
> Either (1) Quant-based (often algebra word problems) or (2) Verbal-based (resemble CR)
> mark 1 answer per column (possible for answers to be the same)
> “select values… that are jointly consistent with the given information. Make only two selections, one in each column”
> Quant is mostly word problems that have two questions using the SAME SCENARIO

Possible Quant topics:
> Word problem - one equation with two variables: Use TRIAL AND ERROR with answer choices to determine the correct values for the variables
> Word problem: Rate-time-distance
> Unit conversions with rates
> Word problems: work (shortest time / longest time)
> Word problems: ratios (remember ratios indicate MULTIPLES of something, can help you shortlist answers; three part ratios, hypothetical situations where you add or subtract to achieve desired ratio)
> Word problems: Percents
> Word problems: Statistics (average, median, range)
> General word problems (interest, how much do I pay, growth)
> Combinatorics
> Sequences

Possible verbal topics:
> CR-based
> RC-based
> Both CR and RC based
> Criteria-based logic qs **
> Order-based logic qs

Tips:
> use calculator smartly (e.g., ugly exponential growth problems where you have to figure out t in expnent, unit conversions requiring high precision, percents, compound interest)
> READ the COLUMN HEADERS CAREFULLY (so you don’t reverse the order of your answer!)—-> FOLLOW ORDER OF THE QUESTION STEM

Question 24

Two part analysis: One equation with two variables

e.g., x + 8y = 42. If x and y are both positive integers, what are possible values for x and y?

x y
1
2
3
4
5

Answer 24

Word problem - one equation with two variables: Use TRIAL AND ERROR with answer choices to determine the correct values for the variables

> we know there must be ONE correct pair
easiest if you make ONE SIDE A SINGLE VARIABLE and other side an operation containing another variable –> plug in easily

Trial and error: x = 42 - 8y
> plug in values for y and see if matching x value appears in the table

ans: x = 2 and y = 5

Other tips
> to reduce number of possible answer choices quickly, use Even and Odd properties

Question 25

Two part analysis: Rate-time-distance question types

Answer 25

Average Rate = total distance/total time

Converging rates and Diverging rates: Distance 1 + Distance 2 = Total distance

Round Trip: Distance 1 = Distance 2

Catch up: Distance 1 = Distance 2

Catch up and Pass: Change Distance/Change Rate

TIPS:
> average speed range can be estimated once you know the two speeds that make up the average speed
> if asked to solve for rate –> sub in either t or d and solve for r directly

Question 26

Two part analysis: Unit conversions

e.g., I bought 13 gallons of fuel and paid $50. If 1 gallon = 3.7854 liters, and 1 EUR = 1.1043 USD, what values are the closet to the unit price of this fuel in USD per gallon and in EUR per liter? Make only two selections, one in each column

0.85
0.9
1.00
3.8
3.85
3.9

Answer 26

Unit conversions often deal with messy decimals
> use the CALCULATOR because answer choices are pretty close

Ans: USD per gallon = 50/13 = ~3.85

EUR per liter = ~0.9

OTHER TIPS:
> you can convert each unit in an expression one at a time, then replace the original units with the new ones

e.g., first convert 50 USD to Eurs, then convert 1 gallon to liters, finally put them together as EUR / Liters

Question 27

Two part analysis: Work

An ant family plans to move a nest of 1.2 million eggs in 12 hours. If N ants, each working at the same constant rate, could move M thousand eggs in 48 hours, then in terms of N and M, select the expression that represents the number of ants that would be required to move all 1.2 million eggs in 12 hours. Then select the expression representing the number of ants that would be required to move only half of the eggs in 8 hours. Make only two selections, one in each column

Answer 27

Changing worker / identical worker problem
> Key thing to note about this question is that we are asked to determine the NUMBER OF WORKERS using VARIABLES that represent number of workers of another “job”
> looking for a NEW NUMBER OF WORKERS
> two approaches

We know:
M/48 is the combined rate of N ants
So one ant’s rate: M/48N

Therefore: if we let X = number of ants required for the job

X(M/48N)12 hours = 1200 eggs (units are thousands)
X = 4800N/M

Similarly:
X(M/48N)8 = 600 eggs
X = 3600N/M

Question 28

Two part analysis: Ratios

e.g., A) in a pantry, there are only bags of chips and pretzels. There are 30 bags altogether. If the ratio of bags of chips to bags of pretzels is 3 to 2, how many bags of chips must be removed so the new ratio of chips to pretzels is 1 to 2?

e.g., B) on a soccer team, the ratio of left-footed players to right-footed players is 3 to 5. If 20 more left-footed players were added to the team, then the ratio of left-footed players to right-footed players would be 8 to 5. What is the original number of left-footed players on the team?

Answer 28

Tips:
> set up ratio table so you can understand MULTIPLES to help you shortlist answers (esp. integer constraints on the ratio multiplier)
> three-part ratio –> connect ratios in table using “like variable”
> Add/subtract unknown number to achieve a desired ratio (example A)
> Add/subtract known number to achieve a desired ratio (example B)

Example A:
> set up ratio matrix and get ratio multiplier = 6
> so we have 18 bags of chips, 12 bags of pretzels, and 30 bags altogether
> Hypothetical situation involves removing P chip bags, reducing the number of chip bags AND total number of bags
> USE ACTUAL QUANTITIES since we have them and set up desired ratio

(18-P)/12 = 1/2
P = 12 bags of chips must be removed

Example B:
> set up ratio matrix
> Hypothetical situation involves adding 20 left-footed players, increasing the number of left-footed players AND total number of players
> Use REPRESENTATIONS OF ACTUAL QUANTITIES with ratio multiplier and set up desired ratio

(3x+20)/5x = 8/5
x = 4
so 3x = 12 left-footed players originally

Question 29

Two part analysis: Statistics

Set A: {5, 6, a, 11}
Set B: {5, b, 10, 12}

The terms of each set are arranged in ascending order, and the median of Set A is equal to the median of Set B.

In the table below, select values of a and b that are consistent with the information provided above

4
6
8
10
14

Answer 29

Statistics
> There is a HIDDEN CONDITION of a and b because of the ORDERED nature of the sets

6 <= a <= 11
5 <= b<= 10

Then median A = median B (even number of terms):
(6+a)/2 = (b+10)/2

a = b + 4 (AND inequalities above)

So only a = 10 and b = 6 works

(Even though a = 8 and b = 4 seems to satisfy the equation, but does not satisfy the inequalities)

Question 30

Two part analysis: weighted average

Brands X and Y offer competing trail mix products. Brand X’s trail mix contains 60 percent raisins and 40 percent peanuts. Brand Y’s trail mix contains 20 percent raisins and 80 percent peanuts. Viviane combines x ounces of Brand X with y ounces of Brand Y, and the resulting blend contains 50 percent raisins.

In the table below, select one value for the percent of Brand X in Viviane’s blend and one value for the percent of Brand Y in her blend

25%
40%
60%
75%
80%

Answer 30

Weighted average
> Interesting that this problem has TWO INGREDIENTS (raisins and peanuts) in each brand of trail mix
> therefore, we can come up with TWO EQUATIONS, both yielding the SAME RATIO of quantities of brands
> so to save time, stick to one equation

RAISIN QUANTITIES before mixture = after mixture

0.6x + 0.2y = 0.5*(x + y)
x = 3y
x/y = 3/1

Therefore x = 75% and y = 25%

OR can use visual approach (weighting the percentages using ounces)

Question 31

Two part analysis: pricing word problem

Two telephone companies, NTT and HALO, charge different rates for long-distance calls to China. NTT charges 45 cents for the first three minutes and x cents for each subsequent minute. On the other hand, HALO charges 50 cents for the first five minutes and y cents for each subsequent minute. If the cost is the same for a 10-minute call to China using either company, and the cost for a 15-minute call to China using HALO costs 5 cents more compared to using NTT, what are the values of x and y?

3
4
5
6
7

Answer 31

When interpreting pricing questions, PAY CLOSE ATTENTION TO NUMBERS AND WORDING

NTT: 45 + x(T minutes - 3)
HALO: 50 + y(T minutes - 5)

Equation 1: 45 + x(10 minutes - 3) = 50 + y(10 minutes - 5)

Equation 2: 45 + x(15 minutes - 3) + 5 = 50 + y(15 minutes - 5)

> difference is 5 cents (NOT 50)

Sub one variable into equation 2

Y = 6
X = 5

Question 32

Two part analysis: linear growth problems

Tim got a video game console with six games for his birthday but would like to increase his collection to 30 games. His father agreed to buy him two new games each month. In addition, if Tim walks the dog daily, he will receive an extra game each month.

How long would it take for Tim to have a collection of 30 games if he walked the dog every day, and how much longer if he did not walk the dog daily?

4
5
6
8
12

Answer 32

Linear growth
> pay attention to WORDING
> Part 1 asks for MONTHS taken to reach 30 if he walked the dog every day (d = 3 per month)
> BUT part 2 asks “HOW MUCH LONGER” = CHANGE IN MONTHS

Part 1:

30 = 6 + 3T
T = 8 months

Part 2:
30 = 6 + 2T
T = 12 months

CHANGE is 4 months

Question 33

Two part analysis: Exponential growth problems

Mary has two catfishes of different species in her aquarium. Catfish A is 12 cm long, and if it remains healthy, it will become 30 percent longer each year than it was at the beginning of that year. Catfish B is 20 cm long, and if it remains healthy, it will become 10 percent longer each year than it was at the beginning of that year.

If both catfishes remain healthy, how long will it take for catfish A to exceed twice its current length, and how long will it take for catfish A to become longer than catfish B?

Years:
2
3
4
5
6

Answer 33

Exponential growth
> since we cannot take logs, we need to LAY OUT in a table what happens over time to figure out the correct answer for t years
> use CALCULATOR to help multiply faster

Catfish A’s length in year t = 12*(1.3)^t years

Catfish B’s length in year t = 20*(1.1)^t years

Part 1) 12*(1.3)^t > 24
1.3^t > 2 —-> t = 3 will exceed 2

Part 2) 12(1.3)^t > 20(1.1)^t
3(1.3)^t > 5(1.1)^t
0.6 > (1.1/1.3)^t ——–> exponent rules, can bring exponent outside

0.6 > (0.846)^t —–> using calculator, will determine t = 4

Question 34

Two-part analysis: simple interest

An investment opportunity is available to multiple investors. The investment will earn interest at a simple annual interest rate of R percent during a fixed investment period of M months.

In terms of R and M, select the expression representing the initial value of investment A, whose final value at the end of the investment period was $5 million, and select the expression representing the final value of investment B, whose initial value was $5 million

Answer 34

Simple Interest amount = A * rate per period * number of periods

TOTAL VALUE including interest = A + ART

Part 1) 5 = A + A(R/100)(M/12)
> need to convert M months to years –> M/12

A = 6000/(1200+RM)

Part 2) F = 5 + 5(R/100)(M/12)

F = (6000+5RM)/1200

BE CAREFUL WITH ALGEBRA!

Question 35

Two-part analysis: combinatorics

In a display case, there are fourteen different candy apples, one of which is caramel flavor and one of which is chocolate flavor. If four candy apples are selected, select the value in the table that represents the number of ways to select the four candy apples so that both the chocolate apple and caramel apple are selected and select the value that represents the number of ways to select four candy apples such that neither the chocolate-flavored apple nor the caramel-flavored apple is selected

55
66
78
495
935
1001

Answer 35

Combinatorics two-part analysis Qs
> read very carefully what you are looking for

Combinations Q
Part 1: MUST be in group
> mentally remove chocolate and caramel from the total number of options AND number of spots

14 –> 12 available apples
4 spots –> 2 spots

12C2 —> 66

Part 2: NEITHER chocolate-flavored apple NOR the caramel-flavored apple is selected
> Only picking from the 12 other apples
> DIFFERENT FROM Total - Together = could still have chocolate without caramel, or caramel without chocolate

14 –> 12 available apples, for 4 spots

12C4 = 495

Question 36

Two part analysis: Verbal qs

Answer 36

3 main formats:
1) Standard verbal format (similar to CR And/or RC, except asked to pick 2 answers)
e.g., pick on weakener and one strengthener
e.g., state the purpose of the passage or describe details of the passage
> pay attention to PROS and CONS of two options –> focus on CONCLUSIVE COMPARATIVE evidence that one is better than the other (e.g., passage states that wind power is less reliable than solar power)

2) Complete the statement (two correct answers will logically fill the two blanks in the STATEMENT)
> must be supported (eliminate speculations)

3) Complete the passage (two correct answers will logically fill the two blanks in the PASSAGE)
> pay attention to STRUCTURAL MARKERS in the passage to understand how the incomplete sentences must relate to what the passage says
> must be supported (eliminate speculations)
> e.g., conclusion? observation? effect? rationale?

Broader tips:
> Ask yourself, “what is this question REALLY asking for?” –> recasting the question in FAMILIAR terms can often make finding the correct answers easier
> don’t forget about RC question types (primary purpose - “primarily concerned with”, detail - “according to the passage”, inference - “most likely agree with”, specific purpose etc.)
> can also have one Two Part analysis question have a CR and RC component! e.g., select one answer that represents a flaw in the author’s argument and another answer that represents a statement with which the author would most likely disagree
> Watch out for the ORDER of the info required in the question stem –> It is often MORE EFFICIENT to answer IN ORDER (second piece of info asked for often depends on or is a logical continuation of the first)

Question 37

Two part analysis - Complete the statement

Engineer: The company is currently considering two different autonomous driving systems. LIDAR systems offer detailed 3D mapping and perform well in different lighting but are costly. Conversely, camera-based systems are less expensive and better at reading signs, but their performance dips in low-light conditions at night. Additionally, both systems have their unique limitations - LIDAR can falter under severe weather conditions, while camera-based systems may not interpret the 3D environment effectively.

If the engineer’s statements are true, the company has good reason to choose a camera-based system if 1 is its highest priority and choose LIDAR if 2 is its highest priority.

Safety
Affordability
Performance at high speeds
Performance at any hour
Navigation efficiency

Answer 37

Logical reasoning –> logically fill the blanks and is SUPPORTED by the passage
> go through each answer choice and see if there is CONCLUSIVE EVIDENCE
> eliminate UNSUPPORTED answers

Safety –> both systems have safety limitations so it is unclear which one is better

Affordability –> Clearly camera-based systems are LESS expensive –> 1

Performance at high speeds –> passage does not explicitly discuss high speed performance

Performance at any hour –> Clearly LIDA systems perform well in all sorts of lighting conditions = at any hour of the day –> 2

Navigation efficiency –> both systems have navigation limitations (camera-based systems may not interpret 3D environment effectively, while LIDA is less good at reading signs)

Question 38

Two Part Analysis: Criteria-based questions (NEW)

Answer 38

Asks us to select answers that FULFILL CERTAIN CRITERIA outlined in the prompt in accordance with instructions given in the question stem
> e.g., passage contains various CRITERIA that something must meet in order to be accepted

Challenges:
> sifting through for the RELEVANT INFORMATION (information overload)
> pay attention to QUALIFIER WORDS (some, all, none, no, not, may, must, always, never, only, either/or, except, unless)

Strategy to solve:
(1) IDENTIFY the criteria a correct answer must meet
(2) determine whether a choice MEETS those criteria

TIPS:
> understand the criteria (make any notes on important ones but don’t write everything down)
> create a TABLE mimicking the answer table (e.g., two columns, one for each of the answers. Each row represents potential answer)
> Then try to eliminate as many options as possible (using Xs) based on EASY CRITERIA FIRST (e.g., courses must be above 200 or below 200)
> Then go top to bottom and evaluate BOTH columns per row at the same time (does this option meet the columns?)

Question 39

Two Part Analysis: Order-based questions (NEW)

e.g., there are 6 people who need to be scheduled to work in a factory on any of 3 days. There is a morning shift and an evening shift to be filled on each day. Each person receives a total of 2 shifts and no person can be scheduled for both shifts on a single day. There are also constraints to WHEN SOME of the people must be scheduled. Person 1 must have a Friday shift, Person 2 can only work in the morning and Person 3 can work only on days when Person 2 and Person 4 don’t work

Answer 39

Special type of criteria-based question where the criteria relate to the ORDER IN WHICH THINGS MUST HAPPEN
e.g., determine on which days a series of events must be scheduled given criteria about how the events must be ordered
> “scheduling”

Challenge:
> Order-based questions present us with ONLY PARTIAL INFORMATION and we have to figure out how to order WITHOUT VIOLATING any of the given constraints

Strategy to Solve:
> Draw a GRID on the notepad (to visually represent the empty spots)
> write out all the possible items to be arranged so you can cross them out
> Start with the “strictest” constraint *** (“must be in a certain spot”)
> Grid in what you know in stages, working from strictest constraint to least strict
> Then we can arrange the REMAINING items around what we know is unchangeable

Question 40

Multi-source reasoning (MSR)

Answer 40

Provided multiple sources of information, each on its own tab (2-3 tabs in total)
> info can be verbal, quant, graphics interpretation, table analysis, combination of each
> e.g., tab describes an experiment, tab 2 shows the experiment results
> e.g., each tab describes a chain of emails
> e.g., each tab represents one person’s argument

Types of question formats (generally 2-3 Qs based on the same data)
> three-statement format (like in Table qs –> need to get every part correct; Yes / No, Inferable / Not Inferable etc.)
> Standard five option multiple choice

Strategy for solving:
> Review EACH TAB BEFORE answering questions (to get a sense of what info each tab contains) –> don’t get bogged down into reading the detail —> REVIEW QUICKLY WHAT INFO you have
(1) WHAT info is presented
(2) WHERE info is located
(3) HOW info is presented (tables - ascending order? by company name?)

> Think about how each tab RELATES to each other (e.g., series of communications, recommendations and data related to recommendations, methods and costs of doing something etc.)

> Mentally identify YOUR MISSION (what do you need to do?) —-> BREAK work into SMALL, DISCRETE STEPS

> then EFFICIENTLY LOCATE the right information (utilizing LABELS of tabs, titles of graph/table, introductory elements in a passage = keywords in the question stem and answer choices)

Other notes:
Inferable –> must be true based on the info (not speculative) —-> READ CLEARLY AND UNDERSTAND STATEMENT’S MEANING
e.g., we are not told what makes a city more or less “desirable overall”, so we cannot make any inferences on which city is more desirable based on “factors that affect desirability”

MSR prompts include both RELEVANT and IRRELEVANT INFO (we may never end up using)
> train yourself to FOCUS ONLY on the information you need in the moment; don’t get distracted by the “noise” surrounding it

Get used to possibly COMBINING INFO FROM MULTIPLE TABS in order to answer a single question or statement

PAY ATTENTION TO DETAILS
> hidden in titles
> jot down any things to be wary of

Question 41

Common DI question –> is this statement true?

Answer 41

View like an inequality ? —> trying to see if the statement is True or False

e.g., Statement says: The median number of cars on the lot will be greater than 100

REPHRASE AS: Median Number (WE CALCULATE) > 100?

Question 42

A note about math in MSR questions

Answer 42

> math in MSR questions are relatively BASIC - questions are testing your ability to FIND and PROCESS details

Ask yourself:
> have I read the table or graph correctly?
> have I pulled the right values from the passage?
> Have I correctly applied a formula or methodology provided in the prompt?
> Am I overlooking a key piece of information or a last step to complete my calculation? ***

DON’T FORGET ANY DETAILS from the QUESTION STEM

Question 43

MSR questions asking to satisfy multiple demands

Answer 43

1) identify each demand that the question requires us to satisfy

2) For EACH potential answer, verify whether the answer satisfies first demand
> TIME SAVING TIP: if there is no order of demands –> START WITH THE STRICTEST DEMANDS so you can ELIMINATE as many options as possible
> then you can evaluate the remaining options based on ordered criteria

3) If yes, then verify whether the choice satisfies the next demand

THEREFORE - consider each demand ONE AT A TIME in the order presented in the question (so you can methodologically check)