numerical reasoning with project management · 2019. 7. 22. · so a numerical reasoning test is...

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Numerical Reasoning with Project Management This PDF takes a look at the numerical reasoning tests that might be useful to anyone coming into project management. I have taken some examples of questions that I think are relevant to understanding charts and graphs. Being able to analyse and read information from graphs is very important and very useful to your career as a project manager. So we will present you with some examples and explanations showing the solutions to these questions. My only problem with numerical reasoning tests is that they are never very logical. If you look at some of the questions they are designed in a way to try and trick you, they are never very clear and you cannot ask questions from the person who requires you to solve the problem. When trying to resolve problems it is always important to ask questions, you want to simplify the problem as much as possible, this is what a proper mathematician would do. Complexity will hide the resolution and simplicity will reveal it. Sometimes it as simple as changing the chart and collecting better data, do more of the calculations with the aid of a computer. We were given tools to make problem solving easier, we should learn to use them correctly. It is still important to understand foundations of numeracy but when you can simplify, you should. So a numerical reasoning test is the type of test, sometimes referred to as a psychometric or aptitude test. It is designed to measure specific numerical abilities relevant for success in a particular course, profession or job. The numerical reasoning tests are a way of assessing someone’s numerical ability it is not always logical or practical. An example of this can be seen below:

Everything that could be wrong is wrong if you look at it from a logical point of view. A baker fills a cup of

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water with ¾ cup of water. He poured ½ a cup of the water into batter; this is quite difficult unless you have markers on the side of the cup. He then spilled 1/8 of a cup of water on the floor, it then asks how much water the baker needed to add to what is left in the cup to have 50% more than he started with. Rather than get his calculator out to work out this quantity, which is 7/8 of a cup, he could have poured out remaining water and started again. He could have planned it out properly in the beginning and had all his ingredients set out properly so he did not need a calculator. The baker has ended up doing maths when he should be baking which is not very efficient. Baking should never be so difficult! This example was just set out to show there should be a lot more communicating done before answering this question or many other questions. Logical or reasonable this should be the question; people are more likely to respond to logical questions rather unreasonable questions, so it is important that the questions makes sense or you defeat the purpose. You could end up with a numerically reasonably competent person who is not very good at understanding illogical requests and communicating this too their colleagues. So the best way to prepare for a test like this is to practice, and the more practice you can get in on a regular basis will aid you greatly. The questions I will present to you will be mostly to do with analysing charts and graphs and extracting information for use within in you project management presentations. PTO….

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Q1 So below is your first line graph and it shows wireless headphone production. The question we want to resolve is, “what is the total value of Grade A and C wireless headphones produced in 2019”?

Answer $490,000 $540,000 $550,000 $790,000 So it is important to properly look at the graph, read and analyse it carefully. The graph has three different grades of headphones. The numbers for each year have had the three zero’s knocked of at the end of each value, so instead of 20 the number is actually 20000. This information can be taken from the ‘Y’ axis.

Ø Answer>Q1 Solution

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Q2 If production of Grade B wireless headphones increased by 26% from 2022 to 2023, what would be the value of Grade B wireless headphones produced in 2023?

Answer $113,400 $126,000 $151,200 $226,800


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Q3 What was the proportionate value of Grade A to C grade wireless headphones produced in 2018?

Answer0.83:10.89:10.94:11.06:1


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Q4WhatisthevalueofGradeCwirelessheadphonesproducedin2020andGradeBwirelessheadphonesin2022?

Answer$300,000$310,000$330,000$390,000


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Q5What’sthedifferencebetweentheaverageprecipitationinTiranaandAlgiers?

Answer64666870


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Q6WhatwasthepercentageincreaseinprecipitationinTiranabetweenAprilandMay?

Answer4.39%4,35%4.28%4.12%


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Q7TherewasanerrorincalculationsofprecipitationlevelsinStockholm.ThefigurerecordedinFebis15%higherthanitshouldbe.What’sthenewpercentagechangeinprecipitationfromFebtoMarinStockholm?

Answer34%38%42%46%


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Q8What’stheratiooflevelofprecipitationinAprilofAlgierstoStockholminitssimplestform?

Answers4:13:12:11:1


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Q9WhatisthevalueofAvtlynplc’sshareofthetextileindustryin2021and2022combined?

Answer$501k$534k$621k$1,035k


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Q10Whichfoodproductincreasedbythesmallestpercentageinyear1?

AnswerBreadFruitMeatMilkCheese


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Q11Theaveragecostofbreadatthestartofyear1is£1.10.Whatistheaveragecostofbreadattheendofyear1.

Answer£1.10£1.11£1.12£1.13£1.14


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Q12Whichfoodproductsincreasedbymorethan8%inyear2?

AnswerBread,fruitandcheese.Fruit,meatandcheese.Fruit,meat,milk,andcheese.Meat,milkandcheese.Meatandcheese.


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Q13WhatproportionofValThorens’snowfalloccurredinJanuary?

Answer26%30%31%35%


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Q14WhatwasthepercentageincreaseinsnowfallinWhistlerfromNovembertoJanuary?

Answer17%20%25%50%


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Q15IfthetotalsnowfallforMarchwaspredictedtoincreaseby20%fromFebruaryinValThorensandWhistleranddecreasesby15%inTignesandLesArcs,whatwouldbethetotalsnowfallacrossalltheresortsinMarch?

Answer85.5cm93.75cm111.25cm118.8cm


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Q16HowmuchsnowfellinWhistlerandLesArcsinDecemberandFebruarycombined?

Answer75cm80cm90cm105cm


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Q17Therewere300differentairfaresinAprilincludedinthecalculationforEasyJet,ifitwasdiscoveredthe10additionalairfaresof£230eachwasmissedwhencalculatingtheaveragethenwhatshouldbethecorrectaverageairfareforAprilforEasyJet.(Tothenearestpound)

Answer£94.00£95.00£96.00£97.00


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Q18IftheaverageairfareofWozzAirlinesdecreasesfromAugusttoSeptemberbythesamepercentageasthepercentageincreasesfromJunetoJuly,whatwouldbetheaverageairfareinSeptember.

Answer£90£100£70£80


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Q19IftheaverageairfareofBryanairdecreasesby15%eachmonthonfromAugust,whatwouldbetheaverageairfareofBryanairinDecember.

Answer£105.24£98.63£83.52£74.52


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Q20Whatistheratio(initssimplestform)oftheaverageairfareoverthe5months(assumingtherewerethesamenumberofairfareseachmonthforeachairline)ofEasyJettoBryanairtoWozzAirlines?

Answer150:150:8875:75:444:2:13:3:1


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Q21–EarnedValueWhatisthechartbelowtellingus?

AnswerBehindscheduleandunderbudget.Onschedule,onbudget.Aheadofschedule,underbudget.Behindschedule,overbudget.


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Q22–EarnedValueWhatisthecostvarianceforthechartbelow?

Answer2956329542134000


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Q23–EarnedValueWhatisthestatusoftheproject?

AnswerAheadofSchedule,onbudget.Behindschedule,overbudget.Onschedule,underbudget.


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Q1 Solution Step 1: Identify from the table how many wireless headphones were produced in 2019.

Step 2: Divide the number produced by 50 because the headphones are sold in batches of 50. Step 3: Multiply this number (i.e. the number of batches of 50) by the cost per batch of 50. Note: You need to perform a separate calculation for each ‘Grade’ of headphone because each batch of 50 costs a different amount: Grade A 2019 = 25,000 / 50 x $500 = $250,000 Grade C 2019 = 80,000 / 50 x $150 = $240,000 Total = $490,000 Tip: At the start of this question you need to identify where the 2019 data is shown. In most questions time will be shown on the X axis (the bottom axis). >Back>Q1

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Q2 Solution Step 1: Calculate the 26% increase from 2022 to 2023. 26/100 *20000 = 5200 + 20000 = 25200. Step 2: Using the selling price data at the bottom of the table calculate the value of the headphones produced: 25200 / 50 * $300 = $151,200 >Back>Q2

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Q3SolutionStep1:Makesureyougettheratiothecorrectwayround.Startbywritingthisdowninratioformat:GradeA:GradeCStep2:Calculatethevalueofthetwoclassesofheadphones:GradeA:20,000/50x$500=$200,000GradeC:75,000/50x$150=$225,000Step3:Writethesevaluesunderneaththeratioyouwrotedowninstep1.GradeA:GradeC$200,000:$225,000Step4:Dividethefirstnumberbythesecondtocalculatetheratio:=0.89:1

>Back>Q3

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Q4SolutionStep1:CalculatethevalueofGradeCheadphonesproducedin2020:GradeC2020=70,000/50x$150Step2:CalculatethevalueofGradeBheadphonesproducedin2022:GradeB2022=20,000/50x$300=$120,000Step3:Addtwovaluestogether:$210,000+$120,000+$330,000Tip:Thisisarelativelysimplequestionbutbecarfultousethecorrectdatafromthegraph.>Back>Q4

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Q5SolutionFirstweworkouttheaverageprecipitationforeachlocation:Tirana(135+150+130+115+120)/5=130Algiers(80+75+55+60+40)/5=62Thenwesubtractthesmallestfromthelargesttofindthedifference:130–62=68>Back>Q5

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Q6 Solution Weusethepercentagechangeformula.(120-115)/115=0.0435=4.35%>Back>Q6

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Q7 Solution Thismeansthatthefigurerecordedis115%oftheactualfigure.Thereforedo(25/115)x100=21.74Henceusingthepercentagechange(increase)formula,thereisa(30-21.74)x100=0.38=38%>Back>Q7

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Q8 Solution Wesetitupasfollows.Algiers:Stockholm60:30Dividebythehighestcommonfactor.Trydividingby10firstifyoucan’tseewhatthehighestoneis.Forexample6:3Youcanseethatyoucandividefurtherby3sotheanswer2:1>Back>Q8

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Q9 Solution Step1:IdentifythatAntlynisrepresentedisrepresentedby12%and18%forthetwoyears.Step2:Indentify,fromthetitle,thevalueofthetextileindustryineachyear.Step3:MultiplyAntlyn’sshareofthetextileindustryineachyearbythetotalvalueofthemarketthatyear:2021=12%x$1.45m=$174,0002022=18%x$2m =$360,000Step4:Addthetwoyearstogether:=$534,000>Back>Q9

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Q10 Solution Step1:Identifytheaxisonyourgraphandthisisaneasycalculation.SotheanswerisMILK,whichincreasedbyonly1%>Back>Q10

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Q11 Solution Step1:Identifythecostofbreadatthestartofyear,whichis£1.10Step2:Identifythepercentageincrease,whichis2%2%x£1.10=0.022Step3:Addtheresulttotheoriginalcost.£1.10+0.022=1.122roundeduptotwoplaces=£1.12>Back>Q11

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Q12 Solution Step1:Identifythepercentageaxisandlookforanybarsthatgoabove8%.Step2:Thisisquiteaneasyquestion,youjustneedtoidentifytheanthingabovethe8%lineandthatis:Fruit,meatandcheese.>Back>Q12

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Q13 Solution Step1:CalculatethetotalsnowfallinValThorensacrossthe4months.35cm+30cm+20cm+30cm=115cmStep2:DividetheJanuaryvaluebythetotalandmultiplyby100tocalculatetheamountasapercentage.30cm/115cmx100=26%>Back>Q13

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Q14 Solution Step1:IdentifyhowmuchsnowfellinWhistlerinNovemberandJanuary:Nov=20cmJan=25cmStep2:Calculatethedifferencebetweenthetwoamounts:25cm–20cm=5cmStep3:DividethedifferencebytheNovemberfigure,(theoldfigure)andmultiplyby100.5cm/20cmx100=25%Tip:Tocalculatepercentageincreasequickly:Subtractthenewestfigurefromtheoldestfigureanddividebytheoldest.>Back>Q14

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Q15 Solution Step1:Calculatea20%increaseintheFebruarysnowfallinValThorensandWhistler:(35cm+40cm)x1.2=90cmStep2:Calculatea15%decreaseintheFebruarysnowfallinTignesandLesArc:(20cm+5cm)x0.85=21.25cm.Step3:Addthetwovaluestogether:90cm+21.25cm=111.25cm>Back>Q15

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Q16 Solution Step1:CalculatehowmuchsnowfellinDecemberinWhistlerandLesArc:Dec=30cm+15cm=45cmStep2:CalculatehowmuchsnowfellinFebruaryinWhistlerandLesArc:Feb=40cm+5cm=45cmStep3:Addthetwofigurestogether:45cm+45cm=90cm>Back>Q16

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Q17 Solution Weknowthat300fareshadanaverageof£90,thereforeusethefigure300x£90=£27,000.Thereare10additionalairfaresof£230eachthereforethetotalofthisportionis£2,300.Then£2,300+£27,000=£29,300.Thisisthesumofall310airfares,thereforedivideby310toobtainthenewaverage.£29,300/310=£94.52=£95.(Tothenearestpound)>Back>Q17

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Q18 Solution WeworkoutthepercentageincreasefromJunetoJulyusingthepercentagechangeformula:PercentageChange=(Difference/Original)x100.((90-60)/60)x100=50%Thenweapplya50%decreasetotheaverageairfareinAugust,i.e.themultiplieris(1-0.5)=0.5,thereforetheaverageairfareinSeptemberis:£180x0.5=£90.>Back>Q18

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Q19 Solution Thisissimilartocompoundinterest.Weusethemultiplier(1-015)=0.85September£160x0.85=£136October£136x0.85=£115.60November£115.60x0.85=£98.26December£98.26x0.85=£83.521.Alternativelyadaptthecompoundinterestformula:CurrentBalance=StartingBalancex(Multiplier^Years)Inthiscase:£160x(0.85^3)=£83.521>Back>Q19

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Q20 Solution Wefirstworkouttheaverage,wecanjustsumtheaveragesofthe5monthsthendivideby5astherewerethesamenumberofairfareseachmonthforeachairline.EasyJet£90+£210+£100+£150+£200=£750£750/5=£150Bryanair£80+£110+£180+£220+£160=£750£750/5=£150WozzAirlines£20+£90+£60+£90+£180=£440£440/5=£88Firstsettheratioup£150:£150:£8875:75:44Theratioinitssimplestformcanbeobtainedbydividingtheratiobythehighestcommonfactorofallthreenumbers.Inthiscaseitis2.>Back>Q20

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Q21 Solution Step1:Youhavetoworkoutifthestatusoftheschedule.Scheduleperformanceindex=earnedvaluedividedbyplannedvalue.SPI=EV/PVSPI=30535/30875=0.988…=0.99IfSPI=1youareonschedule.IfSPI<1youarebehindschedule.IfSPI>1youareaheadofschedule.Sowearebehindschedule.Step2:Youhavetoworkoutstatusofcosts.Costperformanceindex=earnedvaluedividedbyactualcost.CPI=EV/ACCPI=30535/32240=0.94711..=0.95IfSPI=1youareonbudget.IfSPI<1youareoverbudget.IfSPI>1youareunderbudget.Sowearebehindscheduleandoverbudget.>Back>Q20

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Q22 Solution Step1:Youneedtoknowtheformulaforworkingthisoutwhichis:CostVariance=EarnedValue–ActualCostCV=EV–AC26835–23540=3295CV=3295>Back>Q22

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Q23 Solution Step1:Youhavetoworkoutifthestatusoftheschedule.Scheduleperformanceindex=earnedvaluedividedbyplannedvalue.SPI=EV/PVSPI=26835/30875=0.869…=0.87IfSPI=1youareonschedule.IfSPI<1youarebehindschedule.IfSPI>1youareaheadofschedule.Sowearebehindschedule.Step2:Youhavetoworkoutstatusofcosts.Costperformanceindex=earnedvaluedividedbyactualcost.CPI=EV/ACCPI=26835/35040=0.7658..=0.77IfSPI=1youareonbudget.IfSPI<1youareoverbudget.IfSPI>1youareunderbudget.Sowearebehindscheduleandoverbudget.>Back>Q23

numerical reasoning with project management · 2019. 7. 22. · so a numerical reasoning test is...

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