Numerical - Mixed Questions13Numerical Reasoning Practice 08

1、答案：eIn2008，1910 systems were installed in Germany。In2012、9959 systems were installed。the percentage change is calculated as followed :(9959-1910)/1910=4.21 * 100=421%。(2)答案：athis question can be solve using estimation。while the question does ask us for a relative change as opposed to an absolute change，(which is easier to estimate)we can still apply this thisbecause we are asked for arelative change，Web must look at both the difference between the data in 2008 and 2009 and the actual sizes of the numbersDenmark and Spain can easily be eliminated as the leap in numbers between 2008 and 2009 is equal to or greater than 100%。Germany is also close to thes E percentages and can be eliminated as well。we are left with 3 countries : Italy，France and the uk . in this case it is hard to estimate the correct answer，so we shall calculate the perpersItaly: (58-46)/46=26%France: (33-26)/26=26.9%UK (140-110)/110=27.2%The correct answer isItaly。(3)答案：cin order to answer this question web must understand the graph : axis y re presents the change in actual numbers between 2012 and 2013。thus if wesum Up all the data in the graph we will arrive at the total change in the number of systems installed in the uk between 2012 and 2013:10 25 33-6 0-10=52-in the uk in 2013，they were 52 systems more than in 2012。what remains is to calculate the number of systems installed in 2012 in the uk and add 52 to that number。we can find this data in the table : 290 52=342。(4)答案：ein order to answer this question web must understand the graph : axis y re presents the change in actual numbers between 2012 and 2013。thus if wesum Up all the data in the graph we will arrive at the total change in the number of systems installed in the uk between 2012 and 2013:10 25 33-6 0-10=52-in the uk in 2013，they were 52 systems more than in 2012。now we can use the result from the previous calculation to answer this question : 52/290 * 100=17.93 18%。2、(1)答案：ethe proportion of families with an income over 3000 is 25%(according to the middle chart)。25% expressed as a fraction is 25/100，which can be reduced to1/4(using a common denominator of 5)。note that you will get the same answer when using actual numbers 3360 25% of 1500 respondents equals 375.375/1500=1/4。(2)答案：bthe proportion of consumers living in tenements : 30%。the proportion of consumers living in private housing : 70%。the proportion of consumers l Iving in tenements to the proportion of consumers living in private housing，expressed as a fraction，is :(3)答案：bthe proportion of consumers living in tenements : 30%。the proportion of consumers living in private housing : 70%。the proportion of consumers l Iving in tenements to the proportion of consumers living in private housing，expressed as a fraction，is :(4)答案：eAs shown in the graphs，70% of the 1500 house hold s live in private housing，while 44% of the same respondents earn between $ 20001.all house hold s earning $ 2000-$ 3000 live in private housing 3360 44%2.most house hold s earning $ 2000-$ 3000 do not live in private housing 3360 14%the question asks us about the situation descripd in the second option。14% of 1500 equals 210。solving tip-in this type of question，We need to check what happens at the extreme points in order to determine the minimal/maximal valuethis method works as well for，Questions that ask about the range of possibilities(I . e . minimum-maximum)。In this question，the minimal value is when the least number of private house holds that also have an income of $ 2，000-$3，000。for this to happen，We need to assert what is the maximal number of house hold that arent private and may also belong to this income category。the trick is to use the smal Lest number(the restricting element )of either the number of non-private houses，Or the income catesthe 14% remainder represents the number of house hold s in the relev Ant income category that are also resding in a private house。web know the total number of house hold s is 1500 and therefore :14% x 1500=0.14 x 1500=210。(5)答案：cfirst web need to calculate the total percentage of families with 3 children or less and then multiply by 1500。instead of adding up all the data for th Ese families but those with 4 children，We can deduct the percentage of families with 4 children from 100%Alternativeely，wecould have calculated the number of families with 4 children out of 1500:02 * 1500=30 families，And then3、(1)答案：bproportion of water used for washing clothes and using the toilet 3360 21.7% 26.7%=48.4%(out of 100%)。48.4% can be represented as 484/1000，Which can be reduced to 121/250(using a common denominator of 4)。(2)答案：eweknow from the table that for e