加拿大商科研究生GMAT邏輯比例問題干貨解析

加拿大商科研究生留學大家都知道其實很多邏輯題中都包含了一些基本的數(shù)學概念或者說數(shù)學基本規(guī)則，其中像比例問題是邏輯中非常愛考的話題。

Motorcycle-safety courses,offered by a number of organizations,teach motorcyclists important techniques for handling their vehicles and for safely sharing the road with other road with other road users.If more motorcyclists took these courses,there would be fewer serious motorcycle accidents.Data show that 92 percent of the motorcyclists who are involved in a serious motorcycle accident have never taken a motorcycle-safety course.

In assessing whether the data cited provide support for the position taken about more motorcyclists’taking the courses,it would be most useful to determine which of the following?

(A)Whether significantly more than eight percent of motorcyclists have taken a motorcycle-safety course?

(B)Whether it is riskier for a motorcyclist to ride with a passenger behind the rider than to ride alone?

(C)Whether the different organizations that offer motorcycle-safety courses differ in the content of the courses that they offer?

(D)Whether more than 92 percent of serious motorcycle accidents involve collisions between a motorcycle and another vehicle in motion?

(E)Whether variations in the size and potential speed of a motorcycle influence the risk of a serious accident’s occurring?

在看這道題目之前，我們先來舉一個日常生活中的例子：

例一：

在學校里，成績好的學生里女生占20%，成績好的學生里男生占80%。加拿大研究生考試GMAT

因為成績好的學生里男生占比更高，所以我們能據(jù)此認為男生更容易成績好嗎？

并不能！

對邏輯的套路比較了解的同學應該知道我們需要了解基數(shù)的情況。

例二：

在學校里，成績好的學生里女生占20%，成績好的學生里男生占80%。

同時，在學校里，女生占全校人數(shù)的20%，男生占全校人數(shù)的80%。

根據(jù)上面兩個信息，我們能不能認為“男生相比于女生來說，更容易取得高分”呢？

很明顯不能。

假設全校學生數(shù)量是x人，成績好的學生是y人。

那么，成績好的女生/女生人數(shù)=20%y/20%x=y/x

成績好的男生/男生人數(shù)=80%y/80%x=y/x

大家可以發(fā)現(xiàn)，如果考慮到基數(shù)的情況，女生成績好的可能性跟男生成績好的可能性是完全相同的。

女生成績好的可能性=成績好的女生/女生，所以既要知道成績好的女生的情況，還要知道女生總人數(shù)的情況。女生在總人數(shù)中的比例就相當于基數(shù)。

加拿大商科研究生GMAT邏輯比例問題干貨解析

所以，已知成績好的學生里女生占x%，成績好的學生里男生占y%。

①如果女生在全校人數(shù)中占比x%，男生在全校人數(shù)中占比y%，那此時女生成績好的可能性=男生成績好的可能性；

②如果女生在全校人數(shù)中占比超過x%，男生在全校人數(shù)中小于y%，那此時女生成績好的可能性男生成績好的可能性；

③如果女生在全校人數(shù)中占比小于x%，男生在全校人數(shù)中超過y%，那此時女生成績好的可能性>男生成績好的可能性。

所以我們需要警惕：如果光給出一個比例是無法判斷男生和女生相比誰高分的可能性更高的，我們還需要知道他們各自基數(shù)的情況。

一樣的方式，我們來看一下前面這道例題：

Motorcycle-safety courses,offered by a number of organizations,teach motorcyclists important techniques for handling their vehicles and for safely sharing the road with other road with other road users.If more motorcyclists took these courses,there would be fewer serious motorcycle accidents.Data show that 92 percent of the motorcyclists who are involved in a serious motorcycle accident have never taken a motorcycle-safety course.

In assessing whether the data cited provide support for the position taken about more motorcyclists’taking the courses,it would be most useful to determine which of the following?

(A)Whether significantly more than eight percent of motorcyclists have taken a motorcycle-safety course?

(B)Whether it is riskier for a motorcyclist to ride with a passenger behind the rider than to ride alone?

(C)Whether the different organizations that offer motorcycle-safety courses differ in the content of the courses that they offer?

(D)Whether more than 92 percent of serious motorcycle accidents involve collisions between a motorcycle and another vehicle in motion?

(E)Whether variations in the size and potential speed of a motorcycle influence the risk of a serious accident’s occurring?

文章的邏輯關系是：

發(fā)生車禍的車主，92%都沒上過安全課程。所以文章基于【沒上過安全課程的車主在發(fā)生車禍的車主中占的比例非常高，而上過安全課程的車主在發(fā)生車禍的車主中占的比例非常低】，認為這就說明上過安全課程的車主不太會發(fā)生車禍。

跟前面的例子一樣，我們需要知道他們各自的基數(shù)。

在發(fā)生車禍的車主中，上過安全課程的車主占8%，沒上過安全課程的車主占80%。

同時，在總的汽車車主中，上過安全課程的車主占8%，沒上過安全課程的車主占80%。

根據(jù)這兩個數(shù)據(jù)，我們還能認為“上過安全課程的車主發(fā)生車禍的可能性很低”嗎？

很明顯不能。假設總的汽車車主是x人，發(fā)生車禍的車主是y人。

那么，上過安全課程的車主發(fā)生車禍的數(shù)量/上過安全課程的車主數(shù)量=8%y/8%x=y/x

沒上過安全課程的車主發(fā)生車禍的數(shù)量/沒上過安全課程的車主數(shù)量=92%y/92%x=y/x

大家可以發(fā)現(xiàn)，如果考慮到基數(shù)的情況，大家發(fā)生車禍的可能性是完全一樣的，也就意味著上安全課程并沒有降低車禍發(fā)生的概率。

同樣，如果上過安全課程的車主數(shù)量在總車主中的占比>8%，沒上過安全課程的車主數(shù)量在總車主中的占比92%，那此時上過安全課程的車主發(fā)生車禍的可能性沒上過安全課程的車主發(fā)生車禍的可能性，說明安全課程的確會降低車禍發(fā)生的概率。