首页
外语
计算机
考研
公务员
职业资格
财经
工程
司法
医学
专升本
自考
实用职业技能
登录
外语
The operationis defined for all integers x and y as xy = xy - y. If x and y are positive integers, which of the following CANNOT
The operationis defined for all integers x and y as xy = xy - y. If x and y are positive integers, which of the following CANNOT
admin
2014-08-13
51
问题
The operation
is defined for all integers x and y as x
y = xy - y. If x and y are positive integers, which of the following CANNOT be zero?
选项
A、x
y
B、y
x
C、(x-l)
y
D、(x+1)
y
E、x
(y- 1)
答案
D
解析
In the formula x
y = xy - y, the variables x and v are placeholders that can be replaced by integers or by expressions representing integers. Here are two examples.
If x is replaced by 3 and y is replaced by 4, then the formula gives
3
4 =(3)(4)- 4 = 12-4 = 8
If x is replaced by x - 1 and y is replaced by 2, then the formula gives
(x- 1)
2 =((x- l)(2))-2 = 2x-2-2 = 2x-4
Scanning the answer choices, you can see that all of them are of the form
"first expression"
"second expression"
For each answer choice, you must determine whether the answer choice can be equal to 0 for some positive integers x and y. Are there positive integers x and y for which the answer choice is equal to 0 ? If not, then that answer choice is the correct answer.
Choice A: x
y. Using the formula, try to find positive integers x and y for which x
y = 0, that is, for which xy —y = 0. To solve this equation, note that factoring y out of the left-hand side of the equation xy - y = 0 gives the equation(x - l)y = 0. So now you must find positive integers x and y such that the product of the two numbers x -1 and y is 0. Since the product of two numbers is 0 only if at least one of the numbers is 0, it follows that the product of x - 1 and y will be 0 if x = 1, no matter what the value of y is. For example, if x = 1 and y = 2, then x
y = 1
2 =(1)(2)- 2 = 0, and both x and y are positive integers. Therefore, Choice A is not correct, since there are positive integers x and y for which x
y = 0.
Choice B: y
x. This is similar to Choice A, except the x and y are interchanged. Therefore, you might try the example in Choice A but with the values of x and y interchanged: y = 1 and x = 2. Using the formula, y
x=yx-x =(1)(2)-2 = 0. Therefore, Choice B is not correct, since there are positive integers x and y for which y
x = 0.
Choice C:(x - l)
y. Using the formula, try to find positive integers x and y for which(x - l)
y = 0, that is, for which(x - l)y -y = 0. Factoring y out of the left-hand side of the equation(x - 1)y -y = 0 yields(x - 1 - l)y =(x - 2)y = 0. Here the product of the two numbers x - 2 and y is 0. So the product will be 0 if x = 2, no matter what the value of y is. For example, if x = 2 and y = 10, then(x- 1)
y =(2- 1)
10= 1
10 =(1)(10)- 10 = 0, and both x and y are positive integers. Therefore, Choice C is not correct, since there are positive integers x and y for which(x - 1)
y = 0.
Choice D:(x + 1)
y. Using the formula, try to find positive integers x and y for which(x + 1)
y = 0, that is, for which(x + 1)y — y - 0. Factoring y out of the left-hand side of the equation(x + 1)y —y = 0 yields(x + 1 - 1)y = xy = 0. Here the product of x and y is 0, so x = 0 or y = 0. Since both x and y must be positive but 0 is not positive, it follows that there are no positive integers x and y for which(x +1)
y = 0. The correct answer is Choice D.
Choice E: x
(y - 1)cannot be correct, since Choice D is correct, but Choice E is considered here for completeness. Using the formula, try to find positive integers x and y for which x
(y - 1)= 0, that is, for which x(y -1)—(y-l)= 0. Factoring y -1 out of the left-hand side of the equation x(y -1)—(y -1)= 0 yields(x - l)(y - 1)= 0. Here the product of the two numbers x - 1 and y -1 is 0. So the product will be 0 if x = 1 or y = 1, no matter what the value of the other variable is. For example, if x = 20 and y = 1, then x
(y - 1)= 20
(1 - 1)= 20
0 =(20)(0)-0 = 0, and both x and y are positive integers. Therefore, Choice E is not correct, since there are positive integers x and y for which x
(y -1)= 0.
转载请注明原文地址:https://kaotiyun.com/show/R5kO777K
本试题收录于:
GRE QUANTITATIVE题库GRE分类
0
GRE QUANTITATIVE
GRE
相关试题推荐
Itisanunfortunatefactoftoday’slifethatmostpeoplearegrowingupunabletoseethestars.Theprimenightskyexistson
RowanTorrezwillneverbeabletobearhislate(已故的)fathertellhimthatheloveshim,butyesterdayhe【C1】______receivedhisd
Caraccidentskillmorethanonemillionpeopleandinjureapproximately50millioneachyear.【C1】______,millionsoffishcans
WehavequiteabitofinformationaboutancientEgyptianmedicine.Doctors’instructionshavebeenfoundtotellus【56】theydid
WehavequiteabitofinformationaboutancientEgyptianmedicine.Doctors’instructionshavebeenfoundtotellus【56】theydid
JustasProfessorScottioften______it,successisninety-ninepercentmentalattitude.
Theinterviewershouldtakedownnotesatthemomenttheperson______answersthequestions.
Itwasacoldwinterday.AwomandroveuptotheRainbowBridgetollbooth(收费站)."I’mpayingformyself,andforthesixcarsb
Solvetheproblemandindicatethebestoftheanswerchoicesgiven.NUMBERS:Allnumbersusedarerealnumbers.FIGURES:
Intherectangularcoordinatesystemabove,forhowmanyofthepointsthatlieinsideorontheboundaryoftheshadedregiona
随机试题
Thissummerthecity’sDepartmentofTransportationstartsanewbike-shareprogram.People【K1】________liveandworkinNewYork
简述申请律师执业的条件。
简述管理控制的三个基本环节的工作。
《建设工程施工合同(示范文本)》(GF一2013—0201)约定属于承包人工作义务的是()。
某企业2011年末进行财产清查,查明存在的情况有:(1)甲种原材料账面结存1500千克,每千克成本为6元,实际结存1570千克,经查属于收发计量不准确造成,经批准予以处理。(2)乙种原材料账面结存2100千克,每千克成本为10元,实际结存2000千克,
()以言语为工具,所反映的是事物的本质属性和内在规律。
____________。把政策支持作为促进保险业发展的重要力量,加强与国家有关部门、地方政府的协调与合作,完善保险业发展的政策支持体系,推动关系国计民生的保险业务的新发展。一是以税收优惠为突破口,推动养老保险和健康保险的新发展。二是以财政支持为突破口,推
下列关于赤潮的说法,正确的是:
领导交给你一项任务。你如何确保明白领导的意图。并把任务完成好?
HowmanychickensbecometheKFCchain’sfriedmealseveryyear?
最新回复
(
0
)