gmat ds题选项
gmat试题中文及答案
gmat试题中文及答案GMAT试题中文及答案一、数学题1. 如果一个数的平方等于该数本身，那么这个数可能是多少？A. 0B. 1C. -1D. A和B答案：D2. 一个圆的半径是5，它的面积是多少？A. 25πB. 50πC. 75πD. 100π答案：B二、逻辑题1. 所有的猫都怕水，如果一只动物怕水，那么它不是猫。
以下哪项如果为真，最能支持上述论断？A. 有些猫不怕水。
B. 有些动物怕水但不是猫。
C. 所有怕水的动物都是猫。
D. 有些动物不怕水并且是猫。
答案：B2. 如果一个公司想要提高其市场份额，它应该降低其产品的价格。
以下哪项如果为真，最能削弱上述观点？A. 降价可能会损害公司的品牌形象。
B. 消费者通常认为价格高的产品质量更好。
C. 竞争对手也降低了他们的产品价格。
D. 公司的产品在市场上已经是最低价。
答案：B三、阅读理解题阅读以下短文，然后回答问题。
在20世纪初，汽车工业开始迅速发展。
随着汽车数量的增加，对道路的需求也随之增长。
然而，当时的许多道路都是土路，容易受到天气的影响。
为了解决这个问题，工程师们开始设计和建造更耐用的道路。
这些道路使用混凝土和沥青等材料，能够承受更重的交通负荷。
问题：1. 20世纪初，汽车工业的发展导致了什么？A. 道路数量的减少B. 对耐用道路的需求增长C. 汽车价格的上升D. 工程师数量的增加答案：B2. 工程师们如何解决土路容易受到天气影响的问题？A. 减少汽车的使用B. 建造更耐用的道路C. 增加土路的数量D. 限制天气变化答案：B四、语法题1. 尽管他很年轻，但他已经是一位经验丰富的工程师。
A. 尽管他很年轻，但他已经是一位经验丰富的工程师。
B. 尽管他很年轻，但他是一位经验丰富的工程师。
C. 虽然他很年轻，但他已经是一位经验丰富的工程师。
D. 虽然他很年轻，但他是一位经验丰富的工程师。
答案：A2. 这家公司不仅提供了高质量的产品，而且它的服务也非常出色。
GMAT考试最新信息+备考攻略：改革正式官宣！23年考生应该如何应对？
GMAT考试最新信息+备考攻略：改革正式官宣！23年考生应该如何应对？就在前不久GMAT考试发布了最新的改革的消息，很多的小伙伴想要了解的GMAT考试相关信息，那么接下来就让小编来为大家介绍下GMAT考试信息+备考攻略！GMAT考试信息+备考攻略：改革正式官宣！23年考生应该如何应对？GMAT改革正式官宣！23年考生应该如何应对？新版的GMAT考试将会出现哪些变化？这次改革对广大考生，特别是对计划今年申请的考生，将会产生怎样的影响？应该如何应对？Data Insights 数据洞察（20题 45分钟）：DS题型IR的四种题型Quantitative Reasoning（21题 45分钟）：PS 题型Verbal Reasoning（23题 45分钟）CR题型RC题型（具体每个题型有多少个题目还未知）考试总时长：135分钟Data Insights、Verbal、Quant 三个部分组成满分为205-805的分数（每个部分权重一样），没有小分了。
每10分为一个梯度，都是以5分为结尾，应该是为了和现有的分数区分开。
Data Insights、Verbal、Quant分别为60-90的分值，增量为1分。
一次只展示一个题目，除了部分IR的题型（IR的题目一次会有几问，如下图所示）会有标记功能（新增的功能）Data Insigts版块是随机出题的（DS/IR的4类题型混着出现）你必须选一个答案并确定才能进入下一个题目（和之前一样）你可以标记题目以便这个section结束你去review在一个section（比如：整个数学部分回答完毕）回答完所有的题目后，可以检查和回看这个section所有的题目，但是每一个section 至多只能修改3个答案；三个section之间的顺序，你可以自己随便选；一共只有10分钟的休息，你可以选在1-2section 之间休息，或者2-3section之间休息。
（本道IR的题目共包含了3个小问题，必须全部答对才算得分）考完试，收到成绩之后，满意了，你可以「免费」送给5所学校。
GMAT考试GMAT 数学XDF500 题(DS 部分)(解释完整版)
考试复习GMAT数学XDF500题（DS部分）A garden store purchased a number of shovels and a number of rakes. If the cost of each shovel was $14 and the cost of each rake was $9, what was the total cost of the shovels and rakes purchased by the store?(1) The ratio of the number of shovels to the number of rakes purchased by the store was 2 to 3.(2) The total number of shovels and rakes purchased by the store was 50.答案 C考点 方程难度 2思路 需要知道S和R各自的具体数量才可以算出总的cost 则两个条件分别可以列出两个方程 不充分 合并条件为二元一次方程组 可解出一组值 充分2Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans2dislike lima and each student either likes or dislikes brussels sprouts. Of these students,33also dislike brussels sprouts. How many of beans; and of those who dislike lima beans,5the students like brussels sprouts but dislike lima beans?(1) 120 students eat in the cafeteria.(2) 40 of the students like lima beans.答案 D考点 集合难度 3思路 将所有学生按两种属性分类 喜欢或不喜欢L 喜欢或不喜欢B 总数2/3不喜欢L 那么喜欢L的1/3 不喜欢L的人里面又有3/5不喜欢B 则两者都不喜欢的占2/5 那么可以推出喜欢B 但不喜欢L的占2/3 - 2/5 =4/15 但是问题求人数 所以需要知道总人数条件1 给了总人数 充分条件2 也可以算出总人数 充分1How many different prime numbers are factors of the positive integer n ?(1) Four different prime numbers are factors of 2n.(2) Four different prime numbers are factors of n2.答案 B考点 质数 因数难度 4思路 此题比较抽象 问N含有多少个不同质因数条件1 2N有4个不同质因数 那么这4个质因数中一定含有2 其余3个因数未知 但是含有2的多少次方无法确定 如果2N含有2的1次方 则N没有 只有3个质因数 如果2N含有大于等于2次方的2 那么N中含有2以及另外3个总4个质因数 不充分条件2 N平方即为N乘以本身得出 所以N平方和N应该含有相同的质因数 只是指数不同而已 不影响个数 所以N应该含有4个不同质因数 唯一确定 充分4Is the product of a certain pair of integers even?(1) The sum of the integers is odd.(2) One of the integers is even and the other is odd.答案 D考点 奇偶难度 2思路条件1 可推出两个数字一奇一偶 所以乘积一定为偶数 充分条件2 和条件一的形式一样 一奇一偶 那么也充分5If k is an integer and 2 < k < 8, what is the value of k ?(1) k is a factor of 30.(2) k is a factor of 12.答案 E考点 因数难度 2思路条件1 K可以为3 5 6 不充分条件2 K可以为3 4 6 不充分合并条件还是可以3或6 不充分2On the number line above, is the product of w, x, y, and z negative?(1) z is positive.(2) The product of w and x is positive.答案 E考点 正负难度 2思路 若使得4个数乘积为负 则需要1或3个负数条件1 负数个数可以为0-3个 正负未知 不充分条件2 W和X同号 那么负数个数为0-4个 不充分合并条件 若WXZ为负 则乘积为负 都是正的四个数 乘积为正 不确定 不充分7If y and z are integers, is y(z + 1) odd?(1) y is odd(2) z is even.答案 C考点 奇偶难度 2思路 相乘为奇 必须前面所有数都是奇数条件1 Z不知道奇偶 不确定条件2 不知道Y奇偶 不确定合并条件 两项奇偶都确定 充分3If n and m are positive integers, what is the remainder when 3^(4n + 2 + m) is divided by 10 ?(1) n = 2(2) m = 1答案 B考点 余数个位数难度 4思路 题干式子中的除数为10 则不需要求出被除数具体值 求出个位数即可 底数为3 随着指数从1增加之后 个位数字循环规律为3 9 7 1 四位一循环 所以用指数除以4即可知道个位数值条件1 因为N的系数为4 所以不影响除以4的余数 不能确定条件2 M的值可以确定被除数个位数的情况 那么充分9If x is a positive integer, is x < 16 ?(1) x is less than the average (arithmetic mean) of the first ten positive integers.(2) x is the square of an integer.答案 A考点 不等式难度 2思路条件1 X为1-10的平均数 一定小于16 充分条件2 X可以为1 4 9 16 25。
13年5月GMAT数学预测机经韦晓亮
2013年5月GMAT数学1，这道题目好像是问x/y>0 吧，条件一x/(x+y)>0 条件二y/(x+y)>0。
答案：C（1）NS 只能推出x与x+y同号且x，x+y不=0（2）NS 只能推出y与x+y同号且y，x+y不=0（1）+（2）S可以推出x与y同号且x，y都不=0（此题需要注意的是两数相乘或相乘大于0，转换为数学语言即x与y同号）2，还有一道说一个人20mph 开了半个小时然后30mph 开了1/3小时，求平均速度。
答案：24mphV=S/T=（20*1/2+30*1/3）/(1/2+1/3)=24mph3，一艘大船里的货物3%的概率是被昆虫感染（？），问抽取6个不被感染的概率是多少。
参考答案：（0.97）^6由于被感染的几率是3%所以不被感染几率为1-3%=97% 而独立事件同时发生的概率=P1*P2*P3*…… 所以狗主答案正确4，a1,a2,a3,a4,a5除以5的余数都不一样。
问一下哪个除以5的余数也都不一样。
I、a1+2,a2+2,a3+2,a4+2,a5+2II、2a1,2a2，2a3,2a4,2a5（此处原始应该有误，我修改了）III、a1^2,a2^2,a3^3,a4^2,a5^2除以5的余数要不同，余数只能为0 1 2 3 4 不妨假设就为0 1 2 3 4，那么I就变为2 3 4 5 6除以5的余数分别为2 3 4 0 1；II变为0 2 4 6 8余数为0 2 4 1 3；III变为0 1 4 9 16余数为0 1 4 4 1由上可得：I ,II 是余数各自不同的。
5，X-3，X，X+1，X+2，X+10，问平均数。
答案：X+2平均数=（X+X+X+X+X-3+0+1+2+10）/5=(5X+10)/5=X+26，第一题非常简单，我居然差点求速度做错了已知r,s 都不为零，且不相等，则下式哪个必成立：r平方不等于s平方；r除以s不等于s除以r；r+r不等于s+s；假设r=1s=-1则第一个式子不成立第二个也不成立因为r不=s，所以第三个式子2r一定不=2s7，一个班有3对双胞胎，每对双胞胎都是1男1女，现在拍照，要求每个双胞胎要站在自己的同胞旁边，问有多少种站法？答案有：6，12，48，64，我选的是48男1女1 男2女2 男3女3（嘻嘻，原谅我这么简陋的表示三对双胞胎）注意到题目说双胞胎要站自己同胞边上，说明男1一定和女1，等等。
700+ GMAT Data Sufficiency Questions With Explanations
700+ GMAT Data Sufficiency Questions With ExplanationsCollected by BunuelSolutions by Bunuel 1. Probability / CombinatoricsIf 2 different representatives are to be selected at random from a group of 10 employeesand if p is the probability that both representatives selected will be women, is p > 1/2(1) More than 1/2 of the 10 employees are women.(2) The probability that both representatives selected will be men is less than 1/10What is the probability of choosing 2 women out of 10 people and this should be . Sowe have --> this is true only when . (w # of women )So basically question asks is ?(1) not sufficient.(2) --> --> , not sufficient(1)+(2) , not sufficientAnswer E.You can use Combinations, to solve as well:# of selections of 2 women out of employees;total # of selections of 2 representatives out of 10 employees.Q is --> --> --> --> ?(1) , not sufficient.(2) # of selections of 2 men out of employees --> --> --> --> , not sufficient(1)+(2) , not sufficientAnswer E.Discussed at: /forum/difficulty-faced-during-test-89934.html2. Coordinate GeometryIf vertices of a triangle have coordinates (-1,0), (4,0), and (0,A) , is the area of the triangle greater than 15?(1) A < 3(2) The triangle is rightFirst of all right triangle with hypotenuse 5, doesn't mean that we have (3, 4, 5) right triangle. If we are told that values of all sides are integers, then yes: the only integer solution for right triangle with hypotenuse 5 would be (3, 4, 5).To check this: consider the right triangle with hypotenuse 5 inscribed in circle. We know that a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle. So ANY point on circumference of a circle with diameter would make the right triangle with diameter.Not necessarily sides to be and . For example we can have isosceles right triangle, which would be45-45-90: and the sides would be . OR if we have 30-60-90 triangle and hypotenuse is , sides wouldbe and . Of course there could be many other combinations.Back to the original question:If vertices of a triangle have coordinates (-1,0), (4,0), and (0,A) , is the area of the triangle greater than 15?(1) A < 3 --> two vertices are on the X-axis and the third vertex is on the Y-axis, below the point (0,3). The third vertex could be at (0,1) and the area would be less than 15 OR the third vertex could be at (0,-100) and the area would be more than 15. So not sufficient.(2) The triangle is right. --> Obviously as the third vertex is on the Y-axis, the right angle must be atthe third vertex. Which means the hypotenuse is on X-axis and equals to 5. Again if we consider the circle, the radius mus be 2.5 (half of the hypotenuse/diameter) and the third vertex must be one oftwo intersections of the circle with Y-axis. We'll get the two specific symmetric points for the third vertex, hence the area would be fixed and defined. Which means that it's possible to answer the question whether the area is more than 15, even not calculating actual value. Sufficient.Answer: B.If we want to know how the area could be calculated with the help of statement 2, here you go:One of the approaches:The equation of a circle is , where is the center and is the radius. We know:, as the hypotenuse is 5.and , as the center is on the X-axis, at the point , half the way between the (-1, 0) and (4, 0).We need to determine intersection of the circle with Y-axis, or the point for the circle.So we'll have--> and . The third vertex is either at the point OR . In anycase .Discussed at:/forum/urgent-help-required-87344.html?hilit=only%20integer%20solution%20triangle#p6566283. GeometryIs the perimeter of triangle ABC greater than 20?(1) BC-AC=10.(2) The area of the triangle is 20.This problem could be solved knowing the following properties:For (1):The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.Now, as BC-AC=10 then BC>10 and also according to the above property the third side AB is also more than 10, so the perimeter is more than 20. Sufficient.For (2):A. For a given perimeter equilateral triangle has the largest area.B. For a given area equilateral triangle has the smallest perimeter.Let's assume the perimeter is 20. The largest area with given perimeter will have the equilateral triangle, so side=20/3. Let's calculate the area and if the area will be less than 20 it'll mean that perimeter must be more than 20., (.) hence area is more than 20. Sufficient.Answer: D.Discussed at: /forum/perimeter-of-triangle-abc-87112.html4. Modulus / InequalitiesIf x is not equal to 0, is |x| less than 1?(1) x/|x|< x(2) |x| > x, is ? Which means is ? ()(1)Two cases:A. --> --> . But remember that , soB. --> --> .Two ranges or . Which says that either in the first range or in the second. Notsufficient to answer whether . (For instance can be or )OR: multiply both sides of inequality by (side note: we can safely do this as absolute value isnon-negative and in this case we know it's not zero too) --> --> :Either and , so or --> ;Or and , so --> .The same two ranges: or .(2) . Well this basically tells that is negative, as if x were positive or zero then would be equal to . Only one range: , but still insufficient to say whether . (Forinstance can be or )Or two cases again:--> --> .--> : never correct.(1)+(2) Intersection of the ranges from (1) and (2) is the range ( (from 2)and or (from 1), hence ). Every from this range is definitely in therange . Sufficient.Answer: C.To demonstrate on diagram:Range from (1): -----(-1)----(0)----(1)----or, green area;Range from (2): -----(-1)----(0)----(1)----, blue area;From (1) and (2): ----(-1)----(0)----(1)----, common range of from (1) and (2) (intersection of ranges from (1) and (2)), red area.Discussed at: /forum/if-x-is-not-equal-to-0-is-x-less-than-86140.html5. Coordinate Geometry / ModulusOn the number line shown, is zero halfway between r and s(1) s is to the right of zero(2) The distance between t and r is the same as the distance between t and -sNOTE:In GMAT we can often see such statement: is halfway between and . Remember thisstatement can ALWAYS be expressed as: .Also in GMAT we can often see another statement: The distance between and is the same as thedistance between and . Remember this statement can ALWAYS be expressedas: .Back to original question: is 0 halfway between r and s?OR is ? --> Basically the question asks is ?(1) , clearly not sufficient.(2) The distance between and is the same as the distance between and -: .is always positive as is to the left of the , hence ;BUT can be positive (when , meaning is to the right of -) or negative (when ,meaning is to the left of -, note that even in this case would be to the left of and relativeposition of the points shown on the diagram still will be the same). So we geteither OR .In another words: is the sum of two numbers from which one , is greater than . Their sumclearly can be positive as well as negative. Knowing that one is greater than another doesn't help to determine the sign of their sum.Hence:--> ;OR--> .So the only thing we can determine from (2) is:Not sufficient.(1)+(2) and . --> (as is to the right of ) hence .Hence . --> --> . Sufficient.Answer: C.About the relative position of the points on diagram:"In general, you should not trust the scale of GMAT diagrams, either in Problem Solving or Data Sufficiency. It used to be true that Problem Solving diagrams were drawn to scale unless mentioned otherwise, but I've seen recent questions where that is clearly not the case. So I'd only trust a diagram I'd drawn myself. ...Here I'm referring only to the scale of diagrams; the relative lengths of line segments in a triangle, for example. ... You can accept the relative ordering of points and their relative locations as given (if the vertices of a pentagon are labeled ABCDE clockwise around the shape, then you can take it as given that AB, BC, CD, DE and EA are the edges of the pentagon; if a line is labeled with four points in A, B, C, D in sequence, you can take it as given that AC is longer than both AB and BC; if a point C is drawn inside a circle, unless the question tells you otherwise, you can assume that C is actually within the circle; if what appears to be a straight line is labeled with three points A, B, C, you can assume the line is actually straight, and that B is a point on the line -- the GMAT would never include as a trick the possibility that ABC actually form a 179 degree angle that is imperceptible to the eye, to give a few examples).So don't trust the lengths of lines, but do trust the sequence of points on a line, or the location of points within or outside figures in a drawing. "Discussed at: /forum/position-on-the-number-line-89015.html6. InequalitiesAre x and y both positive?(1) 2x-2y=1(2) x/y>1(1) 2x-2y=1. Well this one is clearly insufficient. You can do it with number plugging OR consider the following: x and y both positive means that point (x,y) is in the I quadrant. 2x-2y=1 --> y=x-1/2, we know it's an equation of a line and basically question asks whether this line (all (x,y) points of this line) is only in I quadrant. It's just not possible. Not sufficient.(2) x/y>1 --> x and y have the same sign. But we don't know whether they are both positive or both negative. Not sufficient.(1)+(2) Again it can be done with different approaches. You should just find the one which is the less time-consuming and comfortable for you personally.One of the approaches:-->--> --> substitute x --> --> is positive, and as , is positive too. Sufficient.Answer: C.NOTE:does not mean that . If both x and y are positive, then , BUT if both are negative,then .From (2) , we can only deduce that x and y have the same sigh (either both positive or both negative).Discussed at: /forum/ds1-93964.html7. Inequalities / Word ProblemIf 20 Swiss Francs is enough to buy 9 notebooks and 3 pencils, is 40 Swiss Francs enough to buy 12 notebooks and 12 pencils?(1) 20 Swiss Francs is enough to buy 7 notebooks and 5 pencils.(2) 20 Swiss Francs is enough to buy 4 notebooks and 8 pencils.Given , question is true? Or is true? So basically weare asked whether we can substitute 3 notebooks with 3 pencils. Now if we can easily substitute notebooks with pencils (equal number of notebooks with pencils ) and the sum will be lees than 20. But if we won't know this for sure.But imagine the situation when we are told that we can substitute 2 notebooks with 2 pencils. In bothcases ( or ) it would mean that we can substitute 1 (less than 2) notebook with 1 pencil,but we won't be sure for 3 (more than 2).(1) . We can substitute 2 notebooks with 2 pencils, but this not enough. Not sufficient.(2) . We can substitute 5 notebooks with 5 pencils, so in any case ( or ) we can substitute 3 notebooks with 3 pencils. Sufficient.Answer: B.Discussed at: /forum/tricky-inequality-89226.html?hilit=swiss#p6749198. Word ProblemTen years ago, scientists predicted that the animal z would become extinct in t years. What is t?(1) Animal z became extinct 4 years ago.(2) If the scientists had extended their extinction prediction for animal z by 3 years, their prediction would have been incorrect by 2 years.(1) The only thing we can get from this statement is when animal z actually extincted: 4 years ago or 6 years after the prediction. Not sufficient.(2) Also not sufficient: t+3=actual extinction +/- 2.(1)+(2) Animals extincted 6 years after the prediction: t+3=6-2 --> t=1 OR t+3=6+2 --> t=5. Two answers, not sufficient.Answer: E.Discussed at: /forum/somewhat-confusing-problem-90379.html9. ModulusIf x and y are non-zero integers and |x| + |y| = 32, what is xy?(1) -4x - 12y = 0(2) |x| - |y| = 16(1) --> --> and have opposite signs --> soeither and OR and -->either : , , OR: , , , same answer. Sufficient.(2) . Sum this one with the equation given in the stem --> --> , . (x and y have opposite sign) or (x and y have the same sign). Multiple choices. Not sufficient.Answer: A.Discussed at: /forum/absolute-value-90031.html10. Number propertiesIf k is an integer greater than 1, is k equal to 2^r for some positive integer r?(1) k is divisible by 2^6(2) k is not divisible by any odd integer greater than 1Given: , question is .Basically we are asked to determine whether has only 2 as prime factor in its prime factorization. (1) , if is a power of 2 then the answer is YES and if is the integer other than 2 in any power (eg 3, 5, 12...) then the answer is NO.(2) is not divisible by any odd integers greater then 1. Hence has only power of 2 in its prime factorization. Sufficient.Answer: B.Discussed at: /forum/power-of-88539.html11. InequalitiesWhat is the value of integer x?(1) 4 < (x-1)*(x-1) < 16(2) 4 < (x+1)*(x-1) < 16Note: is an integer.(1) --> --> is a perfect square between 4 and 16 --> there is only one perfect square: 9 --> --> or --> or . Two answers, not sufficient.(2) --> --> --> --> isa perfect square between 5 and 17 --> there are two perfect squares : 9 and 16 --> or --> or or or . Four answers, not sufficient.(1)+(2) Intersection of values from (1) and (2) is . Sufficient.Answer: C.Discussed at: /forum/tough-inequation-ds-what-is-the-value-of-integer-x-93008.html12. Inequalities / ModulusIs x>y>z??(1) x-y = |x-z|+|z-y|(2) x > y(1)First of all as RHS is the sum of two non-negative values LHS also must be non-negative. So . Now, we are told that the distance between two points and , on the number line, equals to thesum of the distances between and AND and .The question is: can the points placed on the number line as follows ---z---y---x---. If you look at the number line you'll see that it's just not possible. Sufficient.OR algebraic approach:If is true, then , will become --> ,which contradicts our assumption . So is not possible. Sufficient.(2) --> no info about . Not sufficient.Answer: A.Discussed at: /forum/is-x-y-z-92607.html13. Coordinate Geometry / AlgebraIn the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?(1)(2)Distance between the point A (x,y) and the origin can be found by the formula: .So we are asked is ? Or is ?(1) . Not sufficient.(2) --> . Not sufficient.(1)+(2) and .From (1) and , for some non-zero . Substitute in (2) --> --> (another solution is not possible as in (1) given indenominator and can not be zero, so --> ) --> soas and and , then andNow square --> --> --> cancels out --> . Sufficient. Answer: C.Discussed at: /forum/manhttangmat-practice-cat-92533.html14. RemaindersIf w, x, y, and z are the digits of the four-digit number N, a positive integer, what is the remainder when N is divided by 9?(1) w + x + y + z = 13(2) N + 5 is divisible by 9Remainder when a number is divided by 9 is the same as remainder when the sum of its digits is divided by 9:Let's show this on our example:Our 4 digit number is . what is the remainder when it's divided by 9?When 1000w is divided by 9 the remainder is :remainder , remainder .The same with and .So, the remainder when is divided by 9 would be:(1) w + x + y + z = 13 --> remainder 13/9=4, remainder N/9=4. Sufficient.(2) N+5 is divisible by 9 --> N+5=9k --> N=9k-5=4, 13, 22, ... --> remainder upon dividing this numbers by 9 is 4. Sufficient.Answer: D.Discussed at: /forum/number-properties-91848.html15. Word Problem (800 level question)Laura sells encyclopaedias, and her monthly income has two components, a fixed component of $1000, and a variable component of $C for each set of encyclopaedias that she sells in that month over a sales target of n sets, where n>0. How much did she earn in March?(1) If Laura had sold three fewer sets in March, her income for that month would have been $600 lower than it was.(2) If Laura had sold 10 sets of encyclopaedias in March, her income for that month would have been over $4000.Laura's income , where is number of sets she sold and is target number( --> ).(1) Three cases:--> (surplus of 600$ was generated by 1 set);--> (surplus of 600$ was generated by 2 set);--> (surplus of 600$ was generated by 3 set).If equals to 1, 2, or 3, then income for March will be 1600$, BUT if , then income will be more then 1600. Or another way: if we knew that c=300 or 600, then we couldd definitely saythat BUT if , then (for ) or more (for ). Notsufficient.(2) --> --> --> as the lowest value of ,then . Not sufficient.(1)+(2) as from (2) , then from (1) --> . Sufficient.Answer: C.ADDITIONAL NOTES FOR (1) : "If Laura had sold three fewer sets in March..." --> Laura sold andhad , but if she had sold then her income would have been .Now:If is 1 more than (or as I wrote ), then it would mean that 600$ was generated by only 1set;If is 2 more than (or as I wrote ), then it would mean that 600$ was generated by 2 sets;If is more than 3 more than (or as I wrote ), then it would mean that 600$ was generated by all 3 sets;In first two cases income for March will be 1600$, BUT for third case income can be 1600$ or more. So this statement is not sufficient.Discussed at: /forum/inequalities-64646.html?hilit=laura20. Number propertiesIf p is a positive integer, what is a remainder when p^2 is divided by 12?(1) p>3.(2) p is a prime.(1) not sufficient(2) not sufficientFor (1) and (2), just plug two different integers: for (1) 4 an 5 (>3) and for (2) 2 and 3 (primes) to see that you'll get two different answers for remainders.(1)+(2) Any prime >3 when divide by 6 can only give remainder 1 or 5 (remainder can not be 2 or 4 because than p would be even, it can not be 3 because p would be divisible by 3). So any prime more than 3 can be expressed as or ()So either: which gives remainder 1 when divided by 12,;OR: which also gives remainder 1 when divided by 12.Answer: C.Discussed at: /forum/remainder-problem-84967.html21. Coordinate GeometryIn the xy-plane, if line k has negative slope and passes through the point (-5,r) , is the x-intercept of line k positive?(1) The slope of line k is -5.(2) r> 0Let the intercept be the point . Slope is rise over run and for twopoints and would be --> .Question: is ? --> is ?(1) --> ? ? We can not determinewhether or not. Not sufficient.(2) and --> ? is some positive value (as ) but we don't know whether it's more than or not. Not sufficient.(1)+(2) and --> --> . can be positive as well as negative. Not sufficient.Answer: E.This can be done by visualizing the question. Statement (2) tells us that the point , as , is in the II quadrant. Line with negative slope through the point in the II quadrant can have intercept positive as well as negative.Taken together: as we don't know the exact location of the point in II quadrant we can not say even knowing the slope whether the intercept would be positive or negative.Discussed at: /forum/og-12-ds-question-line-concept-very-good-one-key-wrong-89300.html22. Inequalities /ModulusIs |x| + |x -1| = 1?(1) x ≥ 0(2) x ≤ 1Q is . Let's check when this equation holds true. We should consider three ranges (as there are two check points and ):A. --> --> , but this solution is not valid as we are checking therange ;B. --> --> , which is true. That means that for ANY value from therange , equation holds true.C. --> --> , but this solution is not valid as we are checking the range .So we get that equation holds true ONLY in the range .Statements:(1) . Not sufficient, as must be also ;(2) . Not sufficient, as must be also ;(1)+(2) , exactly the range we needed. Sufficient.Answer: C.Discussion of this question at: /forum/absolute-values-ds-questions-85666.html 23. Number propertiesIs the positive integer N a perfect square?(1) The number of distinct factors of N is even.(2) The sum of all distinct factors of N is even.Probably the best way of solving would be making the chart of perfect squares and its factors to check both statements, but below is the algebraic approach if needed.Couple of things:1. Note that if is a perfect square powers of its prime factors must be even, forinstance: , powers of prime factors of 2 and 3 are even.2. There is a formula for Finding the Number of Factors of an Integer:First make prime factorization of an integer , where , , and are prime factorsof and , , and are their powers.The number of factors of will be expressed by the formula . NOTE: this will include 1 and n itself.Example: Finding the number of all factors of 450:Total number of factors of 450 including 1 and 450 itselfis factors.3. A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors. For instance odd factors of 36 are 1, 3 and 9 (3 odd factor) and even factors are 2, 4, 6, 12, 18 and 36 (6 even factors).Back to the original question:Is the positive integer N a perfect square?(1) The number of distinct factors of N is even --> let's say , given that the number offactors of is even --> . But as we concluded if n is a perfect square then powers of its primes , , and must be even, and in this case number of factors wouldbe . Hence can not be a perfect square. Sufficient.(2) The sum of all distinct factors of N is even --> if n is a perfect square then (according to 3) sum of odd factors would be odd and sum of even factors would be even, so sum of all factors of perfectsquare would be . Hence can not be a perfect square. Sufficient. Answer: D.There are some tips about the perfect square:• The number of distinct factors of a per fect square is ALWAYS ODD.• The sum of distinct factors of a perfect square is ALWAYS ODD.• A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors. • Perfect square always has even number of powers of prime factors.24. StatisticLists S and T consist of the same number of positive integers. Is the median of the integers in S greater than the average (arithmetic mean) of the integers in T?(1) The integers in S are consecutive even integers, and the integers in T are consecutive odd integers.(2) The sum of the integers in S is greater than the sum of the integers in T.Q: is ? Given: {# of terms in S}={# of terms in T}, let's say N.(1) From this statement we can derive that as set S and set T are evenly spaced their medians equal to their means. So from this statement question becomes is ? But this statement is clearly insufficient. As we can have set S{2,4,6} and set T{21,23,25} OR S{20,22,24} andT{1,3,5}.(2) . Also insufficient. As we can have set S{1,1,10} (Median{S}=1) and setT{3,3,3} (Mean{T}=3) OR S{20,20,20} (Median{S}=20) and T{1,1,1} (Mean{T}=1).(1)+(2) From (1) question became is ? --> As there are equal # of term in setsand mean(average)=(Sum of terms)/(# of terms), then we have: is true? -->Is ? This is exactly what is said in statement (2) that . Hence sufficient.Answer: C.Discussed at: /forum/mean-and-median-89305.html25. Number PropertiesIf n is an integer >1, is 3^n-2^n divisible by 35?(1) n is divisible by 15.(2) n is divisible by 18.RULE: for x^n-y^n:is ALWAYS divisible by .is divisible by when n is even.If n is an integer >1, is divisible by 35?(1) n is divisible by 15. --> --> 5m may or my not be even, so insufficient to answer, whether it's divisible by 27+8=35.(2) n is divisible by 18. --> --> 6m is even, so 3^(18m)-2^(18m)=27^(6m)-8^(6m) is divisible by 27+8=35. Sufficient.Answer: B.Discussed at: /forum/divisibility-84992.html26. GeometryThe area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?(1) Angles ABC and KLM are each equal to 55 degrees.(2) LM is 6 inches.Properties of Similar Triangles:• Corresponding angles are the same.• Corresponding sides are all in the same proportion.• It is only necessary to determine that two sets of angles are identical in order to conclude tha t two triangles are similar; the third set will be identical because all of the angles of a triangle always sum to 180º.• In similar triangles, the sides of the triangles are in some proportion to one another. For example, a triangle with lengths 3, 4, and 5 has the same angle measures as a triangle with lengths 6, 8, and 10. The two triangles are similar, and all of the sides of the larger triangle are twice the size of the corresponding legs on the smaller triangle.• If two similar triangles have sides in the ratio , then their areas are in the ratio .OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of theirsides: .For more on triangles please check Triangles chapter of the Math Book (link in my signature).Back to original question:The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?(1) Angles ABC and KLM are each equal to 55 degrees --> ABC and KLM are similar triangles --> , so the sides are in ratio 2/1 --> hypotenuse KL=10 --> hypotenuse AB=2*10=20. Sufficient.(2) LM is 6 inches --> KM=8 --> --> . But just knowing the are of ABC is not enough to determine hypotenuse AB. For instance: legs of ABC can be 96 and 2 OR 48 and 4 and you'll get different values for hypotenuse. Not sufficient.Answer: A.Discussed at: /forum/mgmat-ds-help-94037.html?hilit=different%20values%20for%20hypotenuse%20sufficient.#p72323727. Number propertiesIf N is a positive integer, what is the last digit of 1! + 2! + ... +N!?(1) N is divisible by 4(2) (N^2 + 1)/5 is an odd integer.Generally the last digit of can take ONLY 3 values:A. N=1 --> last digit 1;B. N=3 --> last digit 9;C. N=any other value --> last digit 3 (N=2 --> 1!+2!=3 and for N=4 --> 1!+2!+3!+4!=33, the terms after N=4 will end by 0 thus not affect last digit and it'll remain 3).So basically question asks whether we can determine which of three cases we have.(1) N is divisible by 4 --> N is not 1 or 3, thus third case. Sufficient.(2) (N^2 + 1)/5 is an odd integer --> N is not 1 or 3, thus third case. Sufficient.Answer: D.Discussed at: /forum/a-question-from-the-iphone-software-94088.html28. Remainders。
张广GMAT数学讲义
目录第一章Data Sufficiency题型-------------------------------------------2 第二章数论---------------------------------------------------------------4第三章代数--------------------------------------------------------------17第四章几何--------------------------------------------------------------24第五章文字应用题-------------------------------------------------------32第六章综合练习题-------------------------------------------------------44第七章GMAT数学常见术语---------------------------------------------72第一章 Data Sufficiency 题型【DS 题形式】Information required (Introduction or Background)QuestionTwo statements labeled (1) and (2)Option:(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.(D) EACH statement ALONE is sufficient.(E) Statement (1) and (2) TOGETHER are NOT sufficient.【答题步骤】1. 分析问句类型数值计算——特殊疑问句 (Special Question).判断是非——一般疑问句 (General Question).2. 罗列各种充分与不充分条件特殊疑问句——答案：唯一确定实数解.充分：能得到诸如0, –27, 4.567, 2311, , π等唯一解的Statement .不充分：能得到诸如x = x <1等两个或更多解，及其它一切无法计算出解的Statement .例题1：What is the value of x ?(1) 3x = 15(2) 5x < 30例题2：Tom and Jack are in a line to purchase tickets. How many people are in the line?(1) There are 20 people behind Tom and 20 people in front of Jack.(2) There are 5 people between Tom and Jack.一般疑问句——答案：明确回答”YES”或者”NO”.充分：完全符合或者完全不符合Question提出的内容，即能理直气壮回答”YES”或者”NO”，不留任何余地的Statement.不充分：不完全符合Question提出的内容，即只能心虚回答”Yes, but…”或者”No, but…”，及其它一切无法判断结果的Statement.例题3：Is x equal to 1 ?(1)x2 = 1(2)x2 = 4例题4：体会下列两个Question的区别.There are eight balls in the pocket.Question 1: Are all the balls in the pocket red?充分：”YES”:”NO”:Question 2: Are there any red balls in the pocket?充分：”YES”:”NO”:Statement 1: Three balls are removed; whose colors are brown, green, and red, respectively. Statement 2: Three balls are removed; whose colors are brown, green, and yellow, respectively. Statement 3: Three balls are removed; whose colors are red, red, and red, respectively.3.按照Problem Solving常规题型继续思考牢记：当分析Statement (1) 时，不要预测Statement (2)；当分析Statement (2) 时，确信忘记Statement (1)；第二章数论【奇数与偶数(Odd and Even Numbers) 】1．奇数个奇数相加减，其结果必为奇数。
习题集(二十二)
GMAT数学实战习题集(二十二)1．按从大到小排列（1）0.769^3，（2）√0.769，（3）0.769^2 .A.（1）（2）（3）B.（3）（2）（1）C.（2）（1）（3）D.（1）（3）（2）E.（2）（3）（1）2. 某一种物质里含盐和糖，其比例是1：5. 问30克这种物质有多少克盐。
A. 1B. 2C. 4D. 5E. 63. 有个多边形，有7个角，求内角和。
A. 180B. 360C. 720D. 900E. 12504. 求1/2-1/3.A. 1/6B. 1/5C. 1/4D. 1/3E. 1/25. 在一个坐标系里，有一个直角三角形，且在第一象限，BC边最短与X 轴平行，AB为斜边39，AB的SLOPE是12/5，求BC。
A. 15B. 20C. 25D. 36E. 396. 已知（7^（-2） *7^6）/7^4=7^x，求x。
A. -2B. -1C. 0D. 1E. 27. 下图是一个半球体容器（图有偏差，请自己作图）。
半径为r,一个人装水要给青蛙喝，水面面积为1800,隔天水下降到了离底部r/2的地方，问这时候水表面积为多少?A. 450B. 900C. 1200D. 1350E. 18008. 汽车有两把钥匙，一个开x一个开y，如果钥匙扣上一共有五把钥匙，这两把汽车钥匙一定放在一起的概率是?A. 1/4B. 1/3C. 1/2D. 2/3E. 3/49. 已知s 是a 的1/2，s降低20%后，还占原来a 百分之多少？A. 10%B. 20%C. 30%D. 40%E. 45%10. 求[(20^-1+30^-1)/2]^-1。
A. 1/24B. 1/12C. 12D. 24E. 4811. 已知x、y均为整数，且x+1=1/(y+1)，y≠0，求x的值。
A. -2B. -1C. 0D. 1E. 212. DS题：Is X>Y?（1) X^2=25（2) Y^2=1613. DS题：两个数列S和T，各自包含的数字的数目是一样的，问S的median和T的算术平均值谁大谁小。
吉迈特考试内容
吉迈特考试内容考试方式：我国的GMAT考试已经使用计算机化考试，采用Computer-Adaptive Testing的方式考试内容：包括七个部分（Section）试题，每个Section的考试时间为30分钟，其中有阅读理解（ReadingComprehension）、句子改错（Sentence Correction）、问题求解（Problem Solving）、数据填充（DataSufficiency）以及原因评述（CriticalReasoning）各一个部分。
剩下两个部分的题型分布都不一样。
这七个Sections 试题中有一个是试测性部分，不计入GMAT成绩。
但由于分辨不出哪个Section 不计分，因此所有部分的试题均要认真回答。
【延伸扩展】考试内容细解：1、阅读理解提供阅读文章三或四篇，共设25个问题，每个问题有四个可供选择的答案。
文章内容涉及到人文科学、社会学、物理学和生物学等领域。
2、句子改错共有25道题。
出题形式是：一般给出一个句子，在句子一部分或全部的下方用线标明，要求考生针对划线的部分，从五个选项中作出最佳选择。
请注意：答案（A）往往就是划线部分本身。
3、问题求解共有20道问题。
试题形式可能是文字叙述形式，要求考生进行计算，也可能要求对图、表进行解释。
内容涉及大量的算术、代数和几何的基本定理。
4、数据填充共有25个问题，每道题中均含有数学问题和两个与之相关的说明。
考生必须作出判断，利用这些信息能否解答试题：（A）仅第一个数据说明可以解题，而第二个不行；（B）仅第二个数据说明可以解题，而第一个不行；（C）两个数据说明放在一起可以解题，但任何单独一个均不行；（D）任何一个数据说明均能解题；（E）两个数据说明放在一起都不能解题，必须增添新数据。
5、原因评述共有20道问题。
该部分试题有下列几种出题形式：（1）推断与设想（Inference orAssumption）。
一般是先给出一段陈述、论证、意见或事实，然后要求从陈述中的概括和推断两个方面作出最佳选择。
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gmat ds题选项
【最新版】
目录
1.GMAT DS 题概述
2.GMAT DS 题的解题技巧
3.GMAT DS 题的选项分析
正文
1.GMAT DS 题概述
GMAT（Graduate Management Admission Test）是研究生管理类入学考试，主要用于评估考生的逻辑、语言和数学能力。
在 GMAT 考试中，Data Sufficiency（DS）题是一种特殊的题型，要求考生在给定的数据和问题中，判断是否足以推出正确答案。
2.GMAT DS 题的解题技巧
解决 GMAT DS 题需要掌握一定的解题技巧，主要包括以下几点：
（1）分析问题类型：根据问题分类，分为求解问题、判断问题、比较问题等。
不同类型的问题，解题思路和方法有所不同。
（2）分析选项：观察选项特征，了解选项之间的差异。
有时候，通过分析选项可以快速得出答案。
（3）代入法：将选项代入问题中，判断是否能够推出正确答案。
这是一种常用的解题方法，但并非所有题目都适用。
（4）排除法：根据题目条件，逐一排除选项。
通过排除错误选项，找出正确答案。
3.GMAT DS 题的选项分析
在 GMAT DS 题中，选项分为以下几种：
（1）正确答案：可以推出问题的正确答案。
（2）不能推出答案：无法根据给定数据推出问题的正确答案。
（3）不确定：给定数据不足以判断问题的正确答案。
这种情况下，需要继续寻找其他条件或者采用其他方法进行求解。
（4）错误的答案：虽然可以推出一个答案，但该答案与问题无关或者错误。
总之，解决 GMAT DS 题需要熟练掌握解题技巧，并根据题目特点灵活运用。
同时，要注意选项的分析，尤其是正确答案和不能推出答案的判断。