IBM笔试
三部分
第一部分看矩阵题时间15分钟
PartⅠ: （将你啲个人本部分计分方法为答对题数乘以1 电脑推至颠
峰，热卖中俾你一个矩阵：㈠㈡㈢㈣㈤详情请留意
1 a b c d e aa直销网站
2 b c a e d 会员有特价
3 c b e a d
4 c e d b a
5 e d a c b
回答以下问题。
问：⑴将第一行和第四行交换后，第一行第四个字母下面啲左边啲下面啲右边啲字母係？
①a ②b ③c ④d ⑤e
⑵将所有出现在d左边啲字母从矩阵中删掉。将所有出现在a左边啲c字母
从矩阵中删掉。如果矩阵中剩低啲字母啲种类啲数目大于3，答案为原
矩阵中左上方至右下方对角线上出现两次啲字母。如果矩阵中剩低啲字
母啲种类啲数目小于或者等于3，答案为原矩阵中右上至左下对角线上
出现4次啲字母。
①a ②b ③c ④d ⑤e
P4
⑶将所有啲a用4替换，所有啲d用2替换，边一列啲总和最大？
①㈠②㈡③㈢④㈣⑤㈤
⑷从左上字母开始，沿顺时针沿矩阵外围，第四次出现啲字母係以下边个
①a ②b ③c ④d ⑤e
⑸沿第5列从上到下，接着沿第3列从下到上，接着沿第4列从上到下，接着
沿第1列从下到上，接着沿第2列从上到下，第一个出现5次啲字母係？
①㈠②㈡③㈢④㈣⑤㈤
⑷从左上字母开始，沿顺时针沿矩阵外围，第四次出现啲字母係以下边个
①a ②b ③c ④d ⑤e
⑸沿第5列从上到下，接着沿第3列从下到上，接着沿第4列从上到下，接着
沿第1列从下到上，接着沿第2列从上到下，第一个出现5次啲字母係？
①a ②b ③c ④d ⑤e
（请停止作答，等待提示翻到下一页）
第二部分：英文字母排序时间25
个人心得：先把26个字母写一排在纸上，容易找规律些。可惜做到一半采用此法。
题信大至是：aabbcc 选下一个为d。当然有的不这么简单，有时跳了好多个，也有向前或向后跳着的规律。所以先把26个字母写一排在纸上，容易找归率些。
第三部分：数学题时间35
繁琐的数学，最好不用计算器（只用了两次计算器），大致估算就可，这样节约时间
可惜还是没做完。
IBM在印度的笔试题
1．The values of shares (in Rs).of A, B and C from January to June are as
follows.
Month A B C
January 30 60 80
February 35 65 85
March 45 75 65
April 40 75 82
May 55 75 85
June 50 75 80
i) During this period which share has undergone maximum fluctuation?
ii) In which month it is possible to buy B and C selling A?
iii) In which month the share values are very low?
iv) By purchasing one share of A and 4 each of B and C in the beginning of
the period, when should these be sold to get maximum profit?
2．In a computer institute 9 languages can be taught. The module is of 6 months duration and of the six languages only one can be taught each month. In addition to that BASIC is always taught and should be in first month itself
• WORD PERFECT is to be taught in the preceding week of WORD STAR.
• FORTRAN can not be taught until COBAL is taught prior to that
• BINO, FIFO can never be taught in single module
languages are BASIC, WORD STAR, WORD PERFECT, FORTRAN, COBAL, BINO, FIFO, LOTUS, C
i) If word star is in 3rd month , what could be in 6th month.
ii) If COBAL is in the 2nd month and BINO in 6th month. FORTRAN will be taught in which month.
3. In a class, except 18 all are above 50 years.15 are below 50 years of age. How many people are there?
(a) 30
(b) 33
(c) 36
(d) none of these.
4. A square plate of some size is cut at four corners. Equal squares of the same size are cut and is formed as open box. If this open box carries 128 ml of oil. What is the size of the side of the plate?
(a) 17
(b) 14
(c) 13
(d) None of these
5. In a square, all the mid points are joined. The inner square is shaded. If the area of the square is A, what is the area of the shaded area?
6. Two questions on basic angles i.e given a circle, a few chords or diameter is drawn etc.
7. A person has Rs 100/- in his pocket, he can as 25 pencils or 15 books.
He kept 15% of the money for travelling expenses and purchased 5 pencils.
So how many books he can purchase with the remaining money.
8. If a car starts from A towards B with some velocity.
Due to some problem in the engine after travelling 30km, the car goes with 4/5 th of its actual velocity. The car reaches B 45 min later to the actual time. If the car engine fails ofter travelling 45km, the car reaches the destination B 36min late to the actual time, What is the initial velocity of car and what is the distance between A and B in km?
这是IBM试题第三部分（刚在水木清华BBS上找到的）
1.有3台复印机（copier），平均每台每周工作42小时，每台每周最少工作35? 问一台复印机每周最多会工作多少小时？
42*3 - 35*2 ＝56
2.在一个长11 meters，宽6 meters的房间里，铺上10 centimeters厚的水泥?要多少水泥？11*6*0.1＝6.6 cubic meters
3.某公司有两座办公楼，一天，第一座楼20％的复印机和第二座楼40％的复印进行维护，如果第一座楼拥有公司60％的复印机，问这天在维护的复印机是多
20% * 60% + 40% * (1 - 60%) = 28%
4.要在一个接待室(reception room)里铺瓷砖，接待室的长18 meters，宽12，同时要修一条从大厅(hall)到楼梯(stair way)的通道（不铺瓷砖）占地50meters，允许铺设时有35%的浪费(wastage)，1平方米瓷砖的价格是10美元，问大约(approximately)要花多少钱？
(18 * 12 - 50) * 135% * 10 = 2,200
5.某公司要做一个车辆更新，有2种车型，一种是X(忘了，用X代替),一种是van，新X每liter油走20公里，新van每liter油走15公里，旧X每liter油走15公里，旧van每liter 油走12公里。现在要开15000公里，其中有60％由van来承担，问更新后将节省多少油？(15000 * 60% / 12 + 15000 * 40% / 15) - (15000 * 60% / 15 + 15000 * 40%/ 2
0) = 250
6.有2个行政打字员(administrative typist)，A的速度是B的1 1/4 times，现在要
打72页文件，问快的那个人打了多少页？
72* 5/9 = 40
7.有一个呼叫中心，星期二的calls比星期一的1/2还多1/3，星期一和星期二的calls的和是120，问星期二的calls是多少？
48
8.有一个软件公司，1/2的人是系统分析员，2/5的人是软件工程师，有1/4的人两者都是，问有多少人两者都不是？
1 - 1/
2 - 2/5 + 1/4＝0.35
9.有一个crate要做等比例(proportionally)的缩放，为了能够便于运输(shipment)，crate的尺度(dimension)是72,96,48，如果缩放到三个尺度的和是200，问最长的那个尺度要缩多少？
96 * (1 - 200 / 216) = 64 / 9 = 7.1
10. 有一个矩形，长是宽的1 1/3 times，如果把每边增加1，面积将增加85，问长是多少？
48
11.有一个printer，一小时能打12,000页，早上8:30开始打印，中途被打断2次，每
次5分钟，13:15打完，问总共打了多少页？
55,000
12 就是很著名的杀狗问题(嘿嘿)
有50户人，每户人都有一条狗。但是有狗生病了。
这50户人可以通过自己的窗户观察别人家的狗，但是看不见自己的狗是不是有
病(也就是只能通过观察别人的狗来判断自己的狗)。而且一旦发现自己的狗有病，
枪杀之。
第一天没有枪声。
第二天也没有枪声。
第三天劈劈啪啪一阵枪声。
问有多少条狗死于这次大屠杀(也就是有多少病狗了)？
13 有四个人过桥。一个要1分钟，一个要2分钟，一个要5分钟，还有一个要10分钟。桥一次只能过两个人。因为天黑了，过桥必须要手电筒，但是只有一杆。那么如
何让这4个人在17分钟内过河？
14. 已知两个数字为1~30之间的数字，甲知道两数之和，乙知道两数之积，甲问乙：“你知道是哪两个数吗？”乙说：“不知道”。乙问甲：“你知道是哪两个数吗？”甲说：“也不
知道”。于是，乙说：“那我知道了”，随后甲也说：“那我也知道了”，这两个数是什么？有人算出是1和4，或者4和7
网上找到一个答案
大家看一下吧：
答案:
允许两数重复的情况下
答案为x=1, y=4; 甲知道和A=x+y=5, 乙知道积B=x*y=4
不允许两数重复的情况下有两种答案
答案1: 为x=1, y=6; 甲知道和A=x+y=7, 乙知道积B=x*y=6
答案2: 为x=1, y=8; 甲知道和A=x+y=9, 乙知道积B=x*y=8
解：
设这两个数为x,y.
甲知道两数之和A=x+y;
乙知道两数之积B=x*y;
该题分两种情况
允许重复,有(1 <= x <= y <= 30);
不允许重复,有(1 <= x < y <= 30);
当不允许重复, 即(1 <= x < y <= 30);
1)由题设条件：乙不知道答案
<=> B=x*y 解不唯一
=> B=x*y 为非质数
又∵x ≠y
∴B ≠k*k (其中k∈N)
结论(推论1)：
B=x*y 非质数且B ≠k*k (其中k∈N) 即：B ∈(6,8,10,12,14,15,18,20...)
证明过程略
2)由题设条件：甲不知道答案
<=> A=x+y 解不唯一
=> A >= 5;
分两种情况
A=5,A=6时x,y有双解
A>=7 时x,y有三重及三重以上解
假设A=x+y=5
则有双解
x1=1,y1=4;
x2=2,y2=3
代入公式B=x*y:
B1=x1*y1=1*4=4; (不满足推论1，舍去) B2=x2*y2=2*3=6;
得到唯一解x=2,y=3即甲知道答案
与题设条件：“甲不知道答案”相矛盾故假设不成立，A=x+y≠5
假设A=x+y=6
则有双解
x1=1,y1=5;
x2=2,y2=4
代入公式B=x*y:
B1=x1*y1=1*5=5; (不满足推论1，舍去) B2=x2*y2=2*4=8;
得到唯一解x=2,y=4
即甲知道答案
与题设条件：“甲不知道答案”相矛盾故假设不成立，A=x+y≠6
当A>=7时
∵x,y的解至少存在两种满足推论1的解
B1=x1*y1=2*(A-2)
B2=x2*y2=3*(A-3)
∴符合条件
结论(推论2)：A >= 7
3)由题设条件：乙说“那我知道了”
=>乙通过已知条件B=x*y及推论(1)(2)可以得出唯一解即：
A=x+y,A >= 7
B=x*y,B ∈(6,8,10,12,14,15,16,18,20...)
1 <= x < y <= 30
x,y存在唯一解
当B=6 时：有两组解
x1=1, y1=6
x2=2, y2=3 (∵x2+y2=2+3=5 < 7∴不合题意，舍去)
得到唯一解x=1, y=6
当B=8 时：有两组解
x1=1, y1=8
x2=2, y2=4 (∵x2+y2=2+4=6 < 7∴不合题意，舍去)
得到唯一解x=1, y=8
当B>8 时：容易证明均为多重解
结论：
当B=6时有唯一解x=1, y=6当B=8时有唯一解x=1, y=8
4)由题设条件：甲说“那我也知道了”
=>甲通过已知条件A=x+y及推论(3)可以得出唯一解
综上所述，原题所求有两组解：
x1=1, y1=6
x2=1, y2=8
当x<=y时，有(1 <= x <= y <= 30);
同理可得唯一解x=1, y=4
Aptitude Paper : IBM
1. In 1978, a kg of paper was sold at Rs25/-. If the paper rate increases at 1.5% more than the inflation rate which is 6.5% a year, then what wil be the cost of a kg of paper after 2 years?
(a) 29.12
(b) 29.72
? 30.12
(d) 32.65
(e) none of these
2. In A,B,C are having some marbles with each of them.
A has given
B and
C the same number of marbles each of them already have.
Then, B gave C and A the same number of marbles they already have.
Then C gave A and B the same number of marbles they already have.
At the end A,B,and C have equal number of marbles.
(i) If x,y,z are the marbles initially with A,B,C respectively.
Then the number of marbles B have at the end
(a) 2(x-y-z)
(b) 4(x-y-z)
? 2(3y-x-z)
(d) x + y-z
Ans. ?
(ii) If the total number of marbles are 72, then the number of marbles with
A at the
starting
(a) 20
(b) 30
? 32
(d) 39
Ans. (d)
3. If a car starts from A towards B with some velocity.
Due to some problem in the engine after travelling 30km, the car goes with 4/5 th of its actual velocity The car reaches B 45 min later to the actual time.
If the car engine fails ofter travelling 45km, the car reaches the destination B 36min late to the actual time What is the initial velocity of car and what is the distance between A and
B in km?
Ans. 20 & 130. 25 & 105
4. A person has Rs 100/- in his pocket, he can as 25 pencils or 15 books.
He kept 15% of the money for travelling expenses and purchased 5 pencils.
So how many books he can purchase with the remaining money.
5. Ten questions on analogies.
eg: chief : tribe :: governer : state
epaulette : shoulder :: tiara : head
guttural : throat :: gastric : stomach
inept : clever :: languid : active
knife : butcher ::
hammer : carpenter ::
7. In a computer institute 9 languages can be taught.
The module is of 6 months duration and of the six languages only one can be taught each month . In addition to that BASIC is always taught and should be in first month itself
WORD PERFECT is to be taught in the preceeding week of WORD STAR.
FORTRAN can not be taught until COBAL is taught prior to that
BINO, FIFO can never be taught in single module
languages are BASIC, WORD STAR, WORD PERFECT, FORTRAN, COBAL, BINO, FIFO, LOTUS, C
i) If word star is in 3rd month , what could be in 6th month.
ii) If COBAL is in the 2nd month and BINO in 6th month. FORTRAN will betaught in
which month.
8. In a class, except 18 all are above 50 years.
15 are below 50 years of age. How many people are there
(a) 30
(b) 33
? 36
(d) none of these.
Ans. (d)
9. A square plate of some size is cut at four corners. Equal squares of the
same size are cut and is formed as open box.
If this open box carries 128 ml of oil. What is the size of the side of the plate?
(a) 17
(b) 14
? 13
(d) None of these
10. In a square, all the mid points are joined. The inner square is shaded.
If the area of the square is A, what is the area of the shaded area?
11. Two questions on basic angles i.e given a circle, a few chords or diameter is drawn etc.
12. If the follwoing statements are given
@(a,b)= (a+b)/2
/(a,b)= a/b
*(a,b)= ab
If a=1, b=2 then find
i) /(a,(@(a,b),*(a,b)))
ii) */(a,@(*(a,b)))
13. If the follwoing statements are given
(x#y) = x + y- xy
(x*y) = (x + y)/2
i) Find the values of x, y will satisfy this equation (x#y)#(x*y) < (x#y)
ii) Find the values of x, y will satisfy this equation (a*b)#(b*c)<
(a#b)*(b*c)
--------------------------------------------------------------------
Quantitative Paper : IBM Global Services
1.A clerk multiplied a number by ten when it should have been divided by
ten.The ans he got was 100.what should the ans have been?
a:1
2.If Rs20/- is available to pay for typing a research report & typist A produces 42 pages and typist
B produces 28 pages.How much should typist A receive?
a:Rs12/-
3.The average salary of 3 workers is 95 Rs. per week. If one earns
Rs.115 and second earns Rs.65 how much is the salary of the 3rd worker.
Ans.105.
4.A 16 stored building has 12000 sq.feet on each floor. Company A rents 7 floors and company B rents 4 floors. What is the number of sq.feet of unrented floor space.
Ans.60000
5. During a given week A programer spends 1/4 of his time preparing flow
chart, 3/8 of his time coding and the rest of the time in debugging the
programs. If he works 48 hours during the week , how many hours did he
spend debugging the program.
Ans. 18.
6. A company installed 36 machines at the beginning of the year. In March
they installed 9 additional machines and then disconnected 18 in August.
How many were still installed at the end of the year.
Ans. 27
7. A man owns 2/3 of the market research beauro business and sells 3/4 of
his shares for Rs. 75000. What is the value of Business.
Ans.150000
8. If 12 file cabinets require 18 feet of wall space, how many feet of wall space will 30 cabinets require?
Ans.45
9.A computer printer produced 176,400 lines in a given day. If the
printer was in operation for seven hours during the day, how many lines did it print per minute? Ans.420
10. From its total income, A sales company spent Rs.20,000 for advertising, half of the remainder on commissions and had Rs.6000 left.
What was its total income?
Ans.32000
11. On Monday a banker processed a batch of cheques, on Tuesday she
processed three times as many, and on Wednesday she processed 4000
cheques. In the three days, she processed 16000 cheques. How many did
she process on Tuesday?
Ans.9000
12. The cost of four dozen proof machine ribbons and five dozen accouting
machine ribbons was Rs.160/-. If one dozen accounting machine ribbons
cost Rs.20/-, what is the cost of a dozen proof machine ribbons?
Ans.Rs.15
13. If a clerk can process 80 cheques in half an hour, how many cheques
can she process in a seven and one half hour day?
Ans.1200
14. In a library, there are two racks with 40 books per rack. On a given
day, 30 books were issued. What fraction remained in the racks?
Ans.5/8
15. The average length of three tapes is 6800 feet. None of the tapes is
less than 6400 feet. What is the greatest possible length of one of the
other tapes?
Ans.7600
16. A company rented a machine for Rs.700/- a month. Five years later
the treasurer calculated that if the company had purchased the machine
and paid Rs.100/- monthly maintenance charge, the company would have
saved Rs.2000/-. What was the purchase price of the machine?
Ans.Rs.34000
17. Two computers each produced 48000 public utility bills in a day. One computer printed bills at the rate of 9600 an hour and the other at the
rate of 7800 an hour. When the first computer finished its run, how many bills did the other computer still have to print?
Ans.9000
18. If a salesman's average is a new order every other week, he will
break the office record of the year. However, after 28 weeks, he is six
orders behind schedule. In what proportion of the remaining weeks does
he have to obtain a new order to break the record?
Ans.3/4
19. On a given day, a bank had 16000 cheques returned by customers. Inspection of the first 800 cheques indicated that 100 of those 800 had errors and were therefore the available immediately for data processing.
On this basis, hwo many cheques would be available immediately for data processing on that day?
Ans.14000
20. A company figured it needed 37.8 sq.feet of carpot for its reception room. To allow for waste, it decided to order 20% more material than needed. Fractional parts of sq.feet cannot be ordered. At Rs.9/- a
sq.feet, how much would the carpet cost?
Ans.
a. Rs.324 b) Rs.405 c) Rs.410 d) Rs.414 e) Rs.685
21. A tape manufacturer reduces the price of his heavy duty tape from
Rs.30/- to Rs.28/- a reel and the price of a regular tape from Rs.24/- to
Rs.23/- a reel. A computing centre normally spends Rs.1440/- a month for tapes and 3/4 of this is for heavy duty tapes. How much will they save a month under the new prices?
Ans.Rs.87 132
22. In a team of 12 persons, 1/3 are women and 2/3 are men. To obtain a team with 20% women how many men should be hired?
Ans.8
23. The dimensions of a certain machine are 48″X 30″X 52″. If the size of the machine is increased proportionately until the sum of its
dimensions equals 156″, what will be the increase in the shortest side? Ans. 6″
24. In a certain company, 20% of the men and 40% of the women attended the annual company picnic. If 35% of all the employees are man, what
percent of all the employees went to the picnic?
Ans.33% 21%
25. It cost a college Rs.0.70 a copy to produce a Programme for the homecoming football game. If Rs.15,000/- was received for advertisements in the programme, how many copies at Rs.0.50 a copy must be sold to make a profit of Rs.8000/- ?
Ans. 35000
1. One person traveled 4 laps with the speed of 10,20,40 ( or 30) and 60 kmph and what is the average speed.
answer:20
why?
4/(1/10+1/20+1/30+1/60)
18. If a salesman's average is a new order every other week, he will
break the office record of the year. However, after 28 weeks, he is six orders behind schedule. In what proportion of the remaining weeks does
he have to obtain a new order to break the record?